Embed Size (px)
DESCRIPTION
Seader - Operações Unitárias
Citation preview
Ex
erci
se 4
.7
S
ub
ject
:
Ste
am (
B)
dis
till
atio
n o
f st
eari
c ac
id (
A).
Giv
en:
T
= 2
00
oC
. V
apo
r p
ress
ure
of
pu
re s
tear
ic a
cid
at
20
0oC
= 0
.40
kP
a.
Ass
um
pti
on
s:
Par
tial
pre
ssu
re o
f st
eari
c ac
id i
n v
apo
r =
70
% o
f th
e p
ure
vap
or
pre
ssu
re.
Fin
d:
Kil
ogra
ms
of
acid
dis
till
ed
per
kil
og
ram
of
stea
m a
dd
ed a
s a
fun
ctio
n o
f to
tal
pre
ssu
re
fro
m 3
.3 k
Pa
to 1
01
.3 k
Pa.
An
aly
sis:
pA =
0.7
(0.4
) =
0.2
8 k
Pa
BA
AB
AA
AA
BB
BB
0.2
8
(1
)
/
(
2)
28
4.5
,
1
8.0
2
Usi
ng
Eq
s. (
1)
and
(2
),
kg
A0
.28(2
84
.5)
=k
g B
(-
=−
=−
=
==
==
ii
pP
pP
yp
P
MM
yM
pM
yM
pM
P
4.4
2=
(3
)0
.28
)(1
8.0
2)
0.2
8−
P
S
olv
ing E
q.
(3)
for
val
ues
of
P f
rom
3.3
to
10
1.3
kP
a giv
es t
he
foll
ow
ing r
esu
lts:
P,
kP
a
kg
A/k
g B
1
01
.3
0.0
43
8
75
0
.05
92
50
0
.08
90
25
0
.17
90
15
0
.30
06
10
0
.45
53
5
0
.93
76
3.3
1
.46
50
Ex
erci
se 4
.7 (c
on
tin
ued
)
Ex
erci
se 4
.8
S
ub
ject
:
Vap
or-
liq
uid
eq
uil
ibri
um
fo
r b
enze
ne
(A)
- to
luen
e (B
) sy
stem
at
1 a
tm
Giv
en:
A
ver
age
rela
tiv
e v
ola
tili
ty =
2.5
. V
apo
r p
ress
ure
dat
a.
Ass
um
pti
on
s:
Rao
ult
's a
nd
Dal
ton
's l
aws.
Fin
d:
x-
y d
iag
ram
fo
r α
A,B
= 2
.5.
x-y
dia
gra
m f
or
Rao
ult
's l
aw u
sin
g v
apo
r p
ress
ure
dat
a.
(a
) T
emp
erat
ure
fo
r 2
5 m
ol%
vap
ori
zati
on
of
a 7
0 m
ol%
A/3
0 m
ol%
B m
ixtu
re.
Co
mp
osi
tio
n o
f co
nd
ense
d v
apo
r an
d l
iqu
id r
esid
ue.
(b
) P
lot
of
Rao
ult
's l
aw K
-val
ues
as
a fu
nct
ion
of
tem
per
atu
re.
An
aly
sis:
F
or
a co
nst
ant
rela
tiv
e v
ola
tili
ty,
Eq
. (4
-8)
app
lies
. F
or
αA
,B =
2.5
,
yx
x
x
xA
A,B
A
AA
,B
A
A
=+
−=
+
α
α1
1
25
11
5�
�.
.
So
lvin
g t
his
eq
uat
ion
fo
r v
alu
es o
f x
A =
0 t
o 1
.0 g
ives
th
e fo
llo
win
g:
xA
yA
0.0
0
.00
00
0.1
0
.21
74
0.2
0
.38
46
0.3
0
.51
72
0.4
0
.62
50
0.5
0
.71
43
0.6
0
.78
95
0.7
0
.85
36
0.8
0
.90
91
0.9
0
.95
74
1.0
1
.00
00
Ex
erci
se 4
.8 (c
on
tin
ued
)
An
aly
sis:
(
con
tin
ued
)
T
o c
alcu
late
y-x
an
d T
-x-y
cu
rves
fro
m v
apo
r p
ress
ure
dat
a, u
sin
g R
aou
lt's
an
d D
alto
n's
law
s, E
q.
(2-4
4 )
ap
pli
es,
as w
ell
as t
he
sum
of
the
mo
le f
ract
ion
s in
th
e p
has
es i
n e
qu
ilib
riu
m.
Th
us,
Ky x
PT
PK
y x
PT
P
yy
xx
ss
AA A
A
BB B
B
AB
AB
,
(1
, 2
)
,
(3
, 4
)
==
==
+=
+=
��
��
11
Ex
erci
se 4
.8 (c
on
tin
ued
)
An
aly
sis:
(
con
tin
ued
)
Eq
uat
ion
s (1
) to
(4
) ca
n b
e re
du
ced
to
th
e fo
llo
win
g e
qu
atio
ns
for
the
mo
le
frac
tio
ns
of
ben
zen
e (A
) in
ter
ms
of
the
K-v
alu
es:
xK
KK
yK
xA
B
AB
AA
A
,
=− −
=1
(5,
6)
If t
he
giv
en v
apo
r p
ress
ure
dat
a in
Ex
erci
se 4
.6 f
or
ben
zen
e, a
nd
th
is e
xer
cise
fo
r to
luen
e ar
e
fitt
ed t
o A
nto
ine
equ
atio
ns,
we
ob
tain
:
PT
PT
s sA B
(
7)
(8
)
=−
+
� ���
=−
+
� ���
exp
.. .
exp
.. .
15
56
45
26
02
34
21
12
71
17
27
41
38
96
3
25
56
7
Wh
ere
vap
or
pre
ssu
re i
s in
to
rr a
nd
tem
per
atu
re i
s in
oC
. S
olv
ing,
Eq
s. (
1)
to (
8),
T,
oC
Ps o
f A
, to
rr
Ps o
f B
, to
rr
KA
KB
xA
yA
80
.1
75
9.9
2
90
.0
0.9
99
8
0.3
81
6
1.0
00
1
.000
8
2.5
8
17
.4
31
4.9
1
.075
5
0.4
14
4
0.8
86
0
.953
8
5.0
8
80
.8
34
2.7
1
.159
0
0.4
51
0
0.7
75
0
.899
8
7.5
9
48
.0
37
2.5
1
.247
4
0.4
90
1
0.6
73
0
.840
9
0.0
1
019
.1
40
4.4
1
.340
9
0.5
32
1
0.5
79
0
.776
9
2.5
1
094
.1
43
8.5
1
.439
6
0.5
76
9
0.4
90
0
.706
9
5.0
1
173
.4
47
4.9
1
.543
9
0.6
24
9
0.4
08
0
.630
9
7.5
1
256
.9
51
3.7
1
.653
9
0.6
76
0
0.3
31
0
.548
1
00
.0
13
45
.0
55
5.2
1
.769
7
0.7
30
5
0.2
59
0
.459
1
02
.5
14
37
.6
59
9.3
1
.891
6
0.7
88
5
0.1
92
0
.363
1
05
.0
15
35
.0
64
6.2
2
.019
8
0.8
50
3
0.1
28
0
.259
1
07
.5
16
37
.3
69
6.1
2
.154
4
0.9
15
9
0.0
68
0
.146
1
10
.0
17
44
.7
74
9.1
2
.295
7
0.9
85
6
0.0
11
0
.025
1
10
.5
17
66
.8
76
0.1
2
.324
8
1.0
00
1
0.0
00
0
.000
Plo
ts o
f y-
x an
d T
-x-y
bas
ed o
n t
he
abo
ve
tab
le f
rom
Rao
ult
's l
aw c
alcu
lati
on
s ar
e sh
ow
n o
n t
he
nex
t p
age.
W
hen
th
e y-x
plo
t is
co
mp
ared
to
th
e p
rev
iou
s y-
x p
lot
bas
ed o
n a
co
nst
ant
rela
tiv
e
vo
lati
lity
, it
is
seen
th
at,
for
a giv
en v
alu
e o
f x
for
ben
zen
e, t
he
val
ues
of
y fo
r b
enze
ne
are
in
fair
ly c
lose
ag
reem
ent.
F
rom
th
e ab
ov
e ta
ble
, th
e R
aou
lt's
law
αA
,B =
P
Ps
s
AB
/ r
ang
es f
rom
2.6
2
at 8
0.1
oC
to
2.3
2 a
t 1
10
.5oC
.
Ex
erci
se 4
.8 (c
on
tin
ued
)
An
aly
sis:
(
con
tin
ued
)
Ex
erci
se 4
.8 (c
on
tin
ued
)
An
aly
sis:
(
con
tin
ued
)
(a)
To
fin
d t
he
tem
per
atu
re a
t 2
5 m
ol%
vap
ori
zati
on
, st
arti
ng w
ith
a l
iqu
id
mix
ture
of
70
mo
l% b
enze
ne
and
30
mo
l% t
olu
ene,
ex
ten
d a
das
hed
, v
erti
cal
lin
e u
pw
ard
fro
m
po
int
M o
n t
he
T-y
-x d
iagra
m o
n t
he
pre
vio
us
pag
e u
nti
l p
oin
t B
is
reac
hed
. A
t th
is p
oin
t, u
sin
g
the
inv
erse
lev
er-a
rm r
ule
, th
e ra
tio
of
the
AB
lin
e le
ngth
to
th
e B
C l
ine
len
gth
is
25
/75
. T
he
tem
per
atu
re i
s 8
8oC
. T
he
ben
zen
e m
ole
fra
ctio
n o
f th
e eq
uil
ibri
um
vap
or
wh
en c
on
den
sed
is
the
sam
e as
th
e eq
uil
ibri
um
vap
or
at p
oin
t C
or
0.8
8.
Th
e b
enze
ne
mo
le f
ract
ion
in
th
e re
sid
ue
liq
uid
is t
he
sam
e as
th
e eq
uil
ibri
um
liq
uid
at
po
int
A o
r 0
.65
.
(b)
Th
e R
aou
lt's
law
K-v
alu
es a
re i
ncl
ud
ed i
n t
he
abo
ve
tab
le,
and
are
plo
tted
bel
ow
.
Ex
erci
se 4
.9
S
ub
ject
: V
apo
r-li
qu
id e
qu
ilib
riu
m f
or
n-h
epta
ne
(A)
- to
luen
e (B
) sy
stem
at
1 a
tm
Giv
en:
Vap
or
pre
ssu
re d
ata
for
n-h
epta
ne
and
to
luen
e, a
nd
ex
per
imen
tal
T-y
-x d
ata.
Ass
um
pti
on
s:
Rao
ult
's a
nd
Dal
ton
's l
aws
Fin
d:
(a)
x-y
plo
t b
ased
on
n-h
epta
ne,
th
e m
ost
vo
lati
le c
om
po
nen
t.
(b
) T
-x b
ub
ble
-po
int
plo
t.
(c
) α
A,B
an
d K
-val
ues
plo
tted
ag
ain
st t
emp
erat
ure
.
(d
) x-
y p
lot
bas
ed o
n t
he
aver
age
αA
,B.
(e
) C
om
par
iso
n o
f x-
y an
d T
-x-y
plo
ts w
ith
ex
per
imen
tal
dat
a.
An
aly
sis:
(
a) T
o c
alcu
late
y-x
an
d T
-x-y
cu
rves
fro
m v
apo
r p
ress
ure
dat
a, u
sin
g R
aou
lt's
an
d
Dal
ton
's l
aws.
E
q.
(2-4
4 )
ap
pli
es,
as w
ell
as t
he
sum
of
the
mo
le f
ract
ion
s in
th
e p
has
es i
n
equ
ilib
riu
m.
Th
us,
Ky x
PT
PK
y x
PT
P
yy
xx
ss
AA A
A
BB B
B
AB
AB
,
(1
, 2
)
,
(3
, 4
)
==
==
+=
+=
��
��
11
Eq
uat
ion
s (1
) to
(4
) ca
n b
e re
du
ced
to
th
e fo
llo
win
g e
qu
atio
ns
for
the
mo
le
frac
tio
ns
of
n-h
epta
ne
(A)
in t
erm
s o
f th
e K
-val
ues
:
xK
KK
yK
xA
B
AB
AA
A
,
=− −
=1
(5,
6)
If t
he
giv
en v
apo
r p
ress
ure
dat
a in
Ex
erci
se 4
.8 f
or
tolu
ene,
an
d t
his
ex
erci
se f
or
n-h
epta
ne
are
fitt
ed t
o A
nto
ine
equ
atio
ns,
we
ob
tain
:
PT
PT
s sA B
(
7)
(8
)
=−
+
� ���
=−
+
� ���
exp
..
.
exp
.. .
15
78
31
28
55
27
21
36
4
17
27
41
38
96
3
25
56
7
Wh
ere
vap
or
pre
ssu
re i
s in
to
rr a
nd
tem
per
atu
re i
s in
oC
. S
olv
ing,
Eq
s. (
1)
to (
8),
Ex
erci
se 4
.9 (c
on
tin
ued
) A
na
lysi
s:
(a)
(c
on
tin
ued
)
T,
oC
Ps o
f A
, to
rr
Ps o
f B
, to
rr
KA
KB
xA
yA
αA
,B
98
.4
76
0.0
5
28
.7
1.0
00
0
0.6
95
6
1.0
00
1
.000
1
.438
9
9.0
7
73
.0
53
8.3
1
.017
2
0.7
08
3
0.9
44
0
.961
1
.436
1
00
.0
79
5.9
5
55
.2
1.0
47
2
0.7
30
5
0.8
51
0
.891
1
.434
1
01
.0
81
9.2
5
72
.5
1.0
78
0
0.7
53
3
0.7
60
0
.819
1
.431
1
02
.0
84
3.1
5
90
.2
1.1
09
4
0.7
76
6
0.6
71
0
.745
1
.428
1
03
.0
86
7.6
6
08
.4
1.1
41
5
0.8
00
6
0.5
85
0
.668
1
.426
1
04
.0
89
2.6
6
27
.1
1.1
74
4
0.8
25
1
0.5
01
0
.588
.
1.4
23
1
05
.0
91
8.1
6
46
.2
1.2
08
0
0.8
50
3
0.4
18
0
.506
1
.421
1
06
.0
94
4.2
6
65
.8
1.2
42
4
0.8
76
1
0.3
38
0
.420
1
.418
1
07
.0
97
0.9
6
85
.9
1.2
77
5
0.9
02
5
0.2
60
0
.332
1
.415
1
08
.0
99
8.1
7
06
.5
1.3
13
3
0.9
29
6
0.1
84
0
.241
1
.413
1
09
.0
10
26
.0
72
7.5
1
.350
0
0.9
57
3
0.1
09
0
.147
1
.410
1
10
.0
10
54
.4
74
9.1
1
.387
4
0.9
85
6
0.0
36
0
.050
1
.408
1
10
.5
10
68
.9
76
0.1
1
.406
4
1.0
00
1
0.0
00
0
.000
1
.406
Fro
m t
his
tab
le,
an x
-y p
lot
is g
iven
bel
ow
.
(b)
Fro
m t
he
abo
ve
tab
le,
a T
-x-y
plo
t is
giv
en b
elo
w.
Th
e x-
curv
e is
th
e b
ub
ble
-po
int
curv
e,
wh
ile
the
y-cu
rve
is t
he
dew
-po
int
curv
e.
(c)
A g
rap
h o
f re
lati
ve
vo
lati
lity
an
d K
-val
ues
as
a fu
nct
ion
of
tem
per
atu
re i
s giv
en o
n t
he
nex
t
pag
e.
(d)
Fro
m t
he
abo
ve
tab
le,
the
arit
hm
etic
av
erag
e re
lati
ve
vo
lati
lity
, u
sin
g t
he
extr
eme
val
ues
is
: (α
A,B
) avg =
(1
.43
8 +
1.4
06
)/2
= 1
.42
2
Ex
erci
se 4
.9 (c
on
tin
ued
) A
na
lysi
s:
(a)
(c
on
tin
ued
)
Ex
erci
se 4
.9 (c
on
tin
ued
)
A
na
lysi
s:
(c)
an
d (
d)
(co
nti
nu
ed)
Rel
ati
ve
Vo
lati
lity
an
d K
-Va
lues
Fo
r a
con
stan
t re
lati
ve
vo
lati
lity
, E
q.
(4-8
) ap
pli
es.
Fo
r α
A,B
= 1
.42
2,
yx
x
x
xA
A,B
A
AA
,B
A
A
=+
−=
+
α
α1
1
14
22
10
42
2�
�.
.
So
lvin
g t
his
eq
uat
ion
fo
r v
alu
es o
f x
A =
0 t
o 1
.0 g
ives
th
e fo
llo
win
g:
x A
y A
0
0.0
00
0
0.1
0
.136
4
0.2
0
.262
3
0.3
0
.378
7
0.4
0
.486
7
0.5
0
.587
1
0.6
0
.680
8
0.7
0
.768
4
0.8
0
.850
5
0.9
0
.927
5
1
1.0
00
0
Ex
erci
se 4
.9 (c
on
tin
ued
)
A
na
lysi
s:
(c)
an
d (
d)
(co
nti
nu
ed)
y-x
Plo
t fo
r a
n a
ver
ag
e re
lati
ve
vo
lati
lity
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.91
00
.10.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Mo
le f
rac
tio
n n
-hep
tan
e i
n l
iqu
id
Mole fraction n-heptane in vapor
(
e)
Rao
ult
’s l
aw c
alcu
lati
on
s co
mp
ared
to
ex
per
imen
tal
are
as f
oll
ow
s:
R
ao
ult
’s l
aw
Ex
pe
rim
en
tal
T
, oC
x
A
y A
xA
y A
11
0.7
5
-0.0
18
-0
.02
6
0.0
25
0
.048
1
06
.80
0
.276
0
.350
0
.129
0
.205
1
04
.50
0
.459
0
.547
0
.250
0
.349
1
02
.95
0
.589
0
.672
0
.354
0
.454
1
01
.35
0
.729
0
.793
0
.497
0
.577
9
9.7
3
0.8
76
0
.910
0
.692
0
.742
9
8.9
0
0.9
54
0
.967
0
.843
0
.864
9
8.5
0
0.9
92
0
.995
0
.940
0
.948
9
8.3
5
1.0
07
1
.005
0
.994
0
.993
Th
e R
aou
lt’s
law
val
ues
are
in
ver
y p
oo
r ag
reem
ent
wit
h t
he
exp
erim
enta
l v
alu
es.
Ex
erci
se 4
.9 (c
on
tin
ued
) A
na
lysi
s:
(e)
(c
on
tin
ued
)
Ex
erci
se 4
.9 (c
on
tin
ued
) A
na
lysi
s:
(e)
(c
on
tin
ued
)
Co
mp
ari
son
wit
h E
xp
erim
enta
l D
ata
Ex
erci
se 4
.10
S
ub
ject
:
Co
nti
nu
ou
s, s
ingle
sta
ge
dis
till
atio
n o
f A
an
d B
to
pro
du
ce a
dis
till
ate
and
bo
tto
ms.
Giv
en:
S
atu
rate
d l
iqu
id f
eed
of
50
mo
l% A
an
d 5
0 m
ol%
B f
ed t
o a
sti
ll a
t 4
0 m
ol/
h.
R
elat
ive
vo
lati
lity
= α
A,B
= 2
. B
ott
om
s ra
te =
30
mo
l/h
(a)
To
tal
con
den
ser
wit
h a
ref
lux
rat
io =
1.
(b
) N
o r
eflu
x.
Ass
um
pti
on
s:
Sti
ll i
s an
eq
uil
ibri
um
sta
ge.
Fin
d:
(a)
C
om
po
siti
on
of
the
two
pro
du
cts.
(b
) C
om
po
siti
on
of
the
two
pro
du
cts.
An
aly
sis:
F
rom
th
e d
efin
itio
n o
f th
e re
lati
ve
vo
lati
lity
,
αA
,BA
B
AB
AA
AA
==
− −=
yx
xy
yx
xy
1 12
��
��
(1
)
(a)
Dis
till
ate
= D
= F
- W
= 4
0 -
30
= 1
0 m
ol/
h
Mat
eria
l b
alan
ce f
or
A:
0
.5(4
0)
= 2
0 =
yA(1
0)
+ x
A(3
0)
(2)
S
olv
ing E
qs.
(1
) an
d (
2)
sim
ult
aneo
usl
y b
y e
lim
inat
ing
yA ,
we
ob
tain
:
33
20
2x
xA
A+
−=
(3
)
So
lvin
g E
q.
(3),
a q
uad
rati
c eq
uat
ion
, g
et o
nly
on
e p
ost
ive
roo
t:
x
A =
0.4
57
5,
x B =
0.5
42
5
for
the
bo
tto
ms
Su
bst
itu
tio
n i
nto
Eq
. (2
), g
ives
,
y
A =
0.6
27
5,
y B =
0.3
72
5
for
the
dis
till
ate
(b)
No
te t
hat
th
e so
luti
on
to
Par
t (a
) w
as i
nd
epen
den
t o
f th
e re
flu
x r
atio
. A
cco
rdin
gly
, th
e
solu
tio
n t
o P
art
(b)
is t
he
as f
or
Par
t (a
)
Ex
erci
se 4
.11
S
ub
ject
:
Dis
till
atio
n o
f an
ace
ton
e (A
) -
wat
er (
B)
mix
ture
th
at i
s p
arti
ally
vap
ori
zed
.
Giv
en:
F
eed
is
57
mo
l% A
an
d 4
3 m
ol%
B a
s a
liq
uid
at
12
5oC
an
d 6
87
kP
a.
It i
s fl
ash
ed
acro
ss a
val
ve
to t
he
colu
mn
pre
ssu
re o
f 1
01
.3 k
Pa,
wit
h a
res
ult
ing t
emp
erat
ure
of
60
oC
.
Vap
or-
liq
uid
eq
uil
ibri
um
dat
a at
co
lum
n p
ress
ure
. E
nth
alp
y d
ata
at c
olu
mn
co
nd
itio
ns.
Co
mp
osi
tio
ns
of
the
dis
till
ate
and
bo
tto
ms.
Ass
um
pti
on
s:
Fee
d i
s at
eq
uil
ibri
um
do
wn
stre
am o
f th
e fe
ed v
alv
e.
Wil
l h
ave
to c
hec
k i
f fe
ed
val
ve
op
erat
es a
dia
bat
ical
ly.
Giv
en h
eat
cap
acit
ies
are
for
the
liq
uid
an
d a
re c
on
stan
t.
Hea
ts o
f
vap
ori
zati
on
are
co
nst
ant.
N
o e
ffec
t o
f p
ress
ure
on
en
thal
py.
Fin
d:
Mo
le r
atio
of
liq
uid
to
vap
or
in t
he
feed
do
wn
stre
am o
f th
e v
alv
e.
Co
nst
ruct
an
H-x
-y
dia
gra
m.
An
aly
sis:
F
rom
th
e eq
uil
ibri
um
dat
a, a
t 6
0oC
, x
A =
0.5
0 a
nd
yA =
0.8
5 .
T
ake
a b
asis
of
F =
fee
d r
ate
= 1
km
ol/
s.
T
ota
l m
ater
ial
bal
ance
aro
un
d f
eed
val
ve:
F
= 1
= V
+ L
(1
)
Ace
ton
e m
ater
ial
bal
ance
aro
un
d f
eed
val
ve:
0.5
7(1
) =
0.8
5V
+ 0
.50
L
(2)
S
olv
ing E
qs.
(1
) an
d (
2)
sim
ult
aneo
usl
y,
V =
0.2
km
ol/
s an
d L
= 0
.8 k
mo
l/s
Th
eref
ore
, af
ter
the
val
ve,
mo
les
L/m
ole
s V
= 0
.8/0
.2 =
4
No
w c
hec
k w
het
her
val
ve
is o
per
atin
g a
dia
bat
ical
ly.
E
nth
alp
y o
f li
qu
id e
nte
rin
g v
alv
e =
0 (
as g
iven
)
E
nth
alp
y o
f fe
ed a
fter
th
e v
alv
e, u
sin
g g
iven
en
thal
pie
s =
27
,20
0(0
.2)
+ (
-5,2
70
)(0
.8)
= 1
22
4 k
J/s
T
her
efo
re,
the
enth
alp
y i
ncr
ease
s ac
ross
th
e v
alv
e b
y 1
22
4 k
J/s
To
co
nst
ruct
an
en
thal
py d
iagra
m f
or
1 a
tm p
ress
ure
, ta
ke
as a
n e
nth
alp
y d
atu
m,
A a
nd
B a
s
liq
uid
s at
25
oC
. T
his
is
a d
iffe
ren
t d
atu
m t
han
th
at u
sed
to
get
th
e giv
en e
nth
alp
y o
f th
e h
ot
feed
.
Pu
re A
: b
oil
s at
56
.7oC
.
Sin
ce C
P o
f li
qu
id =
13
4 k
J/k
mol-
K,
hL a
t 5
6.7
oC
= 1
34
(56
.7-2
5)=
42
48
kJ/
km
ol-
K
hV a
t 5
6.7
oC
=4
24
8 +
lat
ent
hea
t =
42
48
+ 2
97
50
= 3
39
98
kJ/
km
ol-
K
Pu
re B
: b
oil
s at
10
0oC
.
Sin
ce C
P o
f li
qu
id =
75
.3 k
J/k
mol-
K,
hL a
t 1
00
oC
= 7
5.3
(10
0-2
5)=
56
48
kJ/
km
ol-
K
hV a
t 1
00
oC
=5
64
8 +
lat
ent
hea
t =
56
48
+ 4
24
30
= 4
80
78
kJ/
km
ol-
K
Eq
uil
ibri
um
liq
uid
mix
ture
of
50
mo
l% A
an
d 5
0 m
ol%
B h
as a
bu
bb
le p
oin
t at
60
oC
. T
her
efo
re,
h
L =
0.5
(13
4)(
60
-25
) +
0.5
(75
.3)(
60
-25
) =
36
63
kJ/
km
ol-
K
Eq
uil
ibri
um
vap
or
mix
ture
of
85
mo
l% A
an
d 1
5 m
ol%
B h
as d
ew p
oin
t o
f 6
0oC
. T
her
efo
re,
h
V =
0.8
5[(
13
4)(
60
-25
) +
29
75
0]
+ 0
.15
[(7
5.3
)(6
0-2
5)
+ 4
24
30
] =
36
03
4 k
J/km
ol-
K
Cal
cula
tio
ns
for
oth
er e
qu
ilib
riu
m m
ixtu
res
are
do
ne
in a
sim
ilar
man
ner
an
d a
re s
um
mar
ized
in
the
foll
ow
ing t
able
:
Ex
erci
se 4
.11
(c
on
tin
ued
) A
na
lysi
s:
(co
nti
nu
ed)
T,
oC
x
A
x B
hL,
kJ/
km
ol
yA
y B
hV,
kJ/
km
ol
56
.7
1.0
00
0
.000
4
248
1
.000
0
.000
3
399
8
57
.1
0.9
20
0
.080
4
151
0
.944
0
.056
3
465
6
60
.0
0.5
00
0
.500
3
663
0
.850
0
.150
3
603
4
61
.0
0.3
30
0
.670
3
408
0
.837
0
.163
3
629
6
63
.0
0.1
76
0
.824
3
254
0
.805
0
.195
3
688
0
71
.7
0.0
68
0
.932
3
703
0
.692
0
.308
3
906
9
10
0.0
0
.000
1
.000
5
648
0
.000
1
.000
4
807
8
Fro
m t
his
tab
le,
the
h-x
-y p
lot
foll
ow
s, w
ith
tie
lin
es t
o c
on
nec
t th
e v
apo
r-li
qu
id e
qu
ilib
riu
m
alo
ng t
he
dew
-po
int
and
bu
bb
le-p
oin
t li
nes
.
En
thalp
y-C
om
po
siti
on
Plo
t
Ex
erci
se 4
.12
S
ub
ject
:
Vap
ori
zer
and
co
nd
ense
r h
eat
du
ties
fo
r b
enze
ne
(A)
-to
luen
e (B
) m
ixtu
res,
usi
ng a
n
enth
alp
y-c
on
cen
trat
ion
dia
gra
m.
Giv
en:
P
= 1
atm
. V
apo
r p
ress
ure
dat
a.
Sat
ura
ted
liq
uid
an
d v
apo
r en
thal
py d
ata.
Ass
um
pti
on
s:
Rao
ult
's l
aw.
Fin
d:
(a)
C
on
stru
ct a
n h
-x-y
plo
t.
(b
) H
eat
du
ty f
or
50
mo
l% v
apo
riza
tio
n o
f a
30
mo
l% A
mix
ture
, st
arti
ng f
rom
liq
uid
satu
rati
on
tem
per
atu
re.
Hea
t d
uty
to
co
nd
ense
th
e v
apo
r an
d s
ub
coo
l it
10
oC
.
An
aly
sis:
(
a)
Fir
st,
com
pu
te t
he
vap
or
and
liq
uid
eq
uil
ibri
um
co
mp
osi
tio
ns
at 1
atm
an
d
tem
per
atu
res
fro
m 6
0 t
o 1
00
oC
usi
ng R
aou
lt's
law
wit
h t
he
vap
or
pre
ssu
re d
ata.
E
q.
(2-4
4 )
ap
pli
es,
as w
ell
as t
he
sum
of
the
mo
le f
ract
ion
s in
th
e p
has
es i
n e
qu
ilib
riu
m.
Th
us,
Ky x
PT
PK
y x
PT
P
yy
xx
ss
AA A
A
BB B
B
AB
AB
,
(1
, 2
)
,
(3
, 4
)
==
==
+=
+=
��
��
11
Eq
uat
ion
s (1
) to
(4
) ca
n b
e re
du
ced
to
th
e fo
llo
win
g e
qu
atio
ns,
xK
KK
yK
xA
B
AB
AA
A
,
=− −
=1
(5,
6)
Vap
or
pre
ssu
re d
ata
in E
xer
cise
s 4
.6 f
or
ben
zen
e, a
nd
4.8
fo
r to
luen
e giv
e A
nto
ine
equ
atio
ns,
PT
PT
ss
AB
,
(
7,
8)
=−
+
� ���
=−
+
� ���
exp
.. .
exp
.. .
15
56
45
26
02
34
21
12
71
17
27
41
38
96
3
25
56
7
Wh
ere
vap
or
pre
ssu
re i
s in
to
rr a
nd
tem
per
atu
re i
s in
oC
. S
olv
ing,
Eq
s. (
1)
to (
8),
T,
oC
Ps o
f A
, to
rr P
s of
B,
torr
K
A
KB
xA
y A
80
.1
75
9.9
2
90
.0
0.9
99
8
0.3
81
6
1.0
00
1
.000
8
5.0
8
80
.8
34
2.7
1
.159
0
0.4
51
0
0.7
75
0
.899
9
0.0
1
019
.1
40
4.4
1
.340
9
0.5
32
1
0.5
79
0
.776
9
5.0
1
173
.4
47
4.9
1
.543
9
0.6
24
9
0.4
08
0
.630
1
00
.0
13
45
.0
55
5.2
1
.769
7
0.7
30
5
0.2
59
0
.459
1
05
.0
15
35
.0
64
6.2
2
.019
8
0.8
50
3
0.1
28
0
.259
1
10
.5
17
66
.8
76
0.1
2
.324
8
1.0
00
1
0.0
00
0
.000
Th
is c
ov
ers
the
tem
per
atu
re r
ang
e o
f co
-ex
iste
nce
of
vap
or
and
liq
uid
.
Ex
erci
se 4
.12
(c
on
tin
ued
) A
na
lysi
s:
(a)
(c
on
tin
ued
)
Mo
lecu
lar
wei
gh
ts a
re M
A =
78
an
d
MB =
92
F
or
a giv
en t
emp
erat
ure
, co
mp
ute
sat
ura
ted
liq
uid
-ph
ase
mix
ture
en
thal
pie
s in
kJ/
kg o
f
mix
ture
fro
m,
hx
Mh
xM
h
xM
xM
L
LL
=+
−
+−
AA
AB
AA
AB
AB
()
()
1 1
(9)
Sim
ilar
ly f
or
the
vap
or,
h
yM
hy
Mh
yM
yM
V
VV
=+
−
+−
AA
AB
AA
AB
AB
()
()
1 1
(10
)
Wil
l h
ave
to i
nte
rpo
late
an
d e
xtr
apo
late
giv
en s
atu
rate
d e
nth
alp
y d
ata.
L
iqu
id e
nth
alp
y d
ata
are
lin
ear
wit
h t
emp
erat
ure
, th
eref
ore
, it
is
fou
nd
th
at:
hT
hT
LL
AB
,
=−
=−
18
53
21
85
34
..
(
11
, 1
2)
Vap
or
enth
alp
y d
ata
are
no
t q
uit
e li
nea
r, b
ut
fit
the
foll
ow
ing q
uad
rati
c eq
uat
ion
s:
hT
Th
TT
VV
AB
,
=+
+=
++
42
70
85
00
02
54
11
08
50
00
25
22
..
..
(1
3,
14
)
T,
oC
x
A
yA
(hL) A
,
kJ/
kg
(hL) B
,
kJ/
kg
(hV) A
,
kJ/
kg
(hV) B
,
kJ/
kg
hL
,
kJ/
kg
hV
,
kJ/
kg
80
.1
1.0
00
1
.000
1
16
.2
11
4.2
5
11
.1
49
5.1
1
16
.2
51
1.1
8
5.0
0
.775
0
.899
1
25
.3
12
3.3
5
17
.3
50
1.3
1
24
.7
51
5.4
9
0.0
0
.579
0
.776
1
34
.5
13
2.5
5
23
.8
50
7.8
1
33
.6
51
9.7
9
5.0
0
.408
0
.630
1
43
.8
14
1.8
5
30
.3
51
4.3
1
42
.5
52
3.8
1
00
.0
0.2
59
0
.459
1
53
.0
15
1.0
5
37
.0
52
1.0
1
51
.5
52
7.7
1
05
.0
0.1
28
0
.259
1
62
.3
16
0.3
5
43
.8
52
7.8
1
60
.5
53
1.5
1
10
.5
0.0
00
0
.000
1
72
.4
17
0.4
5
51
.5
53
5.5
1
70
.4
53
5.5
Plo
ts o
f h
in
kJ/
kg m
ixtu
re a
s a
fun
ctio
n o
f sa
tura
ted
vap
or
and
liq
uid
mo
le f
ract
ion
s, a
nd
y-x
are
giv
en o
n t
he
nex
t p
age.
(b
) T
ake
a b
asis
of
1 k
mo
l o
f 3
0 m
ol%
A -
70
mo
l% B
fee
d m
ixtu
re.
Th
en,
kg A
= (
0.3
0)(
78
) =
23
.4 k
g
and
kg B
= (
0.7
0)(
92
) =
64
.4 k
g
or
87
.8 k
g t
ota
l fe
ed.
U
se y
-x d
iagra
m t
o o
bta
in c
om
po
siti
on
s o
f v
apo
r an
d l
iqu
id f
or
50
mo
l% v
apo
rize
d.
Fro
m t
he
equ
atio
n
abo
ve
Eq
. (4
-6),
th
e sl
op
e o
f th
e q
-lin
e is
[(V
/F)-
1]/
(V/F
) =
(0
.5-1
.0)/
0.5
= -
1.
Th
e co
nst
ruct
ion
is
sho
wn
on
th
e y-
x d
iag
ram
, w
her
e th
e in
ters
ecti
on
wit
h t
he
equ
ilib
riu
m c
urv
e
giv
es x
A =
0.2
2 a
nd
yA =
0.3
8.
Th
e m
ass
of
liq
uid
= (
0.2
2)(
0.5
)(7
8)
+ (
0.7
8)(
0.5
)(9
2)
= 4
4.5
kg.
Th
e m
ass
of
vap
or
= 8
7.8
- 4
4.5
= 4
3.3
kg.
On
th
e h
-x-y
dia
gra
m,
Po
int
A i
s th
e sa
tura
ted
liq
uid
feed
wit
h h
L =
15
0 k
J/k
g o
f fe
ed.
Po
int
C i
s th
e li
qu
id r
emai
nin
g a
fter
50
mo
l% v
apo
riza
tio
n,
wit
hh
L,
= 1
58
kJ/
kg.
Sin
ce 4
4.5
/87
.8 o
r 0
.50
7 o
f th
e fe
ed i
s le
ft a
s li
qu
id,
this
is
equ
ival
ent
to
(0.5
07
)(1
58
) =
80
kJ/
kg f
eed
. P
oin
t D
is
the
vap
or,
wit
h h
V =
54
0 k
J/k
g v
apo
rize
d.
Sin
ce 0
.49
3
Ex
erci
se 4
.12
(c
on
tin
ued
)
An
aly
sis:
(
b)
(co
nti
nu
ed)
of
the
feed
is
vap
ori
zed
, th
is i
s eq
uiv
alen
t to
(0
.49
3)(
54
0)
= 2
66
kJ/
kg f
eed
. T
her
efo
re,
the
ener
gy r
equ
ired
fo
r p
arti
al v
apo
riza
tio
n =
26
6 +
80
-
15
0 =
19
6 k
J/k
g o
f fe
ed.
P
oin
t B
is
the
com
bin
ed v
apo
r an
d l
iqu
id p
has
es a
fter
par
tial
vap
ori
zati
on
.
Po
int
E i
s
con
den
sed
vap
or
as s
atu
rate
d l
iqu
id,
wit
h a
n e
nth
alp
y o
f 1
45
kJ/
kg.
Th
is i
s eq
uiv
alen
t to
(0.4
93
)(1
45
) =
71
kJ/
kg o
f fe
ed.
Th
eref
ore
, th
e co
nd
ense
r d
uty
= 2
66
- 7
1 =
19
5 k
J/k
g f
eed
.
P
oin
t F
is
10
oC
su
bco
ole
d c
on
den
sate
, w
her
e th
e en
thal
py c
han
ge
fro
m s
atu
rati
on
, b
ased
on
a l
iqu
id s
pec
ific
hea
t o
f 1
.85
kJ/
kg-o
C,
is 1
.85
(10
)(0
.49
3)
= 9
kJ/
kg f
eed
. T
her
efo
re,
the
con
den
ser
du
ty i
s n
ow
19
5 +
9 =
20
4 k
J/k
g f
eed
.
Ex
erci
se 4
.12
(c
on
tin
ued
)
An
aly
sis:
(a
)
En
tha
lpy
– C
om
po
siti
on
Dia
gra
m
Ex
erci
se 4
.13
S
ub
ject
:
Aze
otr
op
e fo
r th
e ch
loro
form
-met
han
ol
syst
em a
t 1
01
.3 k
Pa.
Giv
en:
V
apo
r-li
qu
id e
qu
ilib
riu
m d
ata
fro
m S
ecti
on
13
, p
. 1
1 o
f P
erry
's H
and
bo
ok
, 6
th e
dit
ion
.
Fin
d:
Fro
m d
ata,
co
nst
ruct
y-x
an
d T
-x-y
plo
ts.
Aze
otr
op
e co
nd
itio
ns
An
aly
sis:
S
ee p
lots
bel
ow
. F
rom
th
ese
plo
ts,
a m
inim
um
-bo
ilin
g a
zeo
tro
pe
occ
urs
at
53
.5oC
wit
h a
co
mp
osi
tio
n o
f 6
5 m
ol%
ch
loro
form
an
d 3
5 m
ol%
met
han
ol.
Ex
erci
se 4
.14
S
ub
ject
:
Aze
otr
op
e fo
r th
e w
ater
-fo
rmic
aci
d s
yst
em a
t 1
01
.3 k
Pa.
Giv
en:
V
apo
r-li
qu
id e
qu
ilib
riu
m d
ata
fro
m S
ecti
on
13
, p
. 1
4 o
f P
erry
's H
and
bo
ok
, 6
th e
dit
ion
.
Fin
d:
Fro
m d
ata,
co
nst
ruct
y-x
an
d T
-x-y
plo
ts.
Aze
otr
op
e co
nd
itio
ns
An
aly
sis:
S
ee p
lots
bel
ow
. F
rom
th
ese
plo
ts,
a m
axim
um
-bo
ilin
g a
zeo
tro
pe
occ
urs
at
10
7.6
oC
wit
h a
co
mp
osi
tio
n o
f 4
2 m
ol%
wat
er a
nd
58
mo
l% f
orm
ic a
cid
.
Ex
erci
se 4
.15
Su
bje
ct:
P
arti
al v
apo
riza
tio
n o
f a
wat
er (
A)
-iso
pro
pan
ol
(B)
mix
ture
at
1 a
tm.
Giv
en:
V
apo
r-li
qu
id e
qu
ilib
riu
m d
ata
at 1
atm
an
d v
apo
r-p
ress
ure
dat
a.
Fin
d:
(a)
C
on
stru
ct T
-x-y
an
d
y-x
d
iag
ram
s.
(b
) C
om
po
siti
on
of
vap
or
wh
en a
60
mo
l% A
- 4
0 m
ol%
B m
ixtu
re i
s at
its
bu
bb
le p
oin
t.
(c
) C
om
po
siti
on
of
vap
or
and
liq
uid
fo
r 7
5 m
ol%
vap
ori
zati
on
of
mix
ture
in
Par
t (a
).
(d
) K
-val
ues
an
d α
-val
ues
at
80
an
d 8
9oC
.
(e
) C
om
par
iso
n o
f p
arts
(a)
, (b
), a
nd
(c)
to
res
ult
s fr
om
usi
ng R
aou
lt's
an
d D
alto
n's
law
s.
An
aly
sis:
(
a)
Th
e fo
llo
win
g a
re p
lots
of
the
giv
en e
qu
ilib
riu
m d
ata,
in
clu
din
g t
he
pu
re-
com
po
nen
t n
orm
al b
oil
ing p
oin
ts.
Ex
erci
se 4
.15
(c
on
tin
ued
)
An
aly
sis:
(
a)
con
tin
ued
Ex
erci
se 4
.15
(c
on
tin
ued
)
An
aly
sis:
(b)
Fro
m t
he
y-x
plo
t o
n t
he
pre
vio
us
pag
e, t
he
com
po
siti
on
of
the
firs
t b
ub
ble
of
vap
or
is 5
7 m
ol%
iso
pro
pan
ol
and
43
mo
l% w
ater
. S
ee t
he
q-l
ine
on
th
e d
iagra
m.
(c
) F
or
75
mo
l% v
apo
riza
tio
n,
use
th
e in
ver
se l
ever
-arm
ru
le o
n t
he
T-x
-y
dia
gra
m o
r p
lot
a q
-lin
e o
n t
he
y-x
dia
gra
m.
Fo
r th
e la
tter
, fr
om
th
e eq
uat
ion
ab
ov
e E
q.
(4-6
),
the
slo
pe
of
the
q-l
ine
is [
(V/F
)-1
]/(V
/F)
= (
0.7
5-1
.0)/
0.7
5 =
-0
.33
3.
Th
e co
nst
ruct
ion
is
sho
wn
on
th
e y-
x d
iag
ram
, w
her
e th
e in
ters
ecti
on
wit
h t
he
equ
ilib
riu
m c
urv
e giv
es x
A =
0.1
4 a
nd
yA =
0.5
0.
(d)
Can
no
t co
mp
ute
th
e K
-val
ues
or
α a
t 8
0oC
, b
ecau
se t
his
tem
per
atu
re i
s b
elo
w
the
low
est
bo
ilin
g m
ixtu
re,
wh
ich
is
the
azeo
tro
pe.
A
t 8
9oC
, th
e T
-x-y
dia
gra
m g
ives
th
e fo
llo
win
g c
om
po
siti
on
s fr
om
th
e li
ne
sho
wn
on
th
e
abo
ve
dia
gra
m:
y B =
0.3
5,
yA =
0.6
5
x B
= 0
.03
5,
xA =
0.9
65
Fro
m E
q.
(2-1
9)
for
the
def
init
ion
of
the
K-
val
ue,
B
BA
BA A
0.3
50
.65
01
00
.03
50
.96
5.6
7=
==
==
=K
yy x
Kx
Fro
m E
q.
(2-2
1)
for
the
def
init
ion
of
the
rela
tiv
e v
ola
tili
ty,
α,
no
tin
g t
hat
at
89
oC
an
d 1
atm
,
iso
pro
pan
ol
is m
ore
vo
lati
le,
α
B,A
B A
==
=K K
10
06
71
5.
(e)
To
cal
cula
te T
-x-y
cu
rves
fro
m v
apo
r p
ress
ure
dat
a, u
sin
g R
aou
lt's
an
d
Dal
ton
's l
aws,
Eq
. (2
-44
) a
pp
lies
, as
wel
l as
th
e su
m o
f th
e m
ole
fra
ctio
ns
in t
he
ph
ases
in
equ
ilib
riu
m.
Th
us,
Ky x
PT
PK
y x
PT
P
yy
xx
ss
AA A
A
BB B
B
AB
AB
,
(1
, 2
)
,
(3
, 4
)
==
==
+=
+=
��
��
11
Eq
uat
ion
s (1
) to
(4
) ca
n b
e re
du
ced
to
th
e fo
llo
win
g e
qu
atio
ns
for
the
mo
le
frac
tio
ns
of
ben
zen
e in
ter
ms
of
the
K-v
alu
es:
xK
KK
yK
xA
B
AB
AA
A
,
=− −
=1
(5,
6)
If t
he
giv
en v
apo
r p
ress
ure
dat
a ar
e fi
tted
to
An
toin
e eq
uat
ion
s, w
e o
bta
in:
Ex
erci
se 4
.15
(c
on
tin
ued
)
An
aly
sis:
(
e) c
on
tin
ued
PT
PT
s sA B
(
7)
(8
)
=−
+
� ���
=−
+
� ���
exp
..
.
exp
.. .
18
48
54
39
21
96
23
09
1
25
01
73
80
10
6
35
32
38
Wh
ere
vap
or
pre
ssu
re i
s in
to
rr a
nd
tem
per
atu
re i
s in
oC
. S
olv
ing,
Eq
s. (
1)
to (
8),
T,
oC
P
s of
B
Ps o
f A
K
B
KA
x B
y B
αB
-A
82
.5
76
0.0
3
92
.1
1.0
00
0
0.5
15
9
1.0
00
1
.000
1
.938
8
4.0
8
09
.5
41
6.2
1
.065
1
0.5
47
6
0.8
74
0
.931
1
.945
8
6.0
8
79
.9
45
0.2
1
.157
8
0.5
92
4
0.7
21
0
.835
1
.954
8
8.0
9
55
.7
48
6.6
1
.257
5
0.6
40
2
0.5
83
0
.733
1
.964
9
0.0
1
037
.3
52
5.3
1
.364
9
0.6
91
2
0.4
58
0
.626
1
.975
9
2.0
1
125
.0
56
6.6
1
.480
3
0.7
45
6
0.3
46
0
.513
1
.985
9
4.0
1
219
.3
61
0.6
1
.604
3
0.8
03
5
0.2
45
0
.394
1
.997
9
6.0
1
320
.5
65
7.4
1
.737
5
0.8
65
0
0.1
55
0
.269
2
.009
9
8.0
1
429
.1
70
7.2
1
.880
4
0.9
30
5
0.0
73
0
.138
2
.021
1
00
.0
15
45
.6
76
0.0
2
.033
6
1.0
00
0
0.0
00
0
.000
2
.034
Th
ese
resu
lts
are
plo
tted
bel
ow
. R
aou
lt’s
law
is
bad
ly i
n e
rro
r w
hen
co
mp
ared
to
th
e
exp
erim
enta
l d
ata.
Fo
r p
art
(b),
Rao
ult
's l
aw p
red
icts
a b
ub
ble
-po
int
vap
or
wit
h a
n i
sop
rop
ano
l m
ole
fra
ctio
n o
f
0.5
6.
By c
oin
cid
ence
, th
is c
om
par
es w
ell
wit
h t
he
resu
lt d
eter
min
ed w
ith
th
e ex
per
imen
tal
dat
a.
Fo
r p
art
(c),
ho
wev
er,
Rao
ult
's l
aw p
red
icts
iso
pro
pan
ol
mo
le f
ract
ion
s o
f 0
.28
fo
r th
e li
qu
id a
nd
0.4
3 f
or
the
vap
or.
T
hes
e ar
e d
rast
ical
ly d
iffe
ren
t fr
om
th
e v
alu
es o
f 0
.14
an
d 0
.50
, re
spec
tiv
ely
fro
m t
he
exp
erim
enta
l d
ata.
R
aou
lt's
law
can
no
t b
e u
sed
fo
r th
e is
op
rop
ano
l-w
ater
syst
em,
for
wh
ich
it
also
fai
ls t
o p
red
ict
an a
zeo
tro
pe.
Ex
erci
se 4
.15
(c
on
tin
ued
)
An
aly
sis:
(
e) c
on
tin
ued
Ex
erci
se 4
.16
S
ub
ject
:
Vap
ori
zati
on
of
mix
ture
s o
f n
-hex
ane
(H)
and
n-o
ctan
e (C
) at
1 a
tm
Giv
en:
T
-x-y
dia
gra
m i
n F
ig.
4.3
, an
d y
-x d
iagra
m i
n F
ig.
4.4
. 1
00
km
ol
mix
ture
.
Fin
d:
Tem
per
atu
re,
km
ol
of
vap
or,
mo
le f
ract
ion
s o
f H
in
liq
uid
an
d v
apo
r at
eq
uil
ibri
um
fo
r
var
iou
s fl
ash
co
nd
itio
ns.
An
aly
sis:
L
et z
H =
mo
le f
ract
ion
of
n-h
exan
e in
th
e fe
ed a
nd
Ψ =
V/F
.
U
se i
nv
erse
lev
er-a
rm r
ule
as
dis
pla
yed
by L
ine
DE
F i
n F
ig.
4.3
.
T
he
resu
lts
for
par
ts (
a) t
hro
ugh
(f)
are
as
foll
ow
s:
Giv
en
T,
oF
V
, k
mo
l y H
x
H
(a)
zH
= 0
.5,
Ψ =
0.2
1
96
2
0
0.8
0
0.4
3
(b)
zH
= 0
.4,
yH =
0.6
2
20
4
8.6
0
.60
0
.21
(c)
zH
= 0
.6,
xC =
0.7
2
10
7
3.7
0
.70
0
.30
(d)
zH
= 0
.5,
Ψ =
0.0
1
88
0
.0
0.8
4
0.5
0
(e)
zH
= 0
.5,
Ψ =
1.0
2
30
1
00
0
.50
0
.14
(f)
zH
= 0
.5,
T =
20
0oF
2
00
3
1
0.7
7
0.3
8
Ex
erci
se 4
.17
S
ub
ject
:
Der
ivat
ion
of
equ
ilib
riu
m f
lash
eq
uat
ion
s fo
r a
bin
ary m
ixtu
re (
1,
2).
Giv
en:
E
qs.
(5
), (
6),
an
d (
3)
of
Tab
le 4
.4.
Fin
d:
D
eriv
e giv
en e
qu
atio
ns
for
x 1,
x 2,
y 1,
y 2,
and
Ψ =
V/F
.
An
aly
sis:
F
irst
der
ive
the
equ
atio
n f
or
Ψ =
V/F
. F
rom
Eq
. (3
), T
able
4.4
,
zK
K
zK
K
11
1
12
2
1
11
11
11
0−
+−
+−
−
+−
=��
������
��
ΨΨ
(1)
So
lvin
g E
q.
(1)
for
Ψ,
and
sim
pli
fyin
g,
Ψ=
−−
−−
−
−−
+−
−−
zK
zK
zK
Kz
KK
11
12
11
21
21
11
1
11
11
1
������
����������
=−
−−
−
zK
KK
K
11
22
1
11
1
����
/
(3)
Su
bst
itu
tin
g E
q.
(3)
into
Eq
. (5
) o
f T
able
4.4
an
d s
imp
lify
ing g
ives
th
e re
qu
ired
eq
uat
ion
fo
r x 1
.
Th
en u
se y
1 =
K1x 1
an
d s
imp
lify
, fo
llo
wed
by x
2 =
1 -
x1
an
d
y 2 =
1-
y 1 .
Ex
erci
se 4
.18
S
ub
ject
:
Co
nd
itio
ns
for
Rac
hfo
rd-R
ice
equ
atio
n t
o b
e sa
tisf
ied
.
Giv
en:
E
q.
(3),
Tab
le 4
.4,
wh
ich
is
the
Rac
hfo
rd-R
ice
equ
atio
n.
Fin
d:
Co
nd
itio
ns
un
der
wh
ich
th
e eq
uat
ion
can
be
sati
sfie
d f
or
01
≤≤
V F.
An
aly
sis:
A
nec
essa
ry,
bu
t n
ot
suff
icie
nt,
co
nd
itio
n i
s th
at a
t le
ast
on
e K
-val
ue
is <
1 a
nd
at
leas
t o
ne
K-v
alu
e is
> 1
. I
f al
l K
-val
ues
are
> 1
, th
e su
m:
zK
K
ii
iiC
1
11
1
−
+−
=���
��
Ψ
wil
l b
e n
egat
ive
and
can
no
t b
e ze
ro.
If a
ll K
-val
ues
are
< 1
, th
e n
um
erat
or
in t
he
sum
wil
l b
e p
osi
tiv
e fo
r ea
ch t
erm
. W
ith
Ψ b
etw
een
0 a
nd
1,
the
term
Ψ(K
i -
1)
wil
l al
ways
be
< 1
. T
her
efo
re,
the
den
om
inat
or
wil
l b
e p
osi
tiv
e al
so
and
th
e su
m w
ill
be
po
siti
ve
and
can
no
t b
e ze
ro.
Ex
erci
se 4
.19
S
ub
ject
:
Fla
sh v
apo
riza
tio
n o
f a
ben
zen
e (A
) -
tolu
ene
(B)
mix
ture
fo
r α
A-B
= 2
.3.
Giv
en:
F
eed
is
40
mo
l% A
an
d 6
0 m
ol%
B.
Fin
d:
Per
cen
t o
f A
in
th
e eq
uil
ibri
um
vap
or
if 9
0%
of
the
tolu
ene
leav
es i
n t
he
liq
uid
by
gra
ph
ical
mea
ns.
An
aly
sis:
F
or
con
stan
t re
lati
ve
vo
lati
lity
, E
q.
(4-8
) ap
pli
es,
y
x
xA
A,B
A
AA
,B1
+=
−
α
α1
��
So
lvin
g t
his
eq
uat
ion
fo
r y
A a
s a
fun
ctio
n o
f x
A ,
xA
yA
0.1
0
.20
35
0.2
0
.36
51
0.3
0
.49
64
0.4
0
.60
53
0.5
0
.69
70
0.6
0
.77
53
0.7
0
.84
29
0.8
0
.90
20
0.9
0
.95
39
A p
lot
of
the
calc
ula
ted
eq
uil
ibri
um
cu
rve
is g
iven
bel
ow
. T
o u
se t
his
plo
t fo
r a
gra
ph
ical
solu
tio
n o
f th
e eq
uil
ibri
um
, d
raw
a q
-lin
e, u
sin
g t
he
foll
ow
ing e
qu
atio
n a
bo
ve
Eq
. (4
-6),
fo
r an
assu
med
val
ue
of
Ψ =
V/F
an
d c
hec
k t
he
resu
ltin
g %
rec
ov
ery o
f to
luen
e in
th
e li
qu
id.
Var
y Ψ
un
til
the
% r
eco
ver
y =
90
%.
Th
en c
om
pu
te,
for
the
corr
esp
on
din
g Ψ
, t
he
% r
eco
ver
y o
f
ben
zen
e in
th
e v
apo
r.
y
xz
xA
AA
A=
−� ���
+� ���
=−� ���
+� ���
Ψ
ΨΨ
Ψ
ΨΨ
11
11
04
0.
(1)
Ex
erci
se 4
.19
(co
nti
nu
ed)
An
aly
sis:
(
con
tin
ued
)
Bas
is:
F =
10
0 m
ole
s, 6
0 m
ole
s to
luen
e (B
).
Wan
t 0
.9(6
0)
= 5
4 m
ole
s B
in
liq
uid
. T
her
efo
re,
60
- 5
4 =
6 m
ole
s B
in
vap
or.
T
her
efo
re,
wan
t (n
B) V
= y
BV
= (
1 -
yA)1
00
Ψ =
6.
Th
en c
om
pu
te %
reco
ver
y o
f b
enze
ne
in v
apo
r =
(n
A) V
/40
x 1
00
% =
yAV
/40
x
10
0%
= 2
.5 y
AΨ
x 1
00
%.
Th
e
foll
ow
ing a
re t
yp
ical
val
ues
fo
r th
e tr
ial
and
err
or
pro
ced
ure
, w
ith
th
e fi
nal
res
ult
at
the
bo
tto
m.
Ass
um
ed Ψ
y
A
xA
(nB) V
,
mo
les
% r
eco
ver
y
of
A i
n v
apo
r
0.3
0
.54
0
.35
1
3.8
4
0.5
0.2
0
.56
0
.36
8
.8
28
.0
0.1
5
0.5
75
0
.37
6
.4
21
.6
0.1
42
0
.58
0
.37
5
6.0
2
0.6
Ex
erci
se 4
.20
S
ub
ject
:
Fla
sh v
apo
riza
tio
n o
f a
ben
zen
e (A
) -
tolu
ene
(B)
mix
ture
.
Giv
en:
F
eed
is
40
mo
l% A
an
d 6
0 m
ol%
B.
V
apo
r p
ress
ure
dat
a.
Ass
um
pti
on
s:
Rao
ult
's l
aw (
idea
l so
luti
on
s).
Pre
ssu
re =
1 a
tm.
Fin
d:
Per
cen
t o
f A
in
th
e eq
uil
ibri
um
vap
or
if 9
0%
of
the
tolu
ene
leav
es i
n t
he
liq
uid
.
An
aly
sis:
B
asis
: F
= 1
00
mo
le w
ith
60
mo
les
B a
nd
40
mo
les
A.
Wan
t 0
.9(6
0)
= 5
4 m
ole
s B
in l
iqu
id.
Th
eref
ore
, 6
0 -
54
= 6
mo
les
B i
n v
apo
r.
Th
eref
ore
, w
ant
(nB) V
= y
BV
= (
1 -
yA)1
00
Ψ =
6.
Th
en c
om
pu
te %
rec
ov
ery o
f b
enze
ne
in v
apo
r =
(n
A) V
/40
x 1
00
% =
yAV
/40
x
10
0%
= 2
.5 y
AΨ
x 1
00
%.
Th
e fo
llo
win
g t
rial
an
d e
rro
r p
roce
du
re c
an b
e u
sed
, b
ased
on
mat
eria
l
bal
ance
an
d e
qu
ilib
riu
m e
qu
atio
ns:
(1)
Gu
ess
a te
mp
erat
ure
. (
2)
Rea
d v
apo
r p
ress
ure
s fr
om
Fig
. 2
.4 a
nd
co
mp
ute
K-v
alu
es f
rom
Rao
ult
's l
aw (
Eq
. (3
), T
able
2.3
), K
PP
iis
=/
. (
3)
So
lve
for
Ψ =
V/F
usi
ng t
he
fift
h e
qu
atio
n i
n
Ex
erci
se 4
.17
,
Ψ=
−−
−
−=
−−
−
−
zK
KK
K
KK
K
K
AA
BB
A
AB
B
A
/1
1
1
0.4
0/
11
1
����
����
(4)
So
lve
for
yA f
rom
th
e th
ird
eq
uat
ion
in
Ex
erci
se 4
.17
,
y
KK
KK
KA
AB
AB
A=
−−
���
�/
(5)
Co
mp
ute
(n
B) V
= (
1 -
yA)1
00
Ψ .
If
th
e v
alu
e is
6,
then
tem
per
atu
re g
ues
s is
co
rrec
t.
Oth
erw
ise,
gu
ess
ano
ther
T,
and
rep
eat
step
s (1
) to
(5
).
If 6
, co
mp
ute
% r
eco
ver
y o
f b
enze
ne
in
the
vap
or
fro
m
2.5
yAΨ
x 1
00
%.
Gu
ess
T,
oF
P
s o
f A
,
psi
a
Ps o
f B
,
psi
a
KA
KB
Ψ
yA
Mo
les
B
in v
apo
r
19
5
20
.0
8.0
1
.36
0
.54
4
-0.7
9
20
5
23
.4
9.5
1
.59
0
.64
6
0.1
13
0
.59
6
4.6
20
5.5
2
3.6
9
.6
1.6
05
0
.65
3
0.1
61
0
.58
5
6.7
By i
nte
rpo
lati
on
,
T =
20
5.3
oF
to
ob
tain
6 m
ole
s o
f B
in
th
e v
apo
r.
Th
is c
orr
esp
on
ds
to Ψ
=
0.1
45
an
d y
A =
0.5
88
.
Fro
m a
bo
ve,
% r
eco
ver
y o
f b
enze
ne
in t
he
vap
or
= 2
.5(0
.58
8)(
0.1
45
)10
0%
= 2
1.3
%
Ex
erci
se 4
.21
S
ub
ject
:
Eq
uil
ibri
um
fla
sh o
f a
sev
en-c
om
po
nen
t m
ixtu
re.
Giv
en:
Fee
d m
ole
fra
ctio
ns
and
K-v
alu
es.
Fin
d:
Ψ =
V/F
b
y:
(a
) R
ach
ford
- R
ice
equ
atio
n,
fz
K
Kg
ii
i
iiC
iC
1
1
1
1
1
11
{}
{,
}Ψ
ΨΨ
=−
+−
==
=
��
��
��
(b
) A
lter
nat
ive
flas
h e
qu
atio
n,
fz
K Kg
ii
i iiC
iC
2
1
2
11
1{
}{
,}
ΨΨ
Ψ=
+−
==
=
��
��
M
ake
plo
ts o
f f{
Ψ} v
s. Ψ
fo
r ea
ch m
eth
od
an
d c
om
par
e.
An
aly
sis:
C
alcu
lati
on
s w
ith
a s
pre
adsh
eet,
fo
r v
alu
es o
f Ψ
fro
m 0
to
1.0
in
in
terv
als
of
0.1
:
(a)
I z
F
K
Ψ =
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
g{i,Ψ
1
0.0
079
16.2
-0
.120
-0.0
48
-0.0
30
-0.0
22
-0.0
17
-0.0
14
-0.0
12
-0.0
10
-0.0
09
-0.0
08
-0.0
07
2
0.1
321
5.2
-0
.555
-0.3
91
-0.3
02
-0.2
45
-0.2
07
-0.1
79
-0.1
58
-0.1
41
-0.1
27
-0.1
16
-0.1
07
3
0.0
849
2.6
-0
.136
-0.1
17
-0.1
03
-0.0
92
-0.0
83
-0.0
75
-0.0
69
-0.0
64
-0.0
60
-0.0
56
-0.0
52
4
0.2
690
1.9
8
-0.2
64
-0.2
40
-0.2
20
-0.2
04
-0.1
89
-0.1
77
-0.1
66
-0.1
56
-0.1
48
-0.1
40
-0.1
33
5
0.0
589
0.9
1
0.0
05
0.0
05
0.0
05
0.0
05
0.0
05
0.0
06
0.0
06
0.0
06
0.0
06
0.0
06
0.0
06
6
0.1
321
0.7
2
0.0
37
0.0
38
0.0
39
0.0
40
0.0
42
0.0
43
0.0
44
0.0
46
0.0
48
0.0
49
0.0
51
7
0.3
151
0.2
8
0.2
27
0.2
44
0.2
65
0.2
89
0.3
19
0.3
54
0.3
99
0.4
57
0.5
35
0.6
45
0.8
10
f{Ψ
}:
-0.8
05
-0.5
08
-0.3
45
-0.2
27
-0.1
30
-0.0
42
0.0
45
0.1
37
0.2
45
0.3
80
0.5
68
(b
)
I z
F
K
Ψ =
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
g{i,Ψ
1
0.0
079
16.2
0.1
28
0.0
51
0.0
32
0.0
23
0.0
18
0.0
15
0.0
13
0.0
11
0.0
10
0.0
09
0.0
08
2
0.1
321
5.2
0.6
87
0.4
84
0.3
73
0.3
04
0.2
56
0.2
22
0.1
95
0.1
74
0.1
58
0.1
44
0.1
32
3
0.0
849
2.6
0.2
21
0.1
90
0.1
67
0.1
49
0.1
35
0.1
23
0.1
13
0.1
04
0.0
97
0.0
90
0.0
85
4
0.2
690
1.9
8
0.5
33
0.4
85
0.4
45
0.4
12
0.3
83
0.3
57
0.3
35
0.3
16
0.2
99
0.2
83
0.2
69
5
0.0
589
0.9
1
0.0
54
0.0
54
0.0
55
0.0
55
0.0
56
0.0
56
0.0
57
0.0
57
0.0
58
0.0
58
0.0
59
6
0.1
321
0.7
2
0.0
95
0.0
98
0.1
01
0.1
04
0.1
07
0.1
11
0.1
14
0.1
18
0.1
23
0.1
27
0.1
32
7
0.3
151
0.2
8
0.0
88
0.0
95
0.1
03
0.1
13
0.1
24
0.1
38
0.1
55
0.1
78
0.2
08
0.2
51
0.3
15
f{Ψ
}:
0.8
05
0.4
57
0.2
76
0.1
59
0.0
78
0.0
21
-0.0
18
-0.0
41
-0.0
49
-0.0
38
0.0
00
Th
e v
alu
es o
f f{
Ψ} a
re p
lott
ed o
n t
he
nex
t p
age,
wh
ere
it i
s o
bse
rved
th
at t
he
Rac
hfo
rd-R
ice
and
Alt
ern
ativ
e eq
uat
ion
s giv
e th
e sa
me
resu
lt o
f Ψ
= 0
.55
. H
ow
ever
, th
e al
tern
ativ
e eq
uat
ion
als
o
has
a t
riv
ial
roo
t at
Ψ =
1.0
. W
ith
a N
ewto
n p
roce
du
re,
the
alte
rnat
ive
equ
atio
n m
ay c
on
ver
ge
to
the
triv
ial
roo
t.
Th
eref
ore
, th
e R
ach
ford
-Ric
e eq
uat
ion
is
pre
ferr
ed b
ecau
se o
f it
s u
niq
uen
ess.
Ex
erci
se 4
.21
(co
nti
nu
ou
s)
An
aly
sis:
(
con
tin
ued
)
Ex
erci
se 4
.22
S
ub
ject
: E
qu
ilib
riu
m f
lash
of
a h
yd
roca
rbo
n m
ixtu
re.
Giv
en:
1
00
km
ole
s o
f 2
5 m
o1
% n
C4
, 4
0 m
ol%
nC
5,
an
d 3
5 m
ol%
nC
6 .
K
-val
ues
in
Fig
. 2
.8
Ass
um
pti
on
s:
Am
ou
nts
are
per
ho
ur.
Fin
d:
Pre
ssu
re a
nd
liq
uid
an
d v
apo
r co
mp
osi
tio
ns
for
equ
ilib
riu
m a
t 2
40
oF
to
rec
ov
er,
in t
he
liq
uid
ph
ase,
80
% o
f th
e n
C6 i
n t
he
feed
.
An
aly
sis:
F
or
80
% r
eco
ver
y o
f n
C6 ,
th
e li
qu
id p
rod
uct
mu
st c
on
tain
(0
.35
)(0
.80
)(1
00
) =
28
km
ole
/h o
f n
C6 .
M
ust
so
lve
by t
rial
an
d e
rro
r b
y a
ssu
min
g v
alu
es o
f p
ress
ure
to
ob
tain
th
e K
-
val
ues
fro
m F
ig.
2.8
. T
hen
so
lve
the
Rac
hfo
rd-R
ice
equ
atio
n (
Eq
. (3
), T
able
4.4
),
f
zK
K
ii
iiC
{}
ΨΨ
=−
+−
==�
1
11
01
��
��
for
Ψ =
V/F
b
y a
no
nli
nea
r so
lver
, su
ch a
s N
ewto
n's
met
ho
d.
C
om
pu
te V
fro
m E
q.
(4),
Tab
le
4.4
.
Th
en s
olv
e E
qs.
(5
) an
d (
6),
Tab
le 4
.4 f
or
the
equ
ilil
bri
um
vap
or
and
liq
uid
co
mp
osi
tio
ns.
So
lve
for
the
liq
uid
, L
, fr
om
Eq
. (7
).
Rep
eat
this
pro
ced
ure
un
til
28
km
ol/
h
of
nC
6 a
re f
ou
nd
in
the
equ
ilib
riu
m l
iqu
id a
s co
mp
ute
d f
rom
n
xL
LnC
nC
66
�
=,
no
tin
g t
hat
eac
h a
ssu
med
pre
ssu
re
req
uir
es a
n i
tera
tiv
e p
roce
du
re t
o s
olv
e fo
r Ψ
fro
m t
he
Rac
hfo
rd-R
ice
equ
atio
n.
Th
e ca
lcu
lati
on
s
are
sum
mar
ized
in
th
e fo
llo
win
g t
able
:
Ass
um
ed P
, p
sia
10
0
11
0
11
7
K-v
alu
es:
n
C4
2.4
0
2.3
0
2.2
5
n
C5
1.2
0
1.0
8
1.0
0
n
C6
0.5
3
0.5
0
0.4
8
V/F
0
.70
6
0.4
82
0
.33
5
L,
km
ol/
h
29
.4
51
.8
66
.5
x o
f n
C4
0.5
24
0
.46
1
0.4
24
nL o
f n
C4 ,
km
ol/
h
15
2
4
28
Th
eref
ore
, th
e co
nv
erg
ed p
ress
ure
is
11
7 p
sia.
T
he
equ
ilib
riu
m v
apo
r an
d l
iqu
id c
om
po
siti
on
s in
term
s o
f am
ou
nts
are
:
Co
mp
on
ent
Vap
or
flo
ws,
km
ol/
h
Liq
uid
flo
ws,
km
ol/
h
n
C4
13
1
2
n
C5
13
2
7
n
C6
7
28
.
Ex
erci
se 4
.23
S
ub
ject
: E
qu
ilib
riu
m f
lash
vap
ori
zati
on
of
a h
yd
roca
rbo
n m
ixtu
re.
Giv
en:
E
qu
imo
lar
mix
ture
of
C2,
C3,
nC
4,
and
nC
5.
K-v
alu
es f
rom
Fig
. 2
.8 a
nd
2.9
Fin
d:
Am
ou
nts
an
d c
om
po
siti
on
s o
f eq
uil
ibri
um
liq
uid
an
d v
apo
r at
15
0oF
an
d 2
05
psi
a.
Co
nd
itio
ns
of
T a
nd
P w
her
e 7
0%
of
C2
and
no
mo
re t
han
5%
of
nC
4 i
s in
th
e v
apo
r.
An
aly
sis:
T
ake
as a
bas
is,
a fe
ed o
f 1
00
lb
mo
l/h
. F
rom
Fig
. 2
.8,
at 1
50
oF
an
d 2
05
psi
a, t
he
K-
val
ues
are
as
giv
en i
n t
he
tab
le b
elo
w.
T
hen
so
lve
the
Rac
hfo
rd-R
ice
equ
atio
n (
Eq
. (3
), T
able
4.4
),
fz
K
K
ii
iiC
{}
ΨΨ
=−
+−
==�
1
11
01
��
��
for
Ψ =
V/F
b
y a
no
nli
nea
r so
lver
, su
ch a
s N
ewto
n's
met
ho
d.
C
om
pu
te V
fro
m E
q.
(4),
Tab
le
4.4
. T
hen
so
lve
Eq
s. (
5)
and
(6
), T
able
4.4
fo
r th
e eq
uil
ilb
riu
m v
apo
r an
d l
iqu
id c
om
po
siti
on
s.
Th
e ca
lcu
lati
on
s ar
e su
mm
ariz
ed i
n t
able
bel
ow
, w
hic
h a
lso
in
clu
des
oth
er c
on
dit
ion
s o
f
T a
nd
P t
o o
bta
in 7
0%
of
C2
and
no
mo
re t
han
5%
of
nC
4 i
n t
he
vap
or.
T
hu
s, w
e d
esir
e
(0.7
)(2
5)
= 1
7.5
lb
mo
l/h
of
C2 i
n t
he
vap
or
and
25
- 1
7.5
= 7
.5 l
bm
ol/
hr
of
C2 i
n t
he
liq
uid
. A
t
the
sam
e ti
me
we
des
ire
no
mo
re t
han
(0
.05
)(2
5)
= 1
.25
lb
mo
l/h
of
nC
4 i
n t
he
vap
or,
corr
esp
on
din
g t
o 2
5 -
1.2
5 =
23
.75
lb
mo
l/h
of
nC
4 i
n t
he
liq
uid
. I
n s
earc
hin
g f
or
thes
e
oth
er c
on
dit
ion
s, w
e n
ote
th
at a
t th
e b
ase
con
dit
ion
s, 7
5.8
% o
f th
e C
2 g
oes
to
th
e v
apo
r, w
hic
h i
s
ver
y c
lose
to
th
e d
esir
ed 7
0%
. B
ut
30
% o
f th
e n
C4
als
o g
oes
to
th
e v
apo
r, w
hic
h i
s m
uch
hig
her
than
th
e d
esir
ed 5
%.
Th
e re
lati
ve
vo
lati
lity
of
C2 t
o n
C4 a
t th
e b
ase
con
dit
ion
s is
:
αC
nC
C nC
CC
nC
nC
CC
nC
nC
24
2 4
22
44
22
44
,
/ /
()
/(
)
()
/(
)
(.
/.
)
(.
/.
).
==
==
=K K
yx
yx
nn
nn
VL
VL
19
06
0
75
17
57
39
Bu
t w
e n
eed
a r
elat
ive
vo
lati
lity
of:
αC
nC
CC
nC
nC
24
22
44
,
()
/(
)
()
/(
)
(.
/.
)
(.
/.
).
==
=n
n
nn
VL
VL
17
57
5
12
52
37
54
43
Fo
r id
eal
solu
tio
ns,
wh
ere
the
Rao
ult
's l
aw K
-val
ue
app
lies
, E
q.
(2-2
1)
com
bin
ed w
ith
Eq
. (3
in
Tab
le 2
.3,
giv
es r
elat
ive
vo
lati
lity
as
ind
epen
den
t o
f p
ress
ure
an
d e
qu
al t
o t
he
rati
o o
f v
apo
r
pre
ssu
res,
wh
ich
dep
end
on
ly o
n t
emp
erat
ure
. I
n g
ener
al,
as t
he
tem
per
atu
re i
s re
du
ced
, th
e
rela
tiv
e v
ola
tili
ty i
ncr
ease
s.
Ass
um
e th
at t
he
hyd
roca
rbo
n m
ixtu
re,
alth
ou
gh
no
t an
id
eal
solu
tio
n,
Ex
erci
se 4
.23
(co
nti
nu
ed)
A
na
lysi
s:
(co
nti
nu
ed)
foll
ow
s th
ese
sam
e tr
end
s.
Th
us,
to
in
crea
se t
he
rela
tiv
e v
ola
tili
ty,
the
pre
ssu
re h
as l
ittl
e ef
fect
.
We
mu
st d
ecre
ase
the
tem
per
atu
re t
o o
bta
in t
he
des
ired
rel
ativ
e v
ola
tili
ty,
and
th
en a
dju
st t
he
pre
ssu
re t
o o
bta
in t
he
req
uir
ed c
om
po
siti
on
s.
Th
e b
ase
case
an
d c
alcu
lati
on
s le
adin
g t
o t
he
des
ired
sep
arat
ion
are
su
mm
ariz
ed i
n t
he
foll
ow
ing t
able
:
B
ase
Cas
e
D
esir
ed C
ase
T,
oF
1
50
-7
0
-40
-4
0
P,
psi
a 2
05
1
4.7
1
4.7
1
6.4
K-v
alu
es:
C
2
4.1
4
.0
7.5
6
.7
C
3
1.5
0
.46
1
.11
1
.00
nC
4
0.5
6
0.0
55
0
.16
5
0.1
48
nC
5
0.2
15
0
.07
7
0.0
28
0
.02
5
α o
f C
2 t
o n
C4
7.3
7
3
45
4
5
% C
2 t
o v
apo
r 7
5.8
7
0
% n
C4 t
o v
apo
r 3
0
4.9
Th
us,
at
-40
oF
an
d 1
6.4
psi
a, t
he
des
ired
70
% o
f th
e et
han
e is
fo
un
d i
n t
he
vap
or
pro
du
ct,
wit
h
on
ly 5
% o
f th
e n
-bu
tan
e.
Th
e co
mp
osi
tio
ns
of
the
vap
or
and
liq
uid
pro
du
cts
for
the
bas
e ca
se a
nd
th
e d
esir
ed c
ase
are
as
foll
ow
s:
Bas
e C
ase:
Des
ired
Cas
e:
Co
mp
on
ent
υ,
lbm
ol/
h
y l,
lb
mo
l/h
x
υ,
lbm
ol/
h
y l,
lb
mo
l/h
x
C2
19
.0
0.4
4
6
.0
0.1
1
17
.5
0.6
9
7
.5
0.1
0
C3
13
.4
0.3
1
11
.6
0.2
0
6
.4
0.2
5
18
.6
0.2
5
nC
4
7
.5
0.1
7
17
.5
0.3
1
1.2
2
0.0
5
2
3.7
8
0.3
2
nC
5
3
.5
0.0
8
21
.5
0.3
8
0.2
2
0.0
1
2
4.7
8
0.3
3
T
ota
l:
43
.4
1.0
0
56
.6
1.0
0
25
.34
1
.00
7
4.6
6
1.0
0
Ex
erci
se 4
.24
S
ub
ject
:
Co
oli
ng o
f a
reac
tor
effl
uen
t w
ith
rec
ycl
e li
qu
id f
rom
a p
arti
al c
on
den
sati
on
.
Giv
en:
R
eact
or
effl
uen
t te
mp
erat
ure
of
10
00
oF
an
d c
om
po
siti
on
in
lb
mo
l/h
of
20
00
H2,
20
00
CH
4,
50
0 b
enze
ne,
an
d 1
00
to
luen
e.
Par
tial
co
nd
ensa
tio
n c
on
dit
ion
s o
r 1
00
oF
an
d 5
00
psi
a, a
nd
com
po
nen
t K
-val
ues
at
thes
e co
nd
itio
ns.
T
wo
hea
t ex
chan
ger
s in
a r
ecycl
e lo
op
.
Fin
d:
(a)
C
om
po
siti
on
an
d f
low
rat
e o
f v
apo
r le
avin
g f
lash
dru
m i
n F
ig.
4.3
8.
(b
) P
roo
f th
at v
apo
r fl
ow
rat
e is
in
dep
end
ent
of
qu
ench
rat
e.
An
aly
sis:
(
a)
Ass
um
e th
at v
apo
r ra
te i
s in
dep
end
ent
of
qu
ench
rat
e.
Th
eref
ore
, co
nd
uct
th
e
flas
h c
alcu
lati
on
on
ju
st t
he
reac
tor
effl
uen
t at
th
e fl
ash
dru
m c
on
dit
ion
s o
f te
mp
erat
ure
an
d
pre
ssu
re.
Use
th
e R
ach
ford
-Ric
e eq
uat
ion
s (E
qs.
(3
) an
d (
6),
Tab
le 4
.4):
fz
K
K
ii
iiC
{}
ΨΨ
=−
+−
==�
1
11
01
��
��
(1
)
yz
K Ki
ii i
=+
−1
1��
(2
)
No
nli
nea
r E
q.
(1)
is s
olv
ed f
or
Ψ =
V/F
, f
oll
ow
ed b
y c
alcu
lati
on
of
V =
ΨF
, an
d t
hen
calc
ula
tio
ns
of
vap
or
mo
le f
ract
ion
s fr
om
Eq
. (2
).
Th
e giv
en i
np
ut
for
Eq
. (1
) is
:
Co
mp
on
ent
f, l
bm
ol/
h
z i
Ki
Hyd
rogen
2
,00
0
0.4
34
8
80
Met
han
e 2
,00
0
0.4
34
8
10
Ben
zen
e
50
0
0.1
08
7
0.0
10
To
luen
e
10
0
0.0
21
7
0.0
04
On
e m
eth
od
fo
r so
lvin
g E
q.
(1)
is t
o u
se a
sp
read
shee
t to
mak
e a
plo
t o
f f{
Ψ} v
s. Ψ
in
incr
emen
ts o
f 0
.1 f
rom
0.0
to
1.0
. T
hen
, u
se s
mal
ler
incr
emen
ts i
n Ψ
in
th
e v
icin
ity o
f f
{Ψ
}=
0
to o
bta
in t
he
solu
tio
n.
Th
e re
sult
s ar
e sh
ow
n i
n t
he
two
fig
ure
s o
n t
he
nex
t p
age.
T
he
con
ver
ged
solu
tio
n i
s
Ψ =
0.8
69
7.
Th
eref
ore
, V
= 0
.86
97
(4,6
00
) =
4,0
00
.6 l
bm
ol/
h.
Th
e co
mp
osi
tio
n o
f th
e
equ
ilib
riu
m v
apo
r fr
om
Eq
. (2
) is
as
foll
ow
s:
Co
mp
on
ent
z i
y i
xi
Hyd
rogen
0
.43
48
0
.49
90
0
.00
62
Met
han
e 0
.43
48
0
.49
25
0
.04
93
Ben
zen
e 0
.10
87
0
.00
78
0
.78
20
To
luen
e 0
.02
17
0
.00
07
0
.16
25
Ex
erci
se 4
.24
(c
on
tin
ued
)
A
na
lysi
s:
(a)
(c
on
tin
ued
)
Ex
erci
se 4
.24
(c
on
tin
ued
)
A
na
lysi
s:
(b)
Wh
en t
he
flas
h c
on
dit
ion
s o
f te
mp
erat
ure
an
d p
ress
ure
are
fix
ed,
the
com
po
siti
on
s o
f th
e
equ
ilib
riu
m v
apo
r an
d l
iqu
id a
re i
nd
epen
den
t o
f an
y r
ecycl
e o
f eq
uil
ibri
um
liq
uid
or
vap
or.
T
o
pro
ve
this
, d
raw
a m
ater
ial
bal
ance
en
vel
op
e ar
ou
nd
th
e sy
stem
in
Fig
. 4
.38
as
sho
wn
bel
ow
.
No
w,
the
flas
h e
qu
atio
ns
are
the
sam
e as
in
Tab
le 4
.3,
exce
pt
for
the
ener
gy b
alan
ce,
Eq
. (6
).
Bu
t, t
hat
eq
uat
ion
is
on
ly s
olv
ed a
fter
all
of
the
oth
er e
qu
atio
ns
are
solv
ed.
Th
us,
th
e re
sult
s fo
r
the
com
po
siti
on
s o
f th
e n
et v
apo
r an
d l
iqu
id p
rod
uct
s ar
e th
e sa
me
as w
hen
th
ere
is n
o r
ecycl
e.
Ex
erci
se 4
.25
S
ub
ject
:
Par
tial
co
nd
ensa
tio
n o
f a
gas
mix
ture
at
12
0oF
an
d 3
00
psi
a.
Giv
en:
G
as a
t 3
92
oF
an
d 3
15
psi
a, w
ith
a c
om
po
siti
on
in
km
ol/
h o
f 7
2.5
3 N
2,
7.9
8 H
2,
0.1
3
ben
zen
e, a
nd
15
0 c
ycl
oh
exan
e.
Th
e gas
is
coo
led
an
d p
arti
al c
on
den
sed
to
12
0oF
an
d 3
00
psi
a,
foll
ow
ed b
y p
has
e se
par
atio
n.
Fin
d:
E
qu
ilib
riu
m v
apo
r an
d l
iqu
id f
low
rat
es a
nd
co
mp
osi
tio
ns.
An
aly
sis:
T
he
flas
h c
alcu
lati
on
s ar
e m
ade
con
ven
ien
tly w
ith
a p
roce
ss s
imu
lato
r, u
sin
g a
n
app
rop
riat
e K
-val
ue
corr
elat
ion
. T
he
foll
ow
ing r
esu
lts
wer
e o
bta
ined
wit
h C
HE
MC
AD
, u
sin
g
the
Ch
ao-S
ead
er,
Gra
yso
n-S
tree
d (
CS
GS
) m
eth
od
fo
r K
-val
ues
.
Co
mp
on
ent
CS
GS
K
i f i
, k
mo
l/h
υ υυυ
i , k
mo
l/h
l i
, k
mo
l/h
Hyd
rogen
7
9.7
72
.53
7
0.8
2
1.7
1
Nit
rogen
7
.54
7
.98
6.3
6
1.6
2
Ben
zen
e 0
.02
4
0.1
3
0
.00
16
0
.12
84
Cycl
oh
exan
e 0
.02
2
15
0.0
0
1
.67
1
48
.33
Ex
erci
se 4
.26
S
ub
ject
:
Rap
id d
eter
min
atio
n o
f p
has
e co
nd
itio
n w
ith
ou
t m
akin
g a
fla
sh c
alcu
lati
on
.
Giv
en:
A
hyd
roca
rbo
n m
ixtu
re a
t 2
00
oF
an
d 2
00
psi
a, w
ith
a c
om
po
siti
on
in
lb
mo
l/h
of
12
5 C
3,
20
0 n
C4,
and
17
5 n
C5,
and
K-v
alu
es a
t th
ese
con
dit
ion
s.
Fin
d:
Ph
ase(
s) p
rese
nt
wit
ho
ut
mak
ing a
fla
sh c
on
dit
ion
.
An
aly
sis:
F
rom
Eq
. (4
-12
), h
ave
a su
bco
ole
d l
iqu
id i
f
zK
ii
iC
<=�
11
.
F
rom
Eq
. (4
-13
), h
ave
a su
per
hea
ted
vap
or
if
z K
i iiC
<=�
11
.
Co
mp
on
ent
f i
z i
Ki
z iK
i z i
/Ki
C3
12
5
0.2
5
2.0
56
0
.51
4
0.1
22
nC
4
20
0
0.4
0
0.9
25
0
.37
0
0.4
32
nC
5
17
5
0.3
5
0.5
20
0
.18
2
0.6
73
T
ota
l:
50
0
1.0
0
1
.06
6 >
1
1.2
27
> 1
Th
eref
ore
str
eam
is
par
tial
ly v
apo
rize
d.
Bo
th v
apo
r an
d l
iqu
id p
has
es p
rese
nt.
Ex
erci
se 4
.27
S
ub
ject
:
Det
erm
inat
ion
of
refl
ux
-dru
m p
ress
ure
fo
r a
spec
ifie
d t
emp
erat
ure
an
d t
ota
l d
isti
llat
e
(vap
or
and
liq
uid
ph
ases
) co
mp
osi
tio
n
Giv
en:
O
ver
hea
d p
arti
al c
on
den
sin
g s
yst
em o
f a
dis
till
atio
n c
olu
mn
th
at p
rod
uce
s v
apo
r
dis
till
ate,
liq
uid
dis
till
ate,
an
d l
iqu
id r
eflu
x.
Of
the
tota
l d
isti
llat
e, 1
0 m
ol%
is
vap
or.
R
eflu
x
dru
m t
emp
erat
ure
is
10
0oF
, an
d c
om
po
siti
on
of
tota
l d
isti
llat
e in
mo
le f
ract
ion
s is
0.1
0 C
2,
0.2
0
C3,
and
0.7
0 n
C4.
Ref
lux
pre
ssu
re i
s n
ot
giv
en,
bu
t K
-val
ues
at
10
0oF
an
d 2
00
psi
a ar
e giv
en.
Ass
um
pti
on
s:
K-v
alu
es a
re i
nv
erse
ly p
rop
ort
ion
al t
o p
ress
ure
.
Fin
d:
Pre
ssu
re i
n t
he
refl
ux
dru
m.
An
aly
sis:
A
s sh
ow
n i
n E
xer
cise
4.2
4,
the
com
po
siti
on
s o
f n
et e
qu
ilib
riu
m v
apo
r an
d l
iqu
id a
re
ind
epen
den
t o
f re
cycl
e o
r, i
n t
his
cas
e, r
eflu
x.
Th
eref
ore
, th
e fl
ash
eq
uat
ion
s ca
n b
e ap
pli
ed
usi
ng t
he
tota
l d
isti
llat
e co
mp
osi
tio
n a
s th
e fe
ed c
om
po
siti
on
. T
her
efo
re,
Ψ =
V/F
= 0
.10
. T
he
K-
val
ues
are
giv
en b
y:
KP
KP
KP
CC
nC
23
42
.72
00
,
,
=� ���
=� ���
=� ���
09
52
00
03
42
00
..
Su
bst
itu
tin
g t
hes
e eq
uat
ion
s in
to E
q.
(3),
Tab
le 4
.4,
fP
P
P
P
P
P
P
{}
..
..
..
..
..
..
=
−� ���
� ��� ��
+� ��� −
� ��� ��+
−� ���
� ��� ��
+� ��� −
� ��� ��+
−� ���
� ��� ��
+� ��� −
� ��� ��=
01
12
72
00
10
12
72
00
1
01
10
95
20
0
10
10
95
20
01
01
10
34
20
0
10
10
34
20
01
0
(1)
Eq
. (1
) is
a n
on
lin
ear
equ
atio
n t
hat
can
be
solv
ed b
y v
ario
us
mea
ns.
U
sin
g a
sp
read
shee
t, i
n a
man
ner
sim
ilar
to
th
at u
sed
to
so
lve
Ex
erci
se 4
.24
, w
e o
bta
in P
= 1
26
psi
a.
Ex
erci
se 4
.28
S
ub
ject
:
Co
mp
aris
on
of
flas
h c
alcu
lati
on
s u
sin
g t
hre
e d
iffe
ren
t K
-val
ue
corr
elat
ion
s.
Giv
en:
A
str
eam
at
7.2
oC
an
d 2
,62
0 k
Pa
wit
h t
he
ov
eral
l co
mp
osi
tio
n g
iven
bel
ow
.
Fin
d:
Ph
ase
con
dit
ion
s
An
aly
sis:
U
sin
g t
he
CH
EM
CA
D p
roce
ss s
imu
lato
r, t
he
foll
ow
ing r
esu
lts
are
ob
tain
ed u
sin
g t
he
So
ave-
Red
lich
-Kw
on
g (
SR
K),
Pen
g-R
ob
inso
n (
PR
), a
nd
Ben
edic
t-W
ebb
-Ru
bin
-Sta
rlin
g
(BW
RS
) co
rrel
atio
ns:
K-v
alu
es:
Co
mp
on
ent
SR
K
PR
B
WR
S
N2
17
.5
17
.6
16
.3
C1
5.7
3
5.7
1
6.0
0
C2
1.0
7
1.1
2
0.9
9
C3
0
.32
7
0
.33
7
0
.29
2
nC
4
0
.09
8
0
.10
2
0
.08
7
nC
5
0
.03
6
0
.03
2
0
.02
9
nC
6
0.0
09
6
0.0
11
0
0.0
07
1
Th
e K
-val
ues
fo
r th
e S
RK
an
d P
R c
orr
elat
ion
s ar
e in
rea
son
ably
go
od
agre
emen
t, d
evia
tin
g f
rom
each
oth
er b
y l
ess
than
15
%.
Ex
cep
t fo
r C
1,
the
BW
RS
co
rrel
atio
n p
red
icts
lo
wer
val
ues
, w
ith
the
big
ges
t d
evia
tio
n f
or
nC
6.
Pro
du
ct c
om
po
siti
on
s:
S
RK
:
PR
:
B
WR
:
Co
mp
on
en
t
f, k
mo
l/h
υ υυυ
,
km
ol/
h
l, k
mo
l/h
υ υυυ
,
km
ol/
h
l, k
mo
l/h
υ υυυ
,
km
ol/
h
l, k
mo
l/h
N2
1.0
0.7
0
0.3
0
0
.69
0
.31
0.6
7
0.3
3
C1
12
4.0
5
2.9
2
7
1.0
8
52
.06
71
.94
5
3.0
4
7
0.9
6
C2
8
7.6
1
1.1
3
7
6.4
6
10
.45
77
.15
9.6
3
7
7.9
7
C3
16
1.6
6.8
1
15
4.7
9
6
.42
1
55
.18
5.6
7
15
5.9
3
nC
4
17
6.2
2.3
1
17
3.8
9
2
.16
1
74
.04
1.8
8
17
4.3
2
nC
5
5
8.5
0.2
5
5
8.2
5
0
.26
58
.24
0.2
1
5
8.2
9
nC
6
3
3.7
0.0
5
3
3.6
5
0
.04
33
.66
0.0
3
3
3.6
7
To
tal:
6
42
.60
7
4.1
7
56
8.4
3
72
.08
5
70
.52
7
1.1
3
57
1.4
7
All
th
ree
corr
elat
ion
s p
red
ict
abo
ut
the
sam
e V
/F r
atio
, w
hic
h r
anges
fro
m 0
.11
07
to
0.1
15
4.
Ex
erci
se 4
.29
S
ub
ject
:
Eq
uil
ibri
um
fla
sh c
alcu
lati
on
s at
dif
fere
nt
tem
per
atu
res
and
pre
ssu
res
Giv
en:
M
ixtu
re o
f 1
00
km
ol
of
60
mo
l% b
enze
ne
(A),
25
mo
l% t
olu
ene
(B),
an
d 1
5 m
ol%
o-
xyle
ne
(C).
S
ou
rces
of
vap
or
pre
ssu
re d
ata.
Ass
um
pti
on
s:
Idea
l so
luti
on
s u
sin
g v
apo
r p
ress
ure
wit
h R
aou
lt's
law
.
Fin
d:
Am
ou
nts
an
d c
om
po
siti
on
s o
f v
apo
r an
d l
iqu
id p
rod
uct
s at
:
(a
) 1
00
oC
an
d 1
atm
.
(b
) 1
00
oC
an
d 2
atm
.
(c
) 1
05
oC
an
d 0
.1 a
tm.
(d
) 1
50
oC
an
d 1
atm
.
An
aly
sis:
I
nst
ead
of
Fig
ure
2.4
fo
r th
e v
apo
r p
ress
ure
s o
f b
enze
ne
and
to
luen
e an
d t
hre
e v
apo
r-
pre
ssu
re d
ata
po
ints
fo
r o
-xyle
ne,
use
th
e b
uil
t-in
vap
or
pre
ssu
re d
ata
in t
he
CH
EM
CA
D p
roce
ss
sim
ula
tor
wit
h i
dea
l K
-val
ues
. T
he
resu
lts
are
as f
oll
ow
s:
Ca
se
(a)
10
0oC
,
1 a
tm
(b)
10
0oC
,
2 a
tm.
(c)1
05
oC
,
0.1
atm
.
(d)
15
0oC
,
1 a
tm
Vap
or,
km
ol
67
.64
0
1
00
1
00
Liq
uid
, k
mo
l 3
2.3
6
10
0
0
0
Vap
or
mo
l fr
ac:
Ben
zen
e 0
.69
8
0
.60
0
.60
To
luen
e 0
.22
4
0
.25
0
.25
o
-Xyle
ne
0.0
78
0.1
5
0.1
5
Liq
uid
mo
l fr
ac:
Ben
zen
e 0
.39
5
0.6
0
To
luen
e 0
.30
5
0.2
5
o
-Xyle
ne
0.3
00
0
.15
On
ly i
n t
he
Cas
e (a
), a
re t
wo
ph
ases
fo
rmed
. A
t 1
atm
, th
e b
ub
ble
po
int
is 9
1.3
oC
an
d t
he
dew
po
int
is 1
07
.5oC
.
Ex
erci
se 4
.30
S
ub
ject
:
Pro
ve
that
, at
eq
uil
ibri
um
, v
apo
r is
at
its
dew
po
int
and
liq
uid
is
at i
ts b
ub
ble
po
int.
An
aly
sis:
A
fter
eq
uil
ibri
um
is
ach
iev
ed,
sep
arat
e th
e v
apo
r fr
om
th
e li
qu
id a
nd
an
alyze
the
sep
arat
e p
has
es.
Fo
r th
e li
qu
id:
Ap
ply
Eq
. (5
), T
able
4.4
,
xz K
ii
i
=+
−1
1��
(1
)
At
the
bu
bb
le p
oin
t, Ψ
= V
/F =
0 a
nd
, th
eref
ore
, fr
om
Eq
. (1
),
x i =
zi .
A
lso
, th
en,
Ki x
i = K
i zi
= y
i an
d,
ther
efo
re,
Kx
Kz
yi
i
iC
ii
iC
i
iC
==
==
==
��
�1
11
1,
wh
ich
is
the
bu
bb
le-p
oin
t eq
uat
ion
, E
q.
(4-1
2).
Fo
r th
e v
apo
r:
Ap
ply
Eq
. (6
), T
able
4.4
,
y
Kz K
ii
i i
=+
−1
1��
(2
)
At
the
dew
po
int,
Ψ =
V/F
= 1
an
d,
ther
efo
re,
fro
m E
q.
(2),
y i
= z
i .
Als
o,
then
, x i
= y
i /K
i =
zi /
Ki
and
, th
eref
ore
, y K
z Kx
i iiC
i iiC
i
iC
==
==
==
��
�1
11
1,
wh
ich
is
the
bu
bb
le-p
oin
t eq
uat
ion
, E
q.
(4-1
2).
Ex
erci
se 4
.31
S
ub
ject
:
Bu
bb
le-p
oin
t te
mp
erat
ure
of
feed
to
a d
isti
llat
ion
co
lum
n.
Giv
en:
Fee
d a
t 1
.72
MP
a (2
50
psi
a) w
ith
a c
om
po
siti
on
in
km
ol/
h b
elo
w.
K-v
alu
es i
n F
ig.
2.8
.
Fin
d:
Bu
bb
le-p
oin
t te
mp
erat
ure
.
An
aly
sis:
I
tera
te o
n t
emp
erat
ure
un
til
the
bu
bb
le-p
oin
t eq
uat
ion
, E
q.
(4-1
2),
is
sati
sfie
d,
Kz
ii
iC
==�
11
(1
)
Fo
r th
e fi
rst
gu
ess,
tak
e th
e te
mp
erat
ure
th
at g
ives
th
e K
-val
ue
for
nC
4 =
1.0
, th
at i
s 2
25
oF
. T
his
resu
lt a
nd
on
e fo
r 2
00
oF
is
as f
oll
ow
s:
T
= 2
25
oF
T
= 2
00
oF
Co
mp
on
ent
f i ,
km
ol/
h
z i
Ki
Kiz
i K
i K
izi
C2
1.5
0
.03
4
.8
0.1
44
4
.3
0.1
29
C3
10
.0
0.2
0
2.1
0
.42
0
1.9
0
.38
0
nC
4
18
.5
0.3
6
1.0
0
.36
0
0.8
1
0.2
92
nC
5
17
.5
0.3
4
0.4
4
0.1
50
0
.34
0
.11
6
nC
6
3.5
0
.07
0
.21
0
.01
5
0.1
5
0.0
11
Su
m:
51
.0
1.0
0
1
.08
9
0
.92
8
By l
inea
r in
terp
ola
tio
n,
T =
21
1oF
fo
r E
q.
(1)
to b
e sa
tisf
ied
.
Ex
erci
se 4
.32
S
ub
ject
:
Bu
bb
le a
nd
dew
po
int
pre
ssu
res
of
bin
ary m
ixtu
re a
t co
nst
ant
tem
per
atu
re.
Giv
en:
M
ixtu
re o
f 5
0 m
ol%
ben
zen
e (A
) an
d 5
0 m
ol%
to
luen
e (B
) at
90
oC
(1
94
oF
).
Vap
or
pre
ssu
res
fro
m F
ig.
2.4
(1
9.5
psi
a fo
r A
an
d 7
.9 p
sia
for
B).
Ass
um
pti
on
s:
Rao
ult
's l
aw f
or
K-v
alu
es.
Fin
d:
B
ub
ble
an
d d
ew p
oin
t p
ress
ure
s.
An
aly
sis:
S
ub
stit
uti
on
of
Rao
ult
's l
aw,
Eq
. (3
) in
Tab
le 2
.3,
into
Eq
s. (
4-1
2)
and
(4
-13
) fo
r th
e
bu
bb
le a
nd
dew
po
ints
, re
spec
tiv
ely,
giv
es,
Bu
bb
le p
oin
t:
K
zP
z
PP
zP
ii
iC
i
s
i
iC
is
i=
==
==
��
�1
1
10.
or
i=
1
C
(1
)
Dew
po
int:
z K
zP
P
z PP
i iiC
i i
s
iC
i is=
==
==
��
�1
1
10
1.
o
r
i=1
C
(2
)
Eq
. (1
) giv
es 1
3.7
0 p
sia
for
the
bu
bb
le p
oin
t.
E
q.
(2)
giv
es 1
5.8
psi
a fo
r th
e d
ew p
oin
t.
Ex
erci
se 4
.33
S
ub
ject
:
Bu
bb
le p
oin
t, d
ew p
oin
t, a
nd
fla
sh o
f a
wat
er (
W)
- ac
etic
aci
d (
A)
mix
ture
.
Giv
en:
E
qu
imo
lar
mix
ture
of
W a
nd
A a
t 1
atm
. C
orr
elat
ion
s o
f li
qu
id-p
has
e ac
tiv
ity
coef
fici
ents
fo
r W
an
d A
as
a fu
nct
ion
of
liq
uid
-ph
ase
mo
le f
ract
ion
s an
d t
emp
erat
ure
:
Ass
um
pti
on
s:
Mo
dif
ied
Rao
ult
's l
aw,
Eq
. (4
), T
able
2.3
ap
pli
es.
Fin
d:
Dew
po
int,
bu
bb
le
po
int,
an
d e
qu
ilib
riu
m v
apo
r an
d l
iqu
id a
t a
tem
per
atu
re h
alfw
ay
bet
wee
n t
he
bu
bb
le a
nd
dew
po
ints
.
An
aly
sis:
Th
e R
ach
ford
-Ric
e fl
ash
eq
uat
ion
s ca
n b
e u
sed
fro
m T
able
4.4
:
fz
K
K
ii
iiC
{}
ΨΨ
=−
+−
==�
1
11
01
��
��
(1
)
yz
K Ki
ii i
=+
−1
1��
(2
)
xz K
ii
i
=+
−1
1��
(3
)
wh
ere,
zW
= 0
.5 a
nd
zA =
0.5
an
d t
he
mo
dif
ied
Rao
ult
's l
aw i
s:
KP P
iiL
is
=γ
(4
)
An
toin
e v
apo
r p
ress
ure
eq
uat
ion
s ar
e giv
en i
n P
erry
's H
and
bo
ok
fo
r w
ater
an
d a
ceti
c ac
id:
log
..
()
.
log
..
()
.
PT
C
PT
C
s
o
s
o
W A
(5
)
(6
)
=−
+
=−
+
80
71
31
17
30
63
23
34
26
80
21
00
19
36
01
25
84
51
Th
e eq
uat
ion
s fo
r th
e li
qu
id-p
has
e ac
tiv
ity c
oef
fici
ents
, giv
en i
n t
he
Ch
emic
al E
ngin
eeri
ng
Sci
ence
art
icle
of
19
67
by S
ebas
tian
i an
d L
acq
uan
iti,
are
in
corr
ect.
T
hey a
re o
f th
e R
edli
ch-
Kis
ter
form
(se
e W
alas
, S
. M
., "
Ph
ase
Eq
uil
ibri
a in
Ch
emic
al E
ngin
eeri
ng
", B
utt
erw
ort
h,
19
85
,
pag
e 1
84
) an
d s
ho
uld
be:
log
log
γ γ
WA
WW
AW
AW
WW
AW
(7
)
(8
)
=+
−+
−−
=+
−+
−−
xB
Cx
Cx
xx
xB
Cx
Cx
xx
2 2
41
61
43
65
���
���
���
���
Ex
erci
se 4
.33
(c
on
tin
ued
)
A
na
lysi
s:
(co
nti
nu
ed)
wh
ere,
K)
(9
)
K)
(1
0)
(11
)
AT
BT
C
=+
=−
=
01
18
26
42
4
01
73
54
32
7
01
08
1
.. (
.. (
.
Sin
ce P
= 1
atm
an
d t
he
no
rmal
bo
ilin
g p
oin
ts o
f w
ater
an
d a
ceti
c ac
id a
re 1
00
oC
an
d 1
18
.1oC
,
resp
ecti
vel
y,
it m
igh
t b
e ex
pec
ted
th
at t
he
dew
an
d b
ub
ble
po
int
of
the
mix
ture
wo
uld
be
in t
he
vic
init
y o
f 1
00
oC
, u
nle
ss t
he
liq
uid
-ph
ase
acti
vit
y c
oef
fici
ents
are
mu
ch d
iffe
ren
t fr
om
1.
To
chec
k t
his
, a
ctiv
ity c
oef
fici
ents
are
co
mp
ute
d f
rom
Eq
s. (
7)
and
(8
) w
ith
a s
pre
ad s
hee
t at
10
0oC
,
wit
h t
he
foll
ow
ing r
esu
lt a
s a
plo
t.
It i
s se
en t
hat
in
th
e v
icin
ity o
f m
ole
fra
ctio
ns
equ
al t
o 0
.5,
the
coef
fici
ents
are
no
t la
rge,
bu
t ar
e ab
ou
t 1
.2.
Ex
erci
se 4
.33
(c
on
tin
ued
)
A
na
lysi
s:
(co
nti
nu
ed)
A
t th
e b
ub
ble
po
int,
Ψ =
V/F
= 0
, an
d E
q.
(1),
co
mb
ined
wit
h (
4),
bec
om
es:
fT
zP
T
Pz
PT
P
ss
{}
{}
{}
=−� ��
� +−� ��
� =
WW
WA
AA
(1
2)
11
0γ
γ
Als
o,
at t
he
bu
bb
le p
oin
t, x
i = z
i = 0
.5.
Th
en,
the
on
ly u
nk
no
wn
in
Eq
. (1
2)
is T
.
So
lvin
g n
on
lin
ear
Eq
. (1
2),
wit
h E
qs.
(5
) to
(1
1),
by t
rial
an
d e
rro
r w
ith
a s
pre
adsh
eet,
sta
rtin
g
fro
m a
gu
ess
of
T =
10
0oC
, q
uic
kly
lea
ds
to a
bu
bb
le-p
oin
t te
mp
erat
ure
of
10
1.6
oC
. T
he
com
po
siti
on
of
the
vap
or
bu
bb
le i
s o
bta
ined
fro
m E
q.
(2),
wh
ich
at
the
bu
bb
le p
oin
t re
du
ces
to y
i
= x
iKi =
ziK
i..
Th
e K
-val
ues
at
the
bu
bb
le p
oin
t ar
e co
mp
ute
d t
o b
e K
W =
1.3
64
an
d K
A =
0.6
36
,
giv
ing y
W =
0.6
82
an
d y
A =
0.3
18
.
At
the
dew
po
int,
Ψ =
V/F
=1
, an
d E
q.
(1),
co
mb
ined
wit
h (
4),
bec
om
es:
f{x
W,
xW
, T
} =
zP
xx
TP
Tz
P
xx
TP
Ts
sW
WW
AW
A
AW
AA
γγ
{,
,}
{}
{,
,}
{}
−� ��
� +−
� ���
=1
10
wh
ere
bec
ause
yi =
zi =
0.5
, T
, x
W ,
an
d x
A =
(1
- x
W)
are
left
as
un
kn
ow
ns.
T
he
liq
uid
ph
ase
mo
le f
ract
ion
s ar
e fr
om
Eq
. (3
), x
i =
zi /
Ki .
So
lvin
g t
hes
e eq
uat
ion
s b
y t
rial
an
d e
rro
r w
ith
a
spre
ad s
hee
t, s
tart
ing f
rom
T =
10
5oC
, x W
= 0
.4 a
nd
xA =
0.6
, q
uic
kly
lea
ds
to a
dew
-po
int
tem
per
atu
re o
f 1
05
.8oC
. T
he
K-v
alu
es a
t th
e d
ew p
oin
t ar
e co
mp
ute
d t
o b
e K
W =
1.5
78
an
d K
A =
0.7
32
, w
ith
xW
= 0
.31
69
an
d x
A =
0.6
83
2.
Th
e eq
uil
ibri
um
fla
sh c
alcu
lati
on
is
carr
ied
ou
t at
T =
(1
01
.6 +
10
5.8
)/2
= 1
03
.7oC
. I
n
this
cas
e, t
he
val
ues
of
Ψ,
x W,
and
xA
are
co
mp
ute
d f
rom
Eq
s. (
1)
and
(3
), w
her
e th
e v
apo
r
pre
ssu
res
are
com
pu
ted
fro
m E
qs.
(5
) an
d (
6)
to b
e 8
67
to
rr f
or
W a
nd
47
3 f
or
A.
Val
ues
of
yW
and
yA a
re o
bta
ined
fro
m E
q.
(2).
U
sin
g,
agai
n,
a sp
read
shee
t w
ith
a t
rial
an
d e
rro
r p
roce
du
re,
the
foll
ow
ing r
esu
lt i
s q
uic
kly
ob
tain
ed:
V/F
= 0
.49
x W
= 0
.41
00
x
A =
0.5
90
0
y W =
0.5
93
7
yA =
0.4
06
3
Ex
erci
se 4
.34
S
ub
ject
:
Bu
bb
le p
oin
t, d
ew p
oin
t, a
nd
fla
sh o
f a
tolu
ene
(1)
- n
-bu
tan
ol
(2)
mix
ture
.
Giv
en:
F
eed
of
z 1 =
0.4
an
d z
2 =
0.6
at
1 a
tm.
Liq
uid
-ph
ase
acti
vit
y c
oef
fici
ents
fo
r 1
an
d 2
as
a
fun
ctio
n o
f li
qu
id-p
has
e m
ole
fra
ctio
ns
fro
m t
he
van
Laa
r eq
uat
ion
s.
Ass
um
pti
on
s:
Mo
dif
ied
Rao
ult
's l
aw,
Eq
. (2
-72
) ap
pli
es.
Fin
d:
Dew
po
int,
bu
bb
le
po
int,
an
d e
qu
ilib
riu
m v
apo
r an
d l
iqu
id a
t a
tem
per
atu
re h
alfw
ay
bet
wee
n t
he
bu
bb
le a
nd
dew
po
ints
.
An
aly
sis:
Th
e R
ach
ford
-Ric
e fl
ash
eq
uat
ion
s ca
n b
e u
sed
fro
m T
able
4.4
:
fz
K
K
ii
iiC
{}
ΨΨ
=−
+−
==�
1
11
01
��
��
(1
)
yz
K Ki
ii i
=+
−1
1��
(2
)
xz K
ii
i
=+
−1
1��
(3
)
Th
e m
od
ifie
d R
aou
lt's
law
is:
KP P
iiL
is
=γ
(4
)
An
toin
e v
apo
r p
ress
ure
(in
to
rr)
equ
atio
ns
are
ob
tain
ed b
y f
itti
ng t
he
vap
or
pre
ssu
re d
ata
for
tolu
ene
that
are
giv
en i
n E
xer
cise
4.8
an
d f
rom
Per
ry's
Han
db
oo
k f
or
n-b
uta
no
l:
PT
C
PT
C
s
o
s
o
1
2
(5
)
(6
)
=−
+
� ��� ��
=−
+
exp
..
()
.
log
..
()
.
17
27
41
38
96
3
25
56
7
73
63
66
13
05
19
8
17
34
27
Th
e v
an L
aar
equ
atio
ns,
Tab
le 2
.9,
wit
h t
he
giv
en c
on
stan
ts a
re:
ln. . .
ln. . .
γ γ
1 2
(7
)
(8
)
=
+� ��
� ��
=
+� ��
� ��
08
55
10
85
5
13
06
13
06
11
30
6
08
55
1 2 2 1
x x x x
Ex
erci
se 4
.34
(c
on
tin
ued
)
A
na
lysi
s:
(co
nti
nu
ed)
Sin
ce P
= 1
atm
an
d t
he
no
rmal
bo
ilin
g p
oin
ts o
f to
luen
e an
d n
-bu
tan
ol
are
11
0.8
oC
an
d
11
7oC
, re
spec
tiv
ely,
it m
igh
t b
e ex
pec
ted
th
at t
he
dew
an
d b
ub
ble
po
int
of
the
mix
ture
wo
uld
be
in t
he
vic
init
y o
f 1
10
oC
, u
nle
ss t
he
liq
uid
-ph
ase
acti
vit
y c
oef
fici
ents
are
mu
ch d
iffe
ren
t fr
om
1.
To
ch
eck
th
is,
act
ivit
y c
oef
fici
ents
are
co
mp
ute
d f
rom
Eq
s. (
7)
and
(8
), w
ith
a s
pre
ad s
hee
t, w
ith
the
foll
ow
ing r
esu
lt a
s a
plo
t.
It i
s se
en t
hat
in
th
e v
icin
ity o
f m
ole
fra
ctio
ns
equ
al t
o 0
.5,
the
coef
fici
ents
are
no
t la
rge,
bu
t ar
e ab
ou
t 1
.3.
At
the
bu
bb
le p
oin
t, Ψ
= V
/F =
0,
and
Eq
. (1
), c
om
bin
ed w
ith
(4
), b
eco
mes
:
fT
zP
T
Pz
PT
P
ss
{}
{}
{}
=−� ��
� +−� ��
� =
11
12
22
(9
)1
10
γγ
Ex
erci
se 4
.34
(c
on
tin
ued
)
An
aly
sis:
(
con
tin
ued
)
Als
o,
at t
he
bu
bb
le p
oin
t, x
1 =
z1 =
0.4
an
d x
2 =
z2 =
0.6
. T
hen
, th
e o
nly
un
kn
ow
n i
n E
q.
(9)
is T
. S
olv
ing n
on
lin
ear
Eq
. (9
), b
y t
rial
an
d e
rro
r w
ith
a s
pre
adsh
eet,
sta
rtin
g f
rom
a g
ues
s o
f
T =
10
0oC
, q
uic
kly
lea
ds
to a
bu
bb
le-p
oin
t te
mp
erat
ure
of
10
6.9
oC
. T
he
com
po
siti
on
of
the
vap
or
bu
bb
le i
s o
bta
ined
fro
m E
q.
(2),
wh
ich
at
the
bu
bb
le p
oin
t re
du
ces
to y
i = x
iKi =
ziK
i..
Th
e
K-v
alu
es a
t th
e b
ub
ble
po
int
are
com
pu
ted
to
be
K1 =
1.3
63
an
d K
2 =
0.7
58
, giv
ing y
1 =
0.5
45
and
y2 =
0.4
55
.
At
the
dew
po
int,
Ψ =
V/F
=1
, an
d E
q.
(1),
co
mb
ined
wit
h (
4),
bec
om
es:
f{x 1
, x 2
, T
} =
zP
xx
PT
zP
xx
PT
ss
1
11
21
2
21
22
γγ
{,
}{
}{
,}
{}
−� ��
� +−
� ���
=1
10
wh
ere
bec
ause
y1 =
z1 =
0.4
an
d y
2 =
z2 =
0.6
, x 1
, a
nd
x2 =
(1 -
x1)
are
left
as
un
kn
ow
ns.
T
he
liq
uid
ph
ase
mo
le f
ract
ion
s ar
e fr
om
Eq
. (3
), x
i =
zi /
Ki .
So
lvin
g t
hes
e eq
uat
ion
s b
y t
rial
an
d
erro
r w
ith
a s
pre
ad s
hee
t, s
tart
ing f
rom
T =
10
5oC
, x 1
= 0
.2 a
nd
x2 =
0.8
, q
uic
kly
lea
ds
to a
dew
-
po
int
tem
per
atu
re o
f 1
09
.7oC
. T
he
K-v
alu
es a
t th
e d
ew p
oin
t ar
e co
mp
ute
d t
o b
e K
1 =
1.7
93
an
d
K2 =
0.7
72
, w
ith
x1 =
0.2
23
1 a
nd
x2 =
0.7
76
9.
Th
e eq
uil
ibri
um
fla
sh c
alcu
lati
on
is
carr
ied
ou
t at
T =
(1
09
.7 +
10
6.9
)/2
= 1
08
.3oC
. I
n
this
cas
e, t
he
val
ues
of
Ψ,
x 1,
and
x2
are
co
mp
ute
d f
rom
Eq
s. (
1)
and
(3
), w
her
e th
e v
apo
r
pre
ssu
res
are
com
pu
ted
fro
m E
qs.
(5
) an
d (
6)
to b
e 7
14
to
rr f
or
1 a
nd
53
9 t
orr
fo
r 2
. V
alu
es o
f y 1
and
y2
are
ob
tain
ed f
rom
Eq
. (2
).
Usi
ng,
agai
n,
a sp
read
shee
t w
ith
a t
rial
an
d e
rro
r p
roce
du
re,
the
foll
ow
ing r
esu
lt i
s q
uic
kly
ob
tain
ed:
V/F
= 0
.60
4
x 1 =
0.2
94
9
x 2 =
0.7
05
1
y 1 =
0.4
68
9
y 2 =
0.5
31
1
Ex
erci
se 4
.35
S
ub
ject
:
Bu
bb
le p
oin
t, d
ew p
oin
t, a
nd
aze
otr
op
e o
f an
eth
yl
acet
ate
(A)
- et
hyl
alco
ho
l (E
)
mix
ture
.
Giv
en:
L
iqu
id m
ixtu
re o
f 8
0 m
ol%
A -
20
mo
l% E
at
10
1.3
kP
a (1
atm
).
Liq
uid
-ph
ase
acti
vit
y
coef
fici
ents
fo
r A
an
d E
as
a fu
nct
ion
of
liq
uid
-ph
ase
mo
le f
ract
ion
s fr
om
th
e v
an L
aar
equ
atio
ns.
Ass
um
pti
on
s:
Mo
dif
ied
Rao
ult
's l
aw,
Eq
. (2
-72
) ap
pli
es.
Fin
d:
(a)
Bu
bb
le-p
oin
t te
mp
erat
ure
an
d v
apo
r co
mp
osi
tio
n.
(b
) D
ew p
oin
t.
(c)
Tem
per
atu
re
and
co
mp
osi
tio
n o
f p
oss
ible
aze
otr
op
e.
An
aly
sis:
Th
e R
ach
ford
-Ric
e fl
ash
eq
uat
ion
s ca
n b
e u
sed
fro
m T
able
4.4
:
fz
K
K
ii
iiC
{}
ΨΨ
=−
+−
==�
1
11
01
��
��
(1
)
yz
K Ki
ii i
=+
−1
1��
(2
)
xz K
ii
i
=+
−1
1��
(3
)
Th
e m
od
ifie
d R
aou
lt's
law
fro
m E
q.
(2-7
2)
is:
KP P
iiL
is
=γ
(4
)
An
toin
e v
apo
r p
ress
ure
(in
to
rr)
equ
atio
ns
are
ob
tain
ed f
rom
Sec
tio
n 1
3 o
f P
erry
's H
and
bo
ok
:
log
..
()
.
log
..
()
.
PT
C
PT
C
s
o
s
o
A E
(5
)
(6
)
=−
+
=−
+
71
01
79
12
44
95
1
21
78
81
75
86
70
12
81
59
0
19
37
68
Th
e v
an L
aar
equ
atio
ns,
Tab
le 2
.9,
wit
h t
he
giv
en c
on
stan
ts a
re:
ln. . .
ln. . .
γ γ
A
A E
E
E A
(7
)
(8
)
=
+� ��
� ��
=
+� ��
� ��
08
55
10
85
5
07
53
07
53
10
75
3
08
55
x x x x
Ex
erci
se 4
.35
(c
on
tin
ued
)
A
na
lysi
s:
(co
nti
nu
ed)
(a)
Sin
ce P
= 1
atm
an
d t
he
no
rmal
bo
ilin
g p
oin
ts o
f et
hyl
acet
ate
and
eth
yl
alco
ho
l ar
e
77
.1oC
an
d 7
8.4
oC
, re
spec
tiv
ely,
it m
igh
t b
e ex
pec
ted
th
at t
he
bu
bb
le a
nd
dew
po
ints
of
the
mix
ture
wo
uld
be
in t
he
vic
init
y o
f 7
0oC
, u
nle
ss t
he
liq
uid
-ph
ase
acti
vit
y c
oef
fici
ents
are
mu
ch
dif
fere
nt
fro
m 1
. T
o c
hec
k t
his
, a
ctiv
ity c
oef
fici
ents
are
co
mp
ute
d f
rom
Eq
s. (
7)
and
(8
), w
ith
a
spre
ad s
hee
t, w
ith
th
e fo
llo
win
g r
esu
lt a
s a
plo
t.
It i
s se
en t
hat
th
e co
effi
cien
ts a
re n
ot
larg
e, b
ut
are
as h
igh
as
2.3
5.
At
the
bu
bb
le p
oin
t, Ψ
= V
/F =
0,
and
Eq
. (1
), c
om
bin
ed w
ith
(4
), b
eco
mes
:
fT
zP
T
Pz
PT
P
ss
{}
{}
{}
=−� ��
� +−� ��
� =
AA
AE
EE
(9
)1
10
γγ
Ex
erci
se 4
.35
(c
on
tin
ued
)
An
aly
sis:
(
con
tin
ued
)
Als
o,
at t
he
bu
bb
le p
oin
t, x
A =
zA =
0.8
an
d x
E =
zE =
0.2
. T
hen
, th
e o
nly
un
kn
ow
n i
n E
q.
(9)
is T
. S
olv
ing n
on
lin
ear
Eq
. (9
), b
y t
rial
an
d e
rro
r w
ith
a s
pre
adsh
eet,
sta
rtin
g f
rom
a g
ues
s o
f
T =
70
oC
, q
uic
kly
lea
ds
to a
bu
bb
le-p
oin
t te
mp
erat
ure
of
73
.5oC
. T
he
com
po
siti
on
of
the
vap
or
bu
bb
le i
s o
bta
ined
fro
m E
q.
(2),
wh
ich
at
the
bu
bb
le p
oin
t re
du
ces
to y
i = x
iKi =
ziK
i..
Th
e K
-
val
ues
at
the
bu
bb
le p
oin
t ar
e co
mp
ute
d t
o b
e K
A =
0.9
13
an
d K
E =
1.3
50
, giv
ing
yA =
0.7
30
an
d
y E =
0.2
70
.
(b
) A
t th
e d
ew p
oin
t, Ψ
= V
/F =
1,
and
Eq
. (1
), c
om
bin
ed w
ith
(4
), b
eco
mes
:
f{x A
, x E
, T
} =
zP
xx
PT
zP
xx
PT
ss
A
AA
EA
E
EA
EE
γγ
{,
}{
}{
,}
{}
−� ��
� +−
� ���
=1
10
wh
ere
bec
ause
yA =
zA =
0.8
an
d y
E =
zE =
0.2
, x
A ,
an
d x
E =
(1 -
xA)
are
left
as
un
kn
ow
ns.
T
he
liq
uid
ph
ase
mo
le f
ract
ion
s ar
e fr
om
Eq
. (3
), x
i =
zi /
Ki .
So
lvin
g t
hes
e eq
uat
ion
s b
y t
rial
an
d
erro
r w
ith
a s
pre
ad s
hee
t, s
tart
ing f
rom
T =
70
oC
, x
A =
0.8
an
d x
E =
0.2
, q
uic
kly
lea
ds
to a
dew
-
po
int
tem
per
atu
re o
f 7
4.3
oC
. T
he
K-v
alu
es a
t th
e d
ew p
oin
t ar
e co
mp
ute
d t
o b
e K
A =
0.9
22
an
d
KE =
1.5
08
, w
ith
xA =
0.8
67
4 a
nd
xE =
0.1
32
6.
(c)
To
det
erm
ine
the
exis
ten
ce o
f an
aze
otr
op
e, w
her
e y i
= x
i ,
a se
ries
of
bu
bb
le-p
oin
t
calc
ula
tio
ns
can
be
mad
e, u
sin
g t
he
pro
ced
ure
in
par
t (a
), s
tart
ing f
rom
say,
xA =
0.0
5 i
n
incr
emen
ts o
f 0
.05
. I
f, i
n t
he
ran
ge
of
xA
fro
m 0
.05
to
0.9
5,
the
K-v
alu
e o
f A
sw
itch
es f
rom
mo
re
than
1 t
o l
ess
than
1,
then
an
aze
otr
op
e ex
ists
in
th
is r
ange.
T
he
calc
ula
tio
ns
can
th
en b
e re
fin
ed.
Th
e re
sult
fro
m a
sp
read
shee
t is
a m
inim
um
-bo
ilin
g a
zeo
tro
pe
at 7
2.4
6oC
wit
h a
co
mp
osi
tio
n o
f
54
.4 m
ol%
A a
nd
45
.6 m
ol%
B.
Th
is c
om
par
es t
o e
xp
erim
enta
l v
alu
es f
rom
Per
ry's
Han
db
oo
of
71
.8oC
at
a co
mp
osi
tio
n o
f 5
4 m
ol%
A.
Ex
erci
se 4
.36
S
ub
ject
:
Bu
bb
le p
oin
t, d
ew p
oin
t, a
nd
aze
otr
op
e o
f a
wat
er (
W)
- fo
rmic
aci
d (
F)
mix
ture
.
Giv
en:
L
iqu
id m
ixtu
re o
f 5
0 m
ol%
W -
50
mo
l% F
at
10
7oC
. L
iqu
id-p
has
e ac
tiv
ity
coef
fici
ents
fo
r W
an
d F
as
a fu
nct
ion
of
liq
uid
-ph
ase
mo
le f
ract
ion
s fr
om
th
e v
an L
aar
equ
atio
ns.
Ass
um
pti
on
s:
Mo
dif
ied
Rao
ult
's l
aw,
Eq
. (2
-72
) ap
pli
es.
Fin
d:
(a)
Bu
bb
le-p
oin
t p
ress
ure
. (
b)
Dew
po
int
pre
ssu
re.
(c)
A
zeo
tro
pic
pre
ssu
re a
nd
com
po
siti
on
at
10
7oC
.
An
aly
sis:
Th
e R
ach
ford
-Ric
e fl
ash
eq
uat
ion
s ca
n b
e u
sed
fro
m T
able
4.4
:
fz
K
K
ii
iiC
{}
ΨΨ
=−
+−
==�
1
11
01
��
��
(1
)
yz
K Ki
ii i
=+
−1
1��
(2
)
xz K
ii
i
=+
−1
1��
(3
)
Th
e m
od
ifie
d R
aou
lt's
law
fro
m E
q.
(2-7
2)
is:
KP P
iiL
is
=γ
(4
)
An
toin
e v
apo
r p
ress
ure
(in
to
rr)
equ
atio
ns
are
ob
tain
ed f
rom
Sec
tio
n 1
3 o
f P
erry
's H
and
bo
ok
:
log
..
()
.
log
..
()
.
PT
C
PT
C
s
o
s
o
W F
(5
)
(
6)
=−
+
=−
+
80
71
31
17
30
63
0
23
34
26
69
44
59
12
95
26
0
21
80
0
Th
e v
an L
aar
equ
atio
ns,
Tab
le 2
.9,
wit
h t
he
giv
en c
on
stan
ts a
re:
ln.
(.
)
(.
)
ln.
(.
)
(.
)
γ γ
W
A E
F
E A
(7
)
(8
)
=−
+− −
� ��� ��
=−
+− −
� ��� ��
02
93
5
10
29
35
02
75
7
02
75
7
10
27
57
02
93
5
x x x x
Ex
erci
se 4
.36
(c
on
tin
ued
)
A
na
lysi
s:
(co
nti
nu
ed)
(a)
Sin
ce T
= 1
07
oC
an
d t
he
no
rmal
bo
ilin
g p
oin
ts o
f w
ater
an
d f
orm
ic a
cid
are
10
0oC
and
10
0.8
oC
, re
spec
tiv
ely,
it m
igh
t b
e ex
pec
ted
th
at t
he
bu
bb
le a
nd
dew
po
int
pre
ssu
res
of
the
mix
ture
wo
uld
be
in t
he
vic
init
y o
f 1
atm
, u
nle
ss t
he
liq
uid
-ph
ase
acti
vit
y c
oef
fici
ents
are
mu
ch
dif
fere
nt
fro
m 1
. T
o c
hec
k t
his
, a
ctiv
ity c
oef
fici
ents
are
co
mp
ute
d f
rom
Eq
s. (
7)
and
(8
), w
ith
a
spre
ad s
hee
t, w
ith
th
e fo
llo
win
g r
esu
lt a
s a
plo
t.
It i
s se
en t
hat
th
e co
effi
cien
ts l
ie b
etw
een
0.7
and
1.0
At
the
bu
bb
le p
oin
t, Ψ
= V
/F =
0,
and
Eq
. (1
), c
om
bin
ed w
ith
(4
), b
eco
mes
:
fP
zP
Pz
P
P
ss
{}
{}
{}
=−� ��
� +−� ��
� =W
WW
O
FF
F
OC
C
(
9)
11
07
11
07
0γ
γ
Ex
erci
se 4
.36
(c
on
tin
ued
)
An
aly
sis:
(
con
tin
ued
)
Als
o,
at t
he
bu
bb
le p
oin
t, x
W =
zW
= 0
.5 a
nd
xF =
zF =
0.5
. T
hen
, th
e o
nly
un
kn
ow
n i
n E
q.
(9)
is P
. E
qu
atio
n (
9)
is l
inea
r in
P a
nd
, th
us,
can
be
solv
ed d
irec
tly t
o g
ive
a b
ub
ble
-po
int
pre
ssu
re o
f 7
19
to
rr.
Th
e K
-val
ues
at
the
bu
bb
le p
oin
t ar
e 1
.01
5 f
or
W a
nd
0.9
84
. T
he
com
po
siti
on
of
the
vap
or
bu
bb
le i
s o
bta
ined
fro
m E
q.
(2),
wh
ich
at
the
bu
bb
le p
oin
t re
du
ces
to y
i
= x
iKi =
ziK
i .
Th
is g
ives
y W
= 0
.50
8 a
nd
yF =
0.4
92
.
(b
) A
t th
e d
ew p
oin
t, Ψ
= V
/F =
1,
and
Eq
. (1
), c
om
bin
ed w
ith
(4
), b
eco
mes
:
f{x W
, x
F,
P} =
zP
xx
Pz
P
xx
Ps
sW
WW
FW
oF
FW
FF
oC
Cγ
γ{
,}
{}
{,
}{
}1
07
11
07
10
−� ��
� +−
� ���
=
wh
ere
bec
ause
yW
= z
W =
0.5
an
d y
F =
zF =
0.5
, x
W ,
an
d x
F =
(1 -
xW
) ar
e le
ft a
s u
nk
no
wn
s.
Th
e
liq
uid
ph
ase
mo
le f
ract
ion
s ar
e fr
om
Eq
. (3
), x
i =
zi /
Ki .
So
lvin
g t
hes
e eq
uat
ion
s b
y t
rial
an
d
erro
r w
ith
a s
pre
ad s
hee
t, s
tart
ing f
rom
P
= 7
60
to
rr,
xW
= 0
.5 a
nd
xF =
0.5
, q
uic
kly
lea
ds
to a
dew
-po
int
pre
ssu
re o
f 7
25
.2 t
orr
. T
he
K-v
alu
es a
t th
e d
ew p
oin
t ar
e co
mp
ute
d t
o b
e K
W =
1.0
06
and
KF =
0.9
77
, w
ith
xW
= 0
.49
7 a
nd
xF =
0.5
12
.
(c)
To
det
erm
ine
the
exis
ten
ce o
f an
aze
otr
op
e, w
her
e y i
= x
i ,
a se
ries
of
bu
bb
le-p
oin
t
calc
ula
tio
ns
can
be
mad
e, u
sin
g t
he
pro
ced
ure
in
par
t (a
), s
tart
ing f
rom
say,
x W =
0.0
5 i
n
incr
emen
ts o
f 0
.05
. I
f, i
n t
he
ran
ge
of
xW
fro
m 0
.05
to
0.9
5,
the
K-v
alu
e o
f W
sw
itch
es f
rom
mo
re t
han
1 t
o l
ess
than
1,
then
an
aze
otr
op
e ex
ists
in
th
is r
ange.
T
he
calc
ula
tio
ns
can
th
en b
e
refi
ned
. T
he
resu
lt f
rom
a s
pre
adsh
eet
is a
max
imu
m-b
oil
ing a
zeo
tro
pe
at 7
18
.2 t
orr
wit
h a
com
po
siti
on
of
44
.5 m
ol%
W a
nd
55
.5 m
ol%
F.
Ex
erci
se 4
.37
S
ub
ject
:
Bu
bb
le p
oin
t, d
ew p
oin
t, a
nd
eq
uil
ibri
um
fla
sh o
f a
tern
ary m
ixtu
re.
Giv
en:
M
ixtu
re o
f 4
5 m
ol%
n-h
exan
e (1
), 2
5 m
ol%
n-h
epta
ne,
an
d 3
0 m
ol%
n-o
ctan
e.
Ass
um
pti
on
s:
Ap
pli
cab
ilit
y o
f S
-R-K
met
ho
d f
or
esti
mat
ing K
-val
ues
.
Fin
d:
(a)
B
ub
ble
-po
int
tem
per
atu
re a
t p
ress
ure
s o
f 5
, 1
, an
d 0
.5 a
tm.
Dew
-po
int
tem
per
atu
re a
t p
ress
ure
s o
f 5
, 1
, an
d 0
.5 a
tm.
(b
) T
emp
erat
ure
an
d p
has
e co
mp
osi
tio
ns
for
flas
h o
f V
/F =
0.5
at
5,
1,
and
0.5
atm
.
(c
) n
-oct
ane
in t
he
vap
or
if 9
0%
of
the
n-h
exan
e is
vap
ori
zed
at
1 a
tm.
An
aly
sis:
T
he
foll
ow
ing r
esu
lts
are
ob
tain
ed w
ith
th
e C
HE
MC
AD
sim
ula
tor.
(a
) B
ub
ble
-po
int
and
dew
-po
int
tem
per
atu
res:
Pre
ssu
re,
atm
0
.5
1
5
Bu
bb
le-p
oin
t T
, oF
1
47
1
87
3
07
Dew
-po
int
T,
oF
1
78
2
16
3
30
(b
) 5
0 m
ol%
vap
ori
zati
on
of
feed
:
Pre
ssu
re,
atm
0
.5
1
5
Tem
per
atu
re,
oF
1
62
2
01
3
18
Vap
or
mo
le f
ract
ion
s:
n-H
exan
e 0
.61
5
0.5
99
0
.55
4
n-H
epta
ne
0.2
31
0
.23
3
0.2
39
n-O
ctan
e 0
.15
4
0.1
68
0
.20
7
Liq
uid
mo
le f
ract
ion
s:
n-H
exan
e 0
.28
5
0.3
01
0
.34
6
n-H
epta
ne
0.2
69
0
.26
7
0.2
61
n-O
ctan
e 0
.44
6
0.4
32
0
.39
3
Mo
les
V/m
ole
F
0.5
0
.5
0.5
Mo
les
L/m
ole
F
0.5
0
.5
0.5
(c
) B
y i
tera
tio
n o
n t
he
iso
ther
mal
fla
sh c
alcu
lati
on
, fo
r 9
0 m
ol%
of
n-h
exan
e to
vap
or,
nee
d a
tem
per
atu
re o
f 2
10
.2oF
at
1at
m.
Th
is g
ives
80
.1 m
ol%
vap
ori
zati
on
wit
h 6
5%
vap
ori
zati
on
of
n-o
ctan
e.
Ex
erci
se 4
.38
S
ub
ject
:
Vap
ori
zati
on
of
colu
mn
bo
tto
ms
in a
par
tial
reb
oil
er.
Giv
en:
1
50
km
ol/
h o
f b
ub
ble
-po
int
liq
uid
, L
1,
at 7
58
kP
a, w
ith
a m
ola
r co
mp
osi
tio
n o
f 1
0%
pro
pan
e, 4
0%
n-b
uta
ne,
an
d 5
0%
n-p
enta
ne
leav
ing b
ott
om
sta
ge
of
a d
isti
llat
ion
co
lum
n a
nd
pas
sin
g t
o a
reb
oil
er w
her
e al
l b
y 5
0 k
mo
l/h
is
vap
ori
zed
to
VB.
Ass
um
pti
on
s:
Pre
ssu
re i
n r
ebo
iler
= 7
58
kP
a.
S-R
-K m
eth
od
fo
r K
-val
ues
an
d e
nth
alp
ies.
Fin
d:
C
om
po
siti
on
s an
d a
mo
un
ts o
f b
oil
up
an
d b
ott
om
s, B
, an
d r
ebo
iler
du
ty,
QR,
fro
m a
sim
ula
tio
n p
rogra
m
An
aly
sis:
U
se f
lash
mo
du
le o
f th
e C
HE
MC
AD
sim
ula
tor.
F
eed
(L
1)
tem
per
atu
re i
s co
mp
ute
d
fro
m a
bu
bb
le-p
oin
t ca
lcu
lati
on
at
75
8 k
Pa
to b
e 7
4.9
oC
. F
lash
co
nd
itio
ns
are
P =
75
8 k
Pa
and
V/F
= (
15
0 -
50
)/1
50
= 0
.66
67
. T
he
resu
lt i
s a
tem
per
atu
re o
f 8
7.5
oC
wit
h a
reb
oil
er d
uty
of
2.2
2 x
10
6 k
J/h
, an
d c
om
po
siti
on
s as
fo
llo
ws
in t
erm
s o
f co
mp
on
ent
flo
w r
ates
:
Co
mp
on
ent:
B
ott
om
s, k
mo
l/h
B
oil
up
, k
mo
l/h
P
rop
ane
1
.94
13
.06
n
-Bu
tan
e 1
5.3
9
4
4.6
1
n
-Pen
tan
e 3
2.6
7
4
2.3
3
T
ota
l 5
0.0
0
10
0.0
0
Ex
erci
se 4
.39
S
ub
ject
:
Bu
bb
le-p
oin
t an
d e
qu
ilib
riu
m f
lash
tem
per
atu
res
for
a te
rnar
y m
ixtu
re.
Giv
en:
M
ixtu
re a
t 5
0 p
sia
wit
h a
co
mp
osi
tio
n i
n m
ole
fra
ctio
ns
of
0.0
05
met
han
e, 0
.59
5 e
than
e,
and
0.4
00
n-b
uta
ne.
Fin
d:
(a)
B
ub
ble
-po
int
tem
per
atu
re.
(b
) T
emp
erat
ure
an
d p
has
e co
mp
osi
tio
ns
for
25
mo
l% v
apo
riza
tio
n.
An
aly
sis:
I
nst
ead
of
usi
ng F
igs.
2.8
an
d 2
.9 f
or
K-v
alu
es,
use
S-R
-K m
eth
od
wit
h t
he
CH
EM
CA
D
sim
ula
tor,
wit
h t
he
foll
ow
ing r
esu
lts:
(a
) B
ub
ble
-po
int
tem
per
atu
re =
-6
1oF
. U
se o
f F
igs.
2.8
an
d 2
.9 g
ives
-6
0oF
.
(b
) F
lash
tem
per
atu
re f
or
25
mo
l% v
apo
riza
tio
n =
-4
3.6
oF
, w
ith
co
mp
osi
tio
ns:
Co
mp
on
ent
Vap
or
mo
le f
ract
ion
L
iqu
id m
ole
fra
ctio
n
M
eth
ane
0.0
17
9
0.0
00
7
E
than
e 0
.95
59
0
.47
47
n
-Bu
tan
e 0
.02
62
0
.52
46
Ex
erci
se 4
.40
S
ub
ject
:
Hea
tin
g a
nd
ex
pan
sio
n o
f a
hyd
roca
rbo
n m
ixtu
re.
Giv
en:
1
00
lb
mo
l/h
of
a m
ixtu
re a
t 1
50
oF
an
d 2
60
psi
a, w
ith
a m
ole
fra
ctio
n c
om
po
siti
on
of
0.0
3 e
than
e, 0
.20
pro
pan
e, 0
.37
n-b
uta
ne,
0.3
5 n
-pen
tan
e, a
nd
0.0
5 n
-hex
ane.
M
ixtu
re i
s h
eate
d
to 2
60
oF
at
25
0 p
sia,
fo
llo
wed
by e
xp
ansi
on
to
10
0 p
sia.
Ass
um
pti
on
s:
Ex
pan
sio
n i
s ad
iab
atic
.
S-R
-K m
eth
od
fo
r K
-val
ues
an
d e
nth
alp
ies
Fin
d:
U
sin
g a
sim
ula
tio
n p
rogra
m,
fin
d f
or
each
str
eam
in
th
e p
roce
ss,
the
mo
l% v
apo
r, a
nd
vap
or
and
liq
uid
ph
ase
mo
le f
ract
ion
s.
An
aly
sis:
U
sin
g t
he
CH
EM
CA
D p
roce
ss s
imu
lato
r, t
he
foll
ow
ing r
esu
lts
are
ob
tain
ed.
Th
e fe
ed i
s al
l li
qu
id.
Th
e st
ream
s le
avin
g t
he
hea
ter
and
th
e v
alv
e ar
e al
l v
apo
r.
Th
e fi
nal
tem
per
atu
re i
s 2
35
oF
.
Ex
erci
se 4
.41
S
ub
ject
:
Eq
uil
ibri
um
vap
or
and
liq
uid
str
eam
s le
avin
g t
he
feed
sta
ge
of
a d
isti
llat
ion
co
lum
n
Giv
en:
F
eed
str
eam
, F
, a
nd
str
eam
s V
F+
1 a
nd
LF
-1 as
su
mm
ariz
ed b
elo
w.
Pre
ssu
re =
78
5 k
Pa.
Ass
um
pti
on
s:
VF
+1 i
s at
its
dew
po
int
and
LF
-1 i
s at
its
bu
bb
le p
oin
t.
Ad
iab
atic
co
nd
itio
ns.
Fin
d:
Co
mp
osi
tio
n a
nd
am
ou
nts
of
str
eam
s V
F a
nd
LF.
An
aly
sis:
U
sin
g t
he
S-R
-K m
eth
od
fo
r K
-val
ues
, w
ith
th
e C
HE
MC
AD
pro
cess
sim
ula
tor,
th
e
foll
ow
ing r
esu
lts
are
ob
tain
ed:
Str
eam
F
V
F+
1
LF
-1
VF
LF
Tem
per
atu
re,
oC
6
4.3
7
3.1
6
8.5
7
0.0
7
0.0
Ph
ase
con
dit
ion
L
iqu
id
Vap
or
Liq
uid
V
apo
r L
iqu
id
Flo
w r
ate,
km
ol/
h:
P
rop
ane
32
.0
58
.8
15
.0
69
.6
36
.2
n
-Bu
tan
e 6
4.0
9
8.0
4
5.0
8
9.9
1
17
.1
n
-Pen
tan
e 6
4.0
3
9.2
4
0.0
3
4.5
1
08
.7
To
tal
16
0.0
1
96
.0
10
0.0
1
94
.0
26
2.0
Ex
erci
se 4
.42
S
ub
ject
:
Ad
iab
atic
fla
sh a
cro
ss a
val
ve
of
a h
yd
roca
rbo
n m
ixtu
re.
Giv
en:
F
eed
mix
ture
, o
f co
mp
osi
tio
n b
elo
w,
at 2
50
oF
an
d 5
00
psi
a.
Pre
ssu
re e
xit
ing v
alv
e =
30
0 p
sia.
Fin
d:
(a)
P
has
e co
nd
itio
n o
f fe
ed.
(b
) T
emp
erat
ure
do
wn
stre
am o
f v
alv
e.
(c
) M
ole
fra
ctio
n v
apo
rize
d a
cro
ss v
alv
e.
(d
) M
ole
fra
ctio
n c
om
po
siti
on
s o
f v
apo
r an
d l
iqu
id p
has
es d
ow
nst
ream
of
val
ve.
An
aly
sis:
U
se C
HE
MC
AD
pro
cess
sim
ula
tor
wit
h S
-R-K
met
ho
d f
or
K-v
alu
es a
nd
en
thal
pie
s.
Res
ult
s ar
e as
fo
llo
ws:
Str
eam
F
eed
V
apo
r fr
om
val
ve
Liq
uid
fro
m v
alv
e
Tem
per
atu
re,
oF
2
50
2
07
.6
20
7.6
Pre
ssu
re,
psi
a 5
00
3
00
3
00
Ph
ase
con
dit
ion
L
iqu
id
Vap
or
Liq
uid
Mo
le f
ract
ion
of
feed
1
.00
0
.40
43
0
.59
57
Mo
le f
ract
ion
s:
E
thyle
ne
0.0
2
0.0
34
8
0.0
09
9
E
than
e 0
.03
0
.04
91
0
.01
71
P
rop
yle
ne
0.0
5
0.0
65
8
0.0
39
3
P
rop
ane
0.1
0
0.1
26
0
0.0
82
3
Is
ob
uta
ne
0.2
0
0.1
95
3
0.2
03
2
n
-Bu
tan
e 0
.60
0
.52
90
0
.64
82
Ex
erci
se 4
.43
S
ub
ject
an
d t
o F
ind
: A
lgo
rith
m f
or
flas
h c
alcu
lati
on
wh
en Ψ
= V
/F a
nd
P a
re s
pec
ifie
d.
Giv
en:
Is
oth
erm
al f
lash
alg
ori
thm
of
Fig
. 4
-19
a, a
nd
eq
uat
ion
s o
f T
able
4.4
.
An
aly
sis:
S
pec
ify f
eed
rat
e an
d c
om
po
siti
on
, an
d v
alu
es o
f Ψ
= V
/F a
nd
P.
Use
th
e is
oth
erm
al
flas
h a
lgo
rith
m o
f F
ig.
4-1
9a
as a
n i
nn
er l
oo
p.
Gu
ess
the
flas
h t
emp
erat
ure
an
d e
nte
r th
e in
ner
loo
p.
If
the
calc
ula
ted
Ψ =
V/F
is
no
t th
e sp
ecif
ied
val
ue,
gu
ess
a n
ew v
alu
e o
f T
= s
ay 1
.05
tim
es t
he
init
ial
gu
ess
of
T,
and
rep
eat
the
inn
er l
oo
p.
Fo
r th
e n
ext
and
su
bse
qu
ent
iter
atio
ns,
k,
app
ly t
he
fals
e p
osi
tio
n m
eth
od
to
pro
vid
e a
new
gu
ess
of
T:
TT
TT
kk
kk
kk
k+
++
++
=+
−−
−2
11
11
ΨΨ
ΨΨ
spec
��
��
�/
Th
is a
ssu
mes
th
at T
is
a li
nea
r fu
nct
ion
of
Ψ =
V/F
. I
tera
te u
nti
l th
e co
mp
ute
d Ψ
= V
/F
is w
ith
in
say 0
.1%
of
the
spec
ifie
d v
alu
e.
Ex
erci
se 4
.44
S
ub
ject
an
d t
o F
ind
: A
lgo
rith
ms
for
flas
h c
alcu
lati
on
s w
ith
6 d
iffe
ren
t se
ts o
f sp
ecif
ied
var
iab
les
giv
en i
n t
he
tab
le b
elo
w.
Giv
en:
Is
oth
erm
al f
lash
alg
ori
thm
of
Fig
. 4
-19
a, a
nd
eq
uat
ion
s o
f T
able
4.4
.
Ass
um
pti
on
: A
ll f
lash
es a
re a
dia
bat
ic.
An
aly
sis:
T
he
equ
atio
ns
to b
e so
lved
fo
r ea
ch a
lgo
rith
m a
re t
ho
se f
or
the
stan
dar
d a
dia
bat
ic
flas
h p
roce
du
re,
wh
ere
the
spec
ific
atio
ns
are
ou
tlet
P a
nd
Q =
0.
Rac
hfo
rd-R
ice
Eq
. (3
), T
able
4.4
:
fz
K
K
ii
iiC
1
1
1
11
0=
−
+−
==���
��
Ψ
(1
)
Ad
iab
atic
en
erg
y b
alan
ce,
Eq
. (4
-19
):
fh
hh
VL
F2
1 10
00
=+
−−
ΨΨ
()
,
(2
)
Fo
r ea
ch o
f th
e 6
alg
ori
thm
s, w
e m
ust
ch
oo
se a
tea
r v
aria
ble
, th
e o
utp
ut
var
iab
le f
or
f 1,
and
th
e
ou
tpu
t v
aria
ble
fo
r f 2
. I
f K
-val
ues
are
co
mp
osi
tio
n-d
epen
den
t, t
hen
ou
ter
loo
p i
tera
tio
ns
wit
h f
1
are
nec
essa
ry a
s in
Fig
. 4
.19
. N
ote
th
at t
he
spec
ific
atio
n o
f h
F i
s eq
uiv
alen
t to
sp
ecif
yin
g T
F o
r
Q =
0.
In
so
me
case
s, i
t m
ay b
e n
eces
sary
to
so
lve
f 1 a
nd
f 2
sim
ult
aneo
usl
y.
Ou
tpu
t V
aria
ble
in
Cas
e S
pec
ific
atio
ns
Fin
d
Tea
r
Var
iab
le
f 1
f 2
1
hF ,
P
Ψ,
Τ
TV
Ψ
TV
2
hF ,
T
Ψ,
P
Ψ
PV
Ψ
3
hF ,
Ψ
T,
P
TV
PV
TV
4
Ψ,
T
hF ,
P
hF{T
F}
PV
hF
5
Ψ,
P
hF ,
T
hF{T
F}
TV
hF
6
T,
P
hF ,
Ψ
hF{T
F}
Ψ
hF
As
an e
xam
ple
of
on
e o
f th
e al
go
rith
ms,
co
nsi
der
Cas
e 1
, w
hic
h i
s eq
uiv
alen
t to
th
e st
and
ard
adia
bat
ic f
lash
sp
ecif
icat
ion
. T
he
algo
rith
m i
s sh
ow
n i
n d
iag
ram
fo
rm o
n t
he
foll
ow
ing p
age.
Ex
erci
se 4
.44
(c
on
tin
ued
)
A
na
lysi
s:
(co
nti
nu
ed)
Ex
erci
se 7
.5
S
ub
ject
: N
eed
fo
r te
stin
g o
r p
ilo
tin
g a
dis
till
atio
n s
epar
atio
n.
Fin
d:
C
ircu
mst
ance
s th
at r
equ
ire
lab
ora
tory
or
pil
ot-
pla
nt
test
ing o
f a
pro
po
sed
dis
till
atio
n.
An
aly
sis:
L
abo
rato
ry a
nd
/or
pil
ot-
pla
nt
test
ing i
s re
com
men
ded
fo
r:
1
. A
new
mix
ture
no
t p
rev
iou
sly s
epar
ated
by d
isti
llat
ion
.
2.
A s
har
p a
nd
cri
tica
l se
par
atio
n.
3.
A m
ixtu
re w
ith
un
cert
ain
vap
or-
liq
uid
eq
uil
ibri
a d
ata.
4.
A l
ack
of
exp
erie
nce
wit
h t
ray e
ffic
ien
cy f
or
the
mix
ture
.
Ex
erci
se 7
.6
S
ub
ject
: E
con
om
ic t
rad
eoff
in
dis
till
atio
n.
Fin
d:
R
easo
ns
for
trad
eoff
bet
wee
n t
rays
and
ref
lux
.
An
aly
sis:
I
t is
wel
l k
no
wn
th
at f
or
a giv
en s
epar
atio
n,
as t
he
nu
mb
er o
f tr
ays
is i
ncr
ease
d,
the
refl
ux
rat
io c
an b
e d
ecre
ased
. T
hu
s, a
s th
e to
wer
hei
gh
t is
in
crea
sed
, th
e v
apo
r an
d l
iqu
id t
raff
ic
up
an
d d
ow
n t
he
colu
mn
can
be
dec
reas
ed.
Th
eref
ore
, th
e co
lum
n d
iam
eter
can
be
dec
reas
ed.
Als
o t
he
con
den
ser
and
reb
oil
er d
uti
es a
nd
siz
es,
and
th
e u
tili
ty r
equ
irem
ents
can
be
dec
reas
ed.
Th
eref
ore
, th
ere
is a
tra
deo
ff.
Ex
erci
se 7
.7
Su
bje
ct:
McC
abe-
Th
iele
met
ho
d f
or
bin
ary d
isti
llat
ion
.
Fin
d:
R
easo
ns
for
the
surv
ival
of
the
McC
abe-
Th
iele
gra
ph
ical
met
ho
d.
An
aly
sis:
F
or
a b
inar
y m
ixtu
re,
the
McC
abe-
Th
iele
met
ho
d s
ho
ws
clea
rly t
he
ease
or
dif
ficu
lty
of
the
sep
arat
ion
. P
inch
ed r
egio
ns
are
read
ily s
een
. T
he
effe
ct o
f fe
ed l
oca
tio
n i
s re
adil
y s
een
.
Th
e m
eth
od
is
reas
on
ably
acc
ura
te.
Aze
otr
op
es a
re r
ead
ily a
cco
mm
od
ated
.
Ex
erci
se 7
.8
Su
bje
ct:
Sep
arat
ion
of
eth
yl
alco
ho
l an
d w
ater
at
1 a
tm.
wit
h t
wo
co
un
terc
urr
ent
casc
ades
.
Giv
en:
O
ne
casc
ade
(a)
wit
h g
iven
liq
uid
fee
d t
o t
op
sta
ge
and
giv
en v
apo
r fe
ed t
o b
ott
om
stag
e.
An
oth
er c
asca
de
(b)
wit
h t
ota
l co
nd
ense
r an
d r
eflu
x,
and
giv
en v
apo
r fe
ed t
o b
ott
om
stag
e.
Vap
or-
liq
uid
eq
uil
ibri
um
dat
a fo
r 1
atm
.
Ass
um
pti
on
s:
Co
nst
ant
mo
lar
ov
erfl
ow
to
giv
e st
raig
ht
op
erat
ing l
ines
on
a y
-x d
iagra
m.
Fin
d:
(a
) C
om
po
siti
on
s o
f V
4 a
nd
L1 f
or
4 s
tages
in
cas
cad
e (a
).
(b
) N
um
ber
of
equ
ilib
riu
m s
tages
fo
r 8
5 m
ol%
alc
oh
ol
in e
xit
vap
or
of
casc
ade
(a).
(c
) C
om
po
siti
on
s o
f D
an
d L
1 f
or
4 s
tages
in
cas
cad
e (b
).
(d
) N
um
ber
of
equ
ilib
riu
m s
tages
fo
r 5
0 m
ol
alco
ho
l in
D o
f ca
scad
e (b
).
An
aly
sis:
F
rom
th
e giv
en v
apo
r-li
qu
id e
qu
ilib
riu
m d
ata,
in
th
e co
mp
osi
tio
n r
ange
of
inte
rest
,
eth
yl
alco
ho
l is
mo
re v
ola
tile
th
an w
ater
. T
her
efo
re,
the
y an
d x
co
ord
inat
es i
n a
y-x
plo
t p
erta
in
to e
thyl
alco
ho
l.
(a)
Sin
ce L
= 1
00
mo
l an
d V
= 1
00
mo
l, t
he
slo
pe
of
the
op
erat
ing l
ine
fro
m E
qs.
(7
-6)
or
(7-1
1)
= L
/V =
10
0/1
00
= 1
. T
he
term
inal
po
ints
on
th
e o
per
atin
g l
ine
as (
y, x
) ar
e: (
?,
0.7
) at
th
e to
p
and
(0
.3,
?)
at t
he
bo
tto
m.
To
det
erm
ine
the
com
po
siti
on
s o
f V
4 a
nd
L1 f
or
4 s
tages
, th
is
op
erat
ing l
ine
is l
oca
ted
so
th
at e
xac
tly 4
sta
ges
are
ste
pp
ed o
ff i
n a
y-x
dia
gra
m,
as s
ho
wn
bel
ow
.
Fro
m t
he
dia
gra
m,
the
eth
ano
l co
mp
osi
tio
ns
are
76
mo
l% i
n V
4
and
24
mo
l% i
n L
1.
Ex
erci
se 7
.8 (c
on
tin
ued
) A
na
lysi
s:
(co
nti
nu
ed)
(b
)
It i
s im
po
ssib
le t
o o
bta
in a
n o
ver
hea
d v
apo
r w
ith
85
mo
l% e
than
ol.
W
ith
an
in
fin
ite
nu
mb
er o
f st
ages
, th
e h
igh
est
con
cen
trat
ion
of
eth
ano
l in
th
e o
ver
hea
d v
apo
r co
rres
po
nd
s to
th
at
in e
qu
ilib
riu
m w
ith
th
e to
p l
iqu
id f
eed
co
nta
inin
g 7
0 m
ol%
eth
ano
l.
Fro
m t
he
giv
en v
apo
r-li
qu
id
equ
ilib
riu
m d
ata,
th
e h
igh
est
con
cen
trat
ion
is
an e
than
ol
mo
le f
ract
ion
of
0.8
2.
(c)
Sin
ce t
he
bo
tto
m v
apo
r fe
ed,
V0
= 1
00
mo
l an
d D
=
50
mo
l, b
y o
ver
all
mat
eria
l
bal
ance
, L
1 =
V0 -
D =
10
0 -
50
= 5
0 m
ol.
B
ecau
se o
f th
e as
sum
pti
on
of
con
stan
t m
ola
r
ov
erfl
ow
, L
= L
R =
L1
= 5
0 m
ol.
B
y m
ater
ial
bal
ance
aro
un
d t
he
con
den
ser
or
bec
ause
of
con
stan
t m
ola
r o
ver
flo
w,
V =
V4 =
LR +
D
= 5
0 +
50
= 1
00
mo
l.
Th
e sl
op
e o
f th
e o
per
atin
g
lin
e fr
om
Eq
s. (
7-6
) o
r (7
-11
) =
L/V
= 5
0/1
00
= 0
.5.
To
det
erm
ine
the
com
po
siti
on
s o
f D
an
d L
1
for
4 s
tages
, an
o
per
atin
g l
ine
of
this
slo
pe
is l
oca
ted
so
th
at e
xac
tly 4
sta
ges
are
ste
pp
ed o
ff i
n a
y-x
dia
gra
m,
as s
ho
wn
bel
ow
. F
rom
th
e d
iagra
m,
the
eth
ano
l co
mp
osi
tio
ns
are
45
mo
l% i
n D
and
16
mo
l% i
n L
1.
(d)
Sin
ce t
he
dis
till
ate
is 5
0 m
ol%
eth
ano
l, 2
5 m
ole
s o
f et
han
ol
and
25
mo
les
of
wat
er
leav
e in
th
e d
isti
llat
e.
Bec
ause
th
e fe
ed i
s 3
0 m
ole
s o
f et
han
ol
and
70
mo
les
of
wat
er,
L1 ,
th
e
leav
ing l
iqu
id,
con
tain
s 5
mo
les
of
eth
ano
l an
d 4
5 m
ole
s o
f w
ater
. T
hu
s, t
he
term
inal
po
ints
on
the
op
erat
ing l
ine,
bec
ause
of
the
tota
l co
nd
ense
r, a
s (y
, x)
, ar
e: (
0.5
, 0
.5)
at t
he
top
an
d
(0.3
, 0
.1 )
at
the
bo
tto
m.
Ho
wev
er,
po
int
(0.3
, 0
.1)
abo
ve
the
equ
ilib
riu
m l
ine
is i
mp
oss
ible
.
Ex
erci
se 7
.9
Su
bje
ct:
Sep
arat
ion
of
air
in a
reb
oil
ed s
trip
per
Giv
en:
R
ebo
iled
str
ipp
er w
ith
to
tal
reb
oil
er o
per
atin
g a
t 1
atm
. L
iqu
id a
ir (
79
.1 m
ol%
N2 a
nd
20
.9 m
ol%
O2)
fed
to
to
p s
tage.
6
0%
of
O2
in t
he
feed
is
dra
wn
off
in
vap
or
pro
du
ct f
rom
th
e
reb
oil
er.
Bo
tto
ms
vap
or
pro
du
ct c
on
tain
s 0
.2 m
ol%
N2.
Vap
or-
liq
uid
eq
uil
ibri
a d
ata
are
giv
en.
Ass
um
pti
on
s:
Fee
d i
s a
satu
rate
d l
iqu
id.
Fin
d:
(a)
Mo
l% N
2 i
n v
apo
r fr
om
to
p s
tage.
(b
) M
ole
s o
f v
apo
r gen
erat
ed i
n r
ebo
iler
per
10
0 m
ole
s o
f fe
ed.
(c
) N
um
ber
of
equ
ilib
riu
m s
tages
req
uir
ed.
An
aly
sis:
(a
) T
ake
a b
asis
of
F =
10
0 m
ol/
h.
Th
eref
ore
, 7
9.1
mo
l/h
of
N2
an
d 2
0.9
mo
l/h
of
O2 i
n
the
feed
. B
ott
om
s p
rod
uct
vap
or
con
tain
s 0
.6(2
0.9
) =
12
.54
mo
l/h
of
O2 a
nd
(0
.2/9
9.8
)(1
2.5
4)
=
0.0
25
mo
l/h
N2.
By m
ater
ial
bal
ance
, th
e o
ver
hea
d v
apo
r co
nta
ins
20
.9 -
12
.54
= 8
.36
mo
l/h
O2
and
79
.1 -
0.0
25
= 7
9.0
75
mo
l/h
of
N2.
Th
e m
ol%
N2 i
n t
he
ov
erh
ead
vap
or
= 7
9.0
75
/(8
.36
+
79
.07
5)
x 1
00
% =
90
.4 %
.
(b
) A
ssu
me
con
stan
t m
ola
r o
ver
flo
w.
Th
en b
ecau
se t
he
feed
is
assu
med
to
be
a sa
tura
ted
liq
uid
, th
e m
ole
s o
f v
apo
r gen
erat
ed i
n t
he
reb
oil
er p
er 1
00
mo
les
of
feed
= m
ol/
h o
f o
ver
hea
d
vap
or
= 8
.36
+ 7
9.0
75
= 8
7.4
35
mo
les
per
10
0 m
ole
s o
f fe
ed.
(c)
Use
a y
-x d
iagra
m f
or
N2 b
ecau
se i
t is
th
e m
ore
vo
lati
le.
Th
e sl
op
e o
f th
e o
per
atin
g
lin
e is
L/V
= 1
00
/87
.43
5 =
1.1
4.
At
the
top
of
the
colu
mn
, th
e o
per
atin
g l
ine
term
inat
es a
t a
(y-x
)
of
(0.9
04
, 0
.79
1).
A
t th
e b
ott
om
of
the
colu
mn
, w
ith
a t
ota
l re
bo
iler
, th
e o
per
atin
g l
ine
term
inat
es a
t a
(y-x
) o
f (0
.00
2,
0.0
02
).
To
det
erm
ine
the
nu
mb
er o
f eq
uil
ibri
um
sta
ges
, it
is
con
ven
ien
t to
use
tw
o d
iagra
ms,
th
e u
sual
on
e an
d a
sec
on
d o
ne
for
just
th
e v
ery l
ow
mo
le
frac
tio
n r
egio
n s
o a
s to
gai
n a
ccu
racy
in
th
e re
gio
n o
f th
e lo
wer
en
d o
f th
e o
per
atin
g l
ine.
F
rom
the
two
dia
gra
ms,
it
is s
een
th
at j
ust
les
s th
an 8
eq
uil
ibri
um
sta
ges
are
req
uir
ed.
Ex
erci
se 7
.9 (c
on
tin
ued
) A
na
lysi
s (d
) (
con
tin
ued
):
Ex
erci
se 7
.10
S
ub
ject
: S
tage
com
po
siti
on
dat
a fo
r d
isti
llat
ion
of
an A
-B m
ixtu
re.
Giv
en:
S
atu
rate
d l
iqu
id f
eed
of
40
mo
l% A
. T
est
resu
lts
for
vap
or
and
liq
uid
co
mp
osi
tio
ins
for
3 s
ucc
essi
ve
stag
es b
etw
een
th
e fe
ed s
tage
and
a t
ota
l co
nd
ense
r.
_
__
__
__
__
__
_M
ol
% A
__
__
__
__
__
__
_
T
est
1
T
est
2
Sta
ge
Vap
or
Liq
uid
V
apo
r L
iqu
id
M +
2
79
.5
68
.0
75
.0
68
.0
M +
1
74
.0
60
.0
68
.0
60
.5
M
67
.9
51
.0
60
.5
53
.0
Ass
um
pti
on
:
Co
nst
ant
mo
lar
ov
erfl
ow
.
Fin
d:
R
eflu
x r
atio
an
d o
ver
hea
d c
om
po
siti
on
fo
r ea
ch t
est.
An
aly
sis:
T
est
1:
By m
ater
ial
bal
ance
fo
r co
mp
on
ent
A a
rou
nd
sta
ge
M +
1,
Vy
Lx
Vy
Lx
MM
MM
+=
++
++
21
1
(1
)
So
lvin
g E
q.
(1)
for
L/V
an
d s
ub
stit
uti
ng f
or
y an
d x
val
ues
fro
m a
bo
ve
tab
le,
L V
yy
xx
MM
MM
=− −
=− −
=+
++
1
21
07
40
06
79
06
80
06
00
07
63
..
..
.
Fro
m E
q.
(7-7
), r
eflu
x r
atio
= R
= L
/D =
(L
/V)/
(1 -
L/V
) =
0.7
63
/(1
- 0
.76
3)
= 3
.22
D/V
= (
L/V
)/(L
/D)
= 0
.76
3/3
.22
= 0
.23
7.
No
tin
g t
hat
sta
ges
in
th
e re
ctif
yin
g s
ecti
on
are
co
un
ted
her
e fr
om
th
e b
ott
om
up
in
stea
d o
f th
e to
p d
ow
n,
Eq
. (7
-5)
bec
om
es,
yL V
xD V
xM
MD
++
=+
12
(2)
So
lvin
g E
q.
(2)
for
x D ,
x
yL V
x
DV
D
MM
=
−� ��� ��
=−
=+
+1
20
74
00
76
30
68
0
02
37
09
33
/
.(
.)(
.)
..
Th
eref
ore
th
e co
mp
osi
tio
n o
f th
e d
isti
llat
e is
93
.3 m
ol%
A a
nd
6.7
mo
l% B
.
T
est
2:
Bec
ause
y
xy
xM
MM
M+
++
==
12
1
an
d
,
op
erat
ion
is
at t
ota
l re
flu
x,
i.e.
ref
lux
rat
io =
in
fin
ity.
In t
his
cas
e, E
q.
(2)
can
no
t b
e so
lved
fo
r x D
bec
ause
D/V
= 0
. W
e ca
n n
ot
det
erm
ine
the
com
po
siti
on
of
the
dis
till
ate.
W
e d
o k
no
w t
hat
it
mu
st a
t le
ast
75
mo
l% A
.
Ex
erci
se 7
.11
S
ub
ject
: F
ive
pro
ced
ure
s fo
r co
nti
nu
ou
s d
isti
llat
ion
of
a m
ixtu
re o
f b
enze
ne
(A)
and
to
luen
e
(B).
Giv
en:
O
per
atio
n a
t 1
atm
to
pro
du
ce a
dis
till
ate
of
80
mo
l% b
enze
ne
(i.e
. y D
= 0
.8)
fro
m a
satu
rate
d l
iqu
id f
eed
of
70
mo
l% b
enze
ne
(xF
= 0
.7)
. P
roce
du
res
are:
1
. N
o c
olu
mn
. J
ust
a p
arti
al c
on
den
ser
on
to
p o
f a
par
tial
reb
oil
er.
Fee
d i
s to
th
e
reb
oil
er.
Ref
lux
rat
io,
L/D
= 0
.5.
Vap
or
dis
till
ate
is t
ota
lly c
on
den
sed
.
2
. S
ame
as 1
ex
cep
t th
at o
ne
equ
ilib
riu
m s
tage
sits
bet
wee
n t
he
con
den
ser
and
reb
oil
er.
3
. S
ame
as 1
ex
cep
t tw
o e
qu
ilib
riu
m s
tages
bet
wee
n t
he
con
den
ser
and
reb
oil
er.
4
. S
ame
as 3
ex
cep
t th
at r
eflu
x b
yp
asse
s th
e to
p e
qu
ilib
riu
m s
tage.
5
. S
ame
as 2
ex
cep
t th
at f
eed
is
sen
t to
th
e st
age
bet
wee
n t
he
con
den
ser
and
th
e re
bo
iler
.
Ass
um
pti
on
s:
Co
nst
ant
mo
lar
ov
erfl
ow
. C
on
stan
t re
lati
ve
vo
lati
lity
= α
Α,Β
= 2
.5.
Fin
d:
F
or
each
pro
ced
ure
, d
eter
min
e:
(a
) M
ole
s o
f d
isti
llat
e p
er 1
00
mo
les
of
feed
.
(b
) M
ole
s o
f to
tal
vap
or
gen
erat
ed p
er m
ole
of
dis
till
ate.
(c
) M
ole
per
cen
t o
f b
enze
ne
in t
he
bo
tto
ms
(res
idu
e).
(d
) y
-x d
iagra
m,
ind
icat
ing c
om
po
siti
on
s o
f d
isti
llat
e, r
eflu
x,
and
res
idu
e.
Als
o,
(e)
Fo
r m
axim
izat
ion
of
ben
zen
e re
cov
ery (
in t
he
dis
till
ate)
, w
hic
h p
roce
du
re i
s p
refe
rred
.
An
aly
sis:
F
or
each
pro
ced
ure
, th
e p
arti
al c
on
den
ser
and
th
e p
arti
al r
ebo
iler
are
eq
uil
ibri
um
stag
es.
Ben
zen
e is
th
e m
ore
vo
lati
le c
om
po
nen
t, s
o t
he
y-x
dia
gra
m i
s b
ased
on
ben
zen
e.
Bec
ause
th
e re
lati
ve
vo
lati
lity
= c
on
stan
t =
2.5
, th
e eq
uil
ibri
um
rel
atio
nsh
ip i
s giv
en b
y E
q.
(7-3
),
yx
x
x
x=
+−
=+
α
α1
1
25
11
5(
)
.
.
(1)
Tak
e as
a b
asis
, 1
00
mo
l/s
of
feed
. T
her
efo
re,
the
feed
co
nta
ins
70
mo
l/s
of
A a
nd
30
mo
l/s
of
B.
Fro
m t
he
refl
ux
rat
io,
L =
0.5
D,
V =
L +
D =
1.5
D.
Th
eref
ore
, D
/V =
2/3
an
d L
/V =
1/3
. U
se a
sub
scri
pt
of
C
for
stre
ams
leav
ing t
he
con
den
ser,
R f
or
stre
ams
leav
ing t
he
reb
oil
er,
1 f
or
the
top
stag
e w
hen
use
d,
and
2 f
or
the
seco
nd
sta
ge
wh
en u
sed
.
Pro
ced
ure
1:
So
lve
wit
h m
ater
ial
bal
ance
s an
d E
q.
(1).
T
he
liq
uid
lea
vin
g t
he
par
tial
co
nd
ense
r is
in
equ
ilib
riu
m w
ith
th
e v
apo
r d
isti
llat
e o
f y C
= y
D =
0.8
. S
olv
ing E
q.
(1),
xy
yy
CC
CC
=+
−=
+−
=α
()
.
..
(.
).
1
08
08
25
10
80
61
5
(2)
Ben
zen
e m
ater
ial
bal
ance
aro
un
d c
on
den
ser,
yV
yD
xL
yy
D Vx
L VR
CC
RC
C=
+=� ��� ��+� ��� ��
=� ��� ��+
� ��� ��
=
or
0
80
2 30
61
51 3
07
38
..
.
Ex
erci
se 7
.11
(c
on
tin
ued
) A
na
lysi
s:
P
roce
du
re 1
(c
on
tin
ued
)
Th
e v
apo
r fr
om
th
e re
bo
iler
is
in e
qu
ilib
riu
m w
ith
th
e li
qu
id b
ott
om
s (r
esid
ue)
.
Fro
m t
he
left
-
han
d p
art
of
Eq
. (2
),
0.7
38
(1)
0.7
38
2.5
(10
.53
00
.73
8)
==
=+
α−
+−
R
RR
R
y
yy
x
Ov
eral
l to
tal
mat
eria
l b
alan
ce,
F =
10
0 =
D +
B
(3)
Ov
eral
l b
enze
ne
mat
eria
l b
alan
ce,
xFF
= y
CD
+ x
RB
or
7
0 =
0.8
D +
0.5
30
B
(4)
So
lvin
g E
qs.
(3
) an
d (
4),
D =
62
.9 m
ol/
s o
r 6
2.9
mo
l/1
00
mo
l fe
ed,
and
B
= 3
7.1
mo
l/s.
Th
eref
ore
, v
apo
r gen
erat
ed =
V =
1.5
D =
1.5
(62
.9)
= 9
4.4
mo
l/s.
Th
e o
per
atin
g l
ine
for
the
y-x
dia
gra
m p
asse
s th
rou
gh
th
e (y
, x)
po
int
(0.8
, 0
.8)
wit
h a
slo
pe,
L/V
= 1
/3,
as s
ho
wn
in
th
e d
iagra
m b
elo
w.
Ex
erci
se 7
.11
(c
on
tin
ued
) A
na
lysi
s:
(c
on
tin
ued
)
Pro
ced
ure
2:
Th
e sl
op
e an
d t
op
po
int
of
the
op
erat
ing l
ine
are
the
sam
e as
fo
r P
roce
du
re 1
. W
e ju
st
hav
e to
ste
p o
ff o
ne
mo
re s
tage.
T
her
efo
re f
rom
th
e re
sult
s ab
ov
e, w
e h
ave:
y C =
0.8
0
x C =
0.6
15
y 1
= 0
.73
8
x 1 =
0.5
30
Ben
zen
e m
ater
ial
bal
ance
aro
un
d S
tage
1,
yV
xL
yV
xL
RC
+=
+1
1
(5)
So
lvin
g f
or
y R,
11
1(
)0
.73
8(0
.53
00
.61
5)
0.7
10
3
��
��
=+
−=
+−
=�
��
��
��
�R
C
Ly
yx
xV
Th
e v
apo
r fr
om
th
e re
bo
iler
is
in e
qu
ilib
riu
m w
ith
th
e li
qu
id b
ott
om
s (r
esid
ue)
.
Fro
m t
he
left
-
han
d p
art
of
Eq
. (2
),
0.7
10
(1)
0.7
10
2.5
(10
.49
50
.71
0)
==
=+
α−
+−
R
RR
R
y
yy
x
Ov
eral
l to
tal
mat
eria
l b
alan
ce,
F =
10
0 =
D +
B
(6)
Ov
eral
l b
enze
ne
mat
eria
l b
alan
ce,
xFF
= y
CD
+ x
RB
or
7
0 =
0.8
D +
0.4
95
B
(7)
So
lvin
g E
qs.
(6
) an
d (
7),
D =
67
.2 m
ol/
s o
r 6
7.2
mo
l /
mo
l fe
ed,
and
B
= 3
2.8
mo
l/s.
Th
eref
ore
, v
apo
r gen
erat
ed =
V =
1.5
D =
1.5
(67
.2)
= 1
00
.8 m
ol/
s
Th
e o
per
atin
g l
ine
for
the
y-x
dia
gra
m p
asse
s th
rou
gh
th
e (y
, x)
po
int
(0.8
, 0
.8)
wit
h a
slo
pe,
L/V
= 1
/3,
as s
ho
wn
in
th
e d
iagra
m b
elo
w.
Ex
erci
se 7
.11
(c
on
tin
ued
) A
na
lysi
s:
(c
on
tin
ued
)
Pro
ced
ure
3:
T
he
slo
pe
and
to
p p
oin
t o
f th
e o
per
atin
g l
ine
are
the
sam
e as
fo
r P
roce
du
res
1 a
nd
2.
We
just
hav
e to
ex
ten
d P
roce
du
re 2
by s
tep
pin
g o
ff a
sec
on
d e
qu
ilib
riu
m s
tage.
F
rom
ab
ov
e, t
he
resu
lts
for
the
con
den
ser
and
sta
ge
1 a
re:
y C =
0.8
0
x C =
0.6
15
y 1
= 0
.73
8
x 1 =
0.5
30
y 2
= 0
.71
0
x2 =
0.4
95
Ben
zen
e m
ater
ial
bal
ance
aro
un
d S
tage
2,
yV
xL
yV
xL
R+
=+
12
2
(8)
So
lvin
g f
or
y R,
y
yx
xL V
R=
+−� ��� ��
=+
−� ��� ��
=2
21
07
10
04
95
05
30
1 30
69
8(
).
(.
.)
.
Th
e v
apo
r fr
om
th
e re
bo
iler
is
in e
qu
ilib
riu
m w
ith
th
e li
qu
id b
ott
om
s (r
esid
ue)
.
Fro
m t
he
left
-
han
d p
art
of
Eq
. (2
),
0.6
98
(1)
0.6
98
2.5
(10
.48
00
.69
8)
==
=+
α−
+−
R
RR
R
y
yy
x
Ov
eral
l to
tal
mat
eria
l b
alan
ce,
F =
10
0 =
D +
B
(10
)
Ov
eral
l b
enze
ne
mat
eria
l b
alan
ce,
xFF
= y
CD
+ x
RB
or
7
0 =
0.8
D +
0.4
80
B
(11
)
So
lvin
g E
qs.
(1
0)
and
(1
1),
D =
68
.8 m
ol/
s o
r 6
8.8
mo
l /
10
0 m
ol
feed
, an
d
B =
31
.2 m
ol/
s.
Th
eref
ore
, v
apo
r gen
erat
ed =
V =
1.5
D =
1.5
(68
.8)
= 1
03
.2 m
ol/
s
Th
e o
per
atin
g l
ine
for
the
y-x
dia
gra
m p
asse
s th
rou
gh
th
e (y
, x)
po
int
(0.8
, 0
.8)
wit
h a
slo
pe,
L/V
= 1
/3,
as s
ho
wn
in
th
e d
iagra
m b
elo
w.
Ex
erci
se 7
.11
(c
on
tin
ued
) A
na
lysi
s:
(c
on
tin
ued
)
Pro
ced
ure
4:
If
th
e re
flu
x b
yp
asse
s th
e to
p s
tage,
th
e v
apo
r an
d l
iqu
id p
ass
thro
ugh
th
at s
tage
wit
ho
ut
chan
ge.
T
her
efo
re,
this
pro
ced
ure
is
the
sam
e as
Pro
ced
ure
2,
i.e.
ju
st o
ne
stag
e in
th
e co
lum
n.
Pro
ced
ure
5:
Th
e sl
op
e an
d t
op
po
int
of
the
op
erat
ing l
ine
are
the
sam
e as
fo
r P
roce
du
re 1
. W
e ju
st
hav
e to
ad
d t
he
feed
to
th
e st
age
in t
he
colu
mn
. T
her
efo
re f
rom
th
e re
sult
s ab
ov
e, w
e h
ave:
y C =
0.8
0
x C =
0.6
15
y 1
= 0
.73
8
x 1 =
0.5
30
Ben
zen
e m
ater
ial
bal
ance
aro
un
d S
tage
1,
wh
ich
no
w i
ncl
ud
es t
he
feed
,
x FF
+ y
Vx
Ly
Vx
LR
C+
=+
11
(1
2)
So
lvin
g f
or
y R,
yy
V Vx
L Vx
L Vx
F V
V V
L V
L VV
RC
F=� ��� ��+� ��� ��−� ��� ��−� ��� ��
=� ��� ��+
� ��� ��−
� ��� ��−� ��� ��
11
07
38
05
30
06
15
07
01
00
..
..
(1
3)
Bec
ause
th
e fe
ed i
s a
satu
rate
d l
iqu
id,
, V
VL
L=
=+
and
1
00
Fro
m a
bo
ve,
V
= 1
.5D
an
d
L/V
= 1
/3.
Als
o,
LV
LV
VV
//
//
/=
+=
+1
00
13
10
0
Th
eref
ore
, E
q.
(13
) b
eco
mes
,
yV
VV
DR
=+
+� ��
� ��−� ��� ��−� ��� ��
=−
=−
07
38
05
30
1 3
10
00
61
51 3
07
01
00
07
10
17
07
10
11
33
..
..
..
.
(14
)
Th
e v
apo
r fr
om
th
e re
bo
iler
is
in e
qu
ilib
riu
m w
ith
th
e li
qu
id b
ott
om
s (r
esid
ue)
.
Fro
m t
he
left
-
han
d p
art
of
Eq
. (2
),
xy
yy
RR
RR
=+
−2
51
.(
)
(1
5)
Ov
eral
l to
tal
mat
eria
l b
alan
ce,
F =
10
0 =
D +
B
(16
)
Ov
eral
l b
enze
ne
mat
eria
l b
alan
ce,
xFF
= y
CD
+ x
RB
or
7
0 =
0.8
D +
xRB
(1
7)
So
lvin
g E
qs.
(1
4),
(1
5),
(1
6),
an
d (
17
),
y R =
0.5
65
, x R
= 0
.34
2,
D =
78
.3 m
ol/
s o
r 7
8.3
mo
l/1
00
mo
l fe
ed,
B
= 2
1.7
mo
l/s
Th
eref
ore
, v
apo
r gen
erat
ed =
V =
1.5
D =
1.5
(78
.3)
= 1
17
.5 m
ol/
s
Th
e re
ctif
yin
g s
ecti
on
op
erat
ing l
ine
for
the
y-x
dia
gra
m p
asse
s th
rou
gh
th
e (y
, x)
po
int
(0.8
, 0
.8)
wit
h a
slo
pe,
L/V
= 1
/3,
th
e q
-lin
e (f
eed
lin
e) i
s a
ver
tica
l li
ne,
an
d t
he
stri
pp
ing s
ecti
on
op
erat
ing l
ine
pas
ses
thro
ugh
t th
e (y
, x)
po
int
(0.5
65
, 0
.34
2)
and
th
e in
ters
ecti
on
of
the
oth
er t
wo
lin
es,
as s
ho
wn
in
th
e d
iagra
m o
n t
he
foll
ow
ing p
age.
Th
e re
sult
s fr
om
th
e 5
pro
ced
ure
s ar
e su
mm
ariz
ed a
s fo
llo
ws:
Pro
ced
ure
D
/10
0 m
ole
s o
f fe
ed
V/m
ole
of
D
x o
f b
enze
ne
in B
1
62
.9
1.5
0
.53
0
2
67
.2
1.5
0
.49
5
3
68
.8
1.5
0
.48
0
4
67
.2
1.5
0
.49
5
5
78
.3
1.5
0
.34
2
Ex
erci
se 7
.11
(c
on
tin
ued
) A
na
lysi
s: P
roce
du
re 5
:
(co
nti
nu
ed)
(e)
Pro
ced
ure
5 i
s re
com
men
ded
bec
ause
it
pro
du
ces
by f
ar t
he
mo
st d
isti
llat
e, w
hic
h
corr
esp
on
ds
to t
he
hig
hes
t re
cov
ery o
f b
enze
ne.
Ex
erci
se 7
.12
S
ub
ject
: D
isti
llat
ion
of
a m
ixtu
re o
f b
enze
ne
(A)
and
to
luen
e (B
) at
10
1 k
Pa.
Giv
en:
C
olu
mn
co
nsi
stin
g o
f a
par
tial
reb
oil
er,
on
e th
eore
tica
l p
late
, an
d a
to
tal
con
den
ser.
Pro
du
ce a
dis
till
ate
of
75
mo
l% b
enze
ne
fro
m a
sat
ura
ted
liq
uid
fee
d o
f 5
0 m
ol%
ben
zen
e.
Ass
um
pti
on
s:
Co
nst
ant
mo
lar
ov
erfl
ow
. C
on
stan
t re
lati
ve
vo
lati
lity
= α
Α,Β
= 2
.5.
Fin
d:
Nu
mb
er o
f m
ole
s o
f d
isti
llat
e p
er 1
00
mo
les
of
feed
fo
r:
(a
) F
eed
to
th
e re
bo
iler
an
d n
o r
eflu
x.
(b
) F
eed
to
th
e re
bo
iler
an
d a
ref
lux
rat
io,
L/D
= 3
.
(c
) F
eed
to
th
e p
late
an
d a
ref
lux
rat
io o
f 3
.
(d
) S
ame
as (
c) e
xce
pt
a p
arti
al c
on
den
ser.
(e
) F
eed
to
th
e re
bo
iler
wit
h m
inim
um
ref
lux
.
(f
) F
eed
to
th
e re
bo
iler
wit
h t
ota
l re
flu
x.
An
aly
sis:
E
ith
er a
gra
ph
ical
or
anal
yti
cal
met
ho
d c
an b
e u
sed
. B
ecau
se t
he
rela
tiv
e v
ola
tili
ty i
s
assu
med
co
nst
ant,
use
an
an
alyti
cal
met
ho
d.
Fo
r ea
ch p
art,
th
e th
eore
tica
l p
late
an
d t
he
par
tial
reb
oil
er a
re e
qu
ilib
riu
m s
tages
. B
enze
ne
is t
he
mo
re v
ola
tile
co
mp
on
ent,
so
th
e y-
x d
iagra
m i
s
bas
ed o
n b
enze
ne.
Bec
ause
th
e re
lati
ve
vo
lati
lity
= c
on
stan
t =
2.5
, th
e eq
uil
ibri
um
rel
atio
nsh
ip i
s
giv
en b
y E
q.
(7-3
),
yx
x
x
x=
+−
=+
α
α1
1
25
11
5(
)
.
.
(1)
Tak
e as
a b
asis
, 1
00
mo
les
of
feed
. T
her
efo
re,
the
feed
is
50
mo
les
of
A a
nd
50
mo
les
of
B.
(a)
Wit
h n
o r
eflu
x,
sep
arat
ion
occ
urs
on
ly i
n t
he
reb
oil
er.
Th
e v
apo
r le
avin
g t
he
reb
oil
er
is t
ota
lly c
on
den
sed
to
bec
om
e th
e d
isti
llat
e w
ith
yD =
xD =
0.7
5.
So
lve
Eq
. (1
) fo
r eq
uil
ibri
um
x,
xy
yy
BD
DD
=+
−=
+−
=α
()
.
..
(.
).
1
07
50
07
50
25
10
75
00
54
5
(
2)
Bec
ause
th
e d
isti
llat
e an
d b
ott
om
s h
ave
ben
zen
e m
ole
fra
ctio
ns
gre
ater
th
an t
he
mo
le f
ract
ion
of
the
feed
(0
.5),
it
is i
mp
oss
ible
to
ob
tain
a d
isti
llat
e w
ith
a b
enze
ne
mo
le f
ract
ion
of
0.7
5.
(b)
Fro
m t
he
refl
ux
rat
io,
L =
3D
, V
= L
+ D
= 4
D.
Th
eref
ore
, D
/V =
1/4
an
d L
/V =
3/4
.
Use
a s
ub
scri
pt
of
D f
or
dis
till
ate,
R f
or
refl
ux
, B
fo
r st
ream
s le
avin
g t
he
reb
oil
er,
and
1 f
or
the
theo
reti
cal
pla
te,
wh
en u
sed
. W
ith
1 t
heo
reti
cal
pla
te,
fro
m p
art
(a),
y 1 =
0.7
5
x D =
0.7
5
x 1 =
0.5
45
Ben
zen
e m
ater
ial
bal
ance
aro
un
d p
late
1,
yV
xL
yV
xL
BD
+=
+1
1
(3)
So
lvin
g f
or
y B
yy
xx
L VB
D=
+−� ��� ��
=+
−� ��� ��=
11
07
50
05
45
07
50
3 40
59
6(
).
(.
.)
.
Ex
erci
se 7
.12
(c
on
tin
ued
) A
na
lysi
s:
(b)
(co
nti
nu
ed)
Th
e m
ole
fra
ctio
n o
f b
enze
ne
in t
he
bo
tto
ms
pro
du
ct i
s in
eq
uil
ibri
um
wit
h y
B =
0.5
96
.
Th
eref
ore
,
the
form
of
Eq
. (2
) ap
pli
es,
xy
yy
BB
BB
=+
−=
+−
=α
()
.
..
(.
).
1
05
96
05
96
25
10
59
60
37
1
Ov
eral
l to
tal
mat
eria
l b
alan
ce,
F =
10
0 =
D +
B
(4)
Ov
eral
l b
enze
ne
mat
eria
l b
alan
ce,
xFF
= x
DD
+ x
BB
or
5
0 =
0.7
5D
+ 0
.37
1B
(5
)
So
lvin
g E
qs.
(4
) an
d (
5),
D =
34
.2 m
ole
s o
r 3
4.2
mo
l/1
00
mo
l fe
ed,
an
d
B =
65
.8 m
ole
s.
(c)
Wit
h t
he
feed
to
th
e th
eore
tica
l p
late
, th
e fo
llo
win
g r
esu
lts
app
ly f
rom
par
t (b
), y
1 =
0.7
5
x D
= 0
.75
x 1
= 0
.54
5
Ben
zen
e m
ater
ial
bal
ance
aro
un
d S
tage
1,
wh
ich
no
w i
ncl
ud
es t
he
feed
,
x FF
+ y
Vx
Ly
Vx
LB
D+
=+
11
(6
)
So
lvin
g f
or
y B,
yy
V Vx
L Vx
L Vx
F V
V V
L V
L VV
BD
F=� ��� ��+� ��� ��−� ��� ��−� ��� ��
=� ��� ��+
� ��� ��−
� ��� ��−� ��� ��
11
07
50
05
45
07
50
05
01
00
..
..
(7
)
Bec
ause
th
e fe
ed i
s a
satu
rate
d l
iqu
id,
, V
VL
L=
=+
and
1
00
Fro
m a
bo
ve,
V
= 4
D
and
L
/V =
3/4
. A
lso
, L
VL
VV
V/
//
//
=+
=+
10
03
41
00
Th
eref
ore
, E
q.
(7)
bec
om
es,
yV
VV
DB
=+
+� ��
� ��−� ��� ��−� ��� ��
=−
=−
07
50
05
45
3 4
10
00
75
03 4
05
01
00
05
96
45
05
96
11
25
..
..
..
..
(8
)
Th
e v
apo
r fr
om
th
e re
bo
iler
is
in e
qu
ilib
riu
m w
ith
th
e li
qu
id b
ott
om
s (r
esid
ue)
.
Fro
m t
he
left
-
han
d p
art
of
Eq
. (2
),
xy
yy
BB
BB
=+
−2
51
.(
)
(9
)
Ov
eral
l to
tal
mat
eria
l b
alan
ce,
F =
10
0 =
D +
B
(10
)
Ov
eral
l b
enze
ne
mat
eria
l b
alan
ce,
xFF
= x
DD
+ x
BB
or
5
0 =
0.7
5D
+ x
BB
(1
1)
So
lvin
g E
qs.
(8
), (
9),
(1
0),
an
d (
11
),
y B =
0.6
47
,
x B
= 0
.42
3,
D
= 2
3.5
mo
les
or
23
.5 m
ol/
10
0 m
ol
feed
,
B =
76
.5 m
ole
s
(d)
W
ith
a p
arti
al c
on
den
ser,
th
e m
ole
fra
ctio
n o
f th
e li
qu
id r
eflu
x i
s th
at i
n e
qu
ilib
riu
m
wit
h t
he
vap
or
dis
till
ate.
T
her
efo
re,
fro
m t
he
abo
ve
resu
lts,
y D =
0.7
5
x R =
0.5
45
y 1
= 0
.59
6
x 1 =
0.3
71
Ben
zen
e m
ater
ial
bal
ance
aro
un
d t
he
theo
reti
cal
pla
te,
wh
ich
in
clu
des
th
e fe
ed,
x FF
+ y
Vx
Ly
Vx
LB
R+
=+
11
(1
2)
So
lvin
g f
or
y B,
yy
V Vx
L Vx
L Vx
F V
V V
L V
L VV
BR
F=� ��� ��+� ��� ��−� ��� ��−� ��� ��
=� ��� ��+
� ��� ��−
� ��� ��−� ��� ��
11
05
96
03
71
05
45
05
01
00
..
..
(1
3)
Ex
erci
se 7
.12
(c
on
tin
ued
) A
na
lysi
s:
(d)
(co
nti
nu
ed)
Bec
ause
th
e fe
ed i
s a
satu
rate
d l
iqu
id,
, V
VL
L=
=+
and
1
00
Fro
m a
bo
ve,
V
= 4
D
and
L
/V =
3/4
. A
lso
, L
VL
VV
V/
//
//
=+
=+
10
03
41
00
Th
eref
ore
, E
q.
(13
) b
eco
mes
,
yV
VV
DB
=+
+� ��
� ��−� ��� ��−� ��� ��
=−
=−
05
96
03
71
3 4
10
00
54
53 4
05
01
00
04
66
12
90
46
63
23
..
..
..
..
(1
4)
Th
e v
apo
r fr
om
th
e re
bo
iler
is
in e
qu
ilib
riu
m w
ith
th
e li
qu
id b
ott
om
s (r
esid
ue)
.
Fro
m t
he
left
-
han
d p
art
of
Eq
. (2
),
xy
yy
BB
BB
=+
−2
51
.(
)
(1
5)
Ov
eral
l to
tal
mat
eria
l b
alan
ce,
F =
10
0 =
D +
B
(16
)
Ov
eral
l b
enze
ne
mat
eria
l b
alan
ce,
xFF
= y
DD
+ x
BB
o
r
50
= 0
.75
D +
xBB
(1
7)
So
lvin
g E
qs.
(1
4),
(1
5),
(1
6),
an
d (
17
),
y B =
0.4
05
, x B
= 0
.21
4,
D =
53
.4 m
ole
s o
r 5
3.4
/10
0 m
ol
feed
,
B
= 4
6.6
mo
les
(e)
At
min
imu
m r
eflu
x,
wit
h t
he
feed
sen
t to
th
e st
ill
po
t (p
arti
al r
ebo
iler
), a
n i
nfi
nit
e n
um
ber
of
theo
reti
cal
pla
tes
is n
eed
ed b
etw
een
th
e co
nd
ense
r an
d r
ebo
iler
. T
his
par
t is
no
t co
mp
lete
ly
spec
ifie
d.
In
ord
er t
o c
om
pu
te t
he
dis
till
ate,
we
mu
st a
ssu
me
a b
ott
om
s b
enze
ne
mo
le f
ract
ion
less
th
an t
hat
in
th
e fe
ed.
Su
pp
ose
we
cho
ose
th
at m
ole
fra
ctio
n t
o b
e 0
.45
. T
hen
th
e o
per
atin
g
lin
e w
ill
inte
rsec
t th
e eq
uil
ibri
um
lin
e at
x =
0.4
5,
crea
tin
g t
he
pin
ch z
on
e o
f in
fin
ite
stag
es.
Th
e
val
ue
of
y at
th
e in
ters
ecti
on
is
giv
en b
y E
q.
(1):
y=
+=
25
04
5
11
50
45
06
72
.(
.)
.(
.)
.
Th
eref
ore
th
e o
per
atin
g l
ine
pas
ses
thro
ugh
th
e tw
o p
oin
ts,
as {
y, x
},
of
{0
.75
, 0
.75
} a
nd
{0
.67
2,
0.4
50
}.
Th
eref
ore
, th
e sl
op
e =
L/V
= (
0.7
5 -
0.6
72
)/(0
.75
- 0
.45
) =
0.2
60
. N
ow
co
mp
ute
the
ov
eral
l m
ater
ial
bal
ance
s:
Ov
eral
l to
tal
mat
eria
l b
alan
ce,
F =
10
0 =
D +
B
(18
)
Ov
eral
l b
enze
ne
mat
eria
l b
alan
ce,
xFF
= y
DD
+ x
BB
o
r
50
= 0
.75
D +
0.4
5B
(1
9)
So
lvin
g E
qs.
(1
8)
and
(1
9),
D
= 1
6.6
7 m
ole
s o
r 1
6.6
7 m
ol/
10
0 m
ol
feed
, an
d B
= 8
3.3
3 m
ole
s
Cal
cula
tio
ns
for
oth
er v
alu
es o
f th
e b
enze
ne
mo
le f
ract
ion
in
th
e b
ott
om
s ca
n b
e m
ade
in t
he
sam
e m
ann
er.
(f)
At
tota
l re
flu
x,
ther
e is
no
dis
till
ate,
bu
t th
ere
is a
bo
ilu
p.
Th
e m
ole
s o
f d
isti
llat
e p
er 1
00
mo
les
of
feed
= 0
.
Ex
erci
se 7
.13
Su
bje
ct:
Dis
till
atio
n o
f a
mix
ture
of
ben
zen
e an
d t
olu
ene
at 1
01
kP
a fo
r sp
ecif
ied
ref
lux
rati
o a
nd
pro
du
ct c
om
po
siti
on
s.
Giv
en:
F
eed
of
30
kg/h
of
satu
rate
d l
iqu
id f
eed
co
nta
inin
g 4
0 m
ass%
ben
zen
e an
d 6
0 m
ass%
tolu
ene.
D
isti
llat
e to
co
nta
in 9
7 m
ass%
ben
zen
e an
d b
ott
om
s to
co
nta
in 9
8 m
ass%
to
luen
e.
Ref
lux
rat
io =
3.5
an
d f
eed
is
to o
pti
mal
sta
ge.
T
able
of
vap
or-
liq
uid
eq
uil
ibri
um
dat
a in
mo
le
frac
tio
ns.
At
10
1 k
Pa.
Ass
um
pti
on
s:
To
tal
con
den
ser
and
par
tial
reb
oil
er.
Sat
ura
ted
liq
uid
ref
lux
. C
on
stan
t m
ola
r
ov
erfl
ow
.
Fin
d:
(a
) F
low
rat
es o
f d
isti
llat
e an
d b
ott
om
s.
(b
) N
um
ber
of
equ
ilib
riu
m s
tages
nee
ded
.
An
aly
sis:
F
irst
so
lve
the
mat
eria
l b
alan
ce i
n m
ass
un
its.
T
hen
co
nv
ert
to m
ole
s an
d m
ole
frac
tio
ns
so t
hat
th
e M
cCab
e-T
hie
le m
eth
od
can
be
use
d f
or
par
t (b
).
Ov
eral
l to
tal
mas
s b
alan
ce:
3
0 =
D +
B
(1
)
Ov
eral
l b
enze
ne
mas
s b
alan
ce:
0
.40
(30
) =
12
= 0
.97
D +
0.0
2B
(2
)
So
lvin
g E
qs.
(1
) an
d (
2):
D
= 1
2.1
kg/h
B =
17
.9 k
g/h
Co
nv
erti
ng t
o m
ole
s w
ith
mo
lecu
lar
wei
gh
ts o
f 7
8.1
1 f
or
ben
zen
e an
d 9
2.1
3 f
or
tolu
ene,
Ben
zen
e
To
luen
e
Pro
du
ct
km
ol/
h
Ma
ss f
ract
ion
M
ole
fra
ctio
n
Ma
ss f
ract
ion
M
ole
fra
ctio
n
Dis
till
ate
0.1
54
0
.97
0
.97
4
0.0
3
0.0
23
5
Bo
tto
ms
0.1
96
0
.02
0
.02
6
0.9
8
0.9
76
5
To
tal:
0
.35
0
1.0
0
1.0
00
1
.00
1
.00
00
(b)
B
ecau
se b
enze
ne
is t
he
mo
re v
ola
tile
co
mp
on
ent
of
the
feed
, th
e x
and
y c
oo
rdin
ates
wil
l b
e
tho
se o
f b
enze
ne
in t
he
dia
gra
m o
n t
he
nex
t p
age.
.
In m
ole
s, t
he
feed
co
nsi
sts
of:
Co
mp
on
ent
km
ol/
h
Mo
le f
ract
ion
Ben
zen
e 0
.15
4
0.4
4
To
luen
e 0
.19
6
0.5
6
To
tal:
0.3
50
1
.00
Fo
r a
satu
rate
d l
iqu
id f
eed
, th
e q
-lin
e is
ver
tica
l an
d p
asse
s th
rou
gh
x =
0.4
4.
Th
e sl
op
e o
f th
e
rect
ifyin
g o
per
atin
g l
ine,
L/V
, is
ob
tain
ed f
rom
Eq
. (7
-7),
usi
ng t
he
spec
ifie
d r
eflu
x r
atio
= 3
.5,
L/V
= R
/(1
+ R
) =
3.5
/4.5
= 0
.77
8
Fo
r sa
tura
ted
liq
uid
ref
lux
, th
e re
ctif
yin
g o
per
atin
g l
ine
pas
ses
thro
ugh
th
e p
oin
t {0
.97
4,
0.9
74
}.
See
th
e M
cCab
e-T
hie
le c
on
stru
ctio
n o
n t
he
nex
t p
age,
wh
ere
it i
s se
en t
hat
sli
gh
tly m
ore
th
an 1
0
stag
es +
a p
arti
al r
ebo
iler
act
ing a
s an
eq
uil
ibri
um
sta
ge
are
req
uir
ed.
Th
e to
p 5
sta
ges
are
in
th
e
rect
ifyin
g s
ecti
on
.
Ex
erci
se 7
.13
(c
on
tin
ued
) A
na
lysi
s:
(b)
(co
nti
nu
ed)
McC
ab
e-T
hie
le D
iag
ram
Ex
erci
se 7
.14
S
ub
ject
: D
isti
llat
ion
of
a m
ixtu
re o
f b
enze
ne
and
ch
loro
ben
zen
e w
ith
sp
ecif
ied
nu
mb
er o
f
equ
ilib
riu
m s
tages
, b
oil
up
rat
io,
and
ref
lux
rat
io.
Giv
en:
F
eed
is
a sa
tura
ted
liq
uid
of
54
.5 m
ol%
ben
zen
e.
Co
lum
n c
on
tain
s tw
o e
qu
ilib
riu
m
pla
tes
wit
h f
eed
to
th
e b
ott
om
pla
te.
Co
lum
n i
s eq
uip
ped
wit
h t
ota
l co
nd
ense
r an
d p
arti
al
reb
oil
er.
Bo
ilu
p i
s V
/F =
0.8
55
. R
eflu
x r
atio
, L
/V =
0.5
. V
apo
r-li
qu
id e
qu
ilib
riu
m d
ata
giv
en.
Fin
d:
C
om
po
siti
on
s o
f d
isti
llat
e an
d b
ott
om
s, a
ssu
min
g c
on
stan
t m
ola
r o
ver
flo
w.
An
aly
sis:
T
ake
as a
bas
is,
F =
10
0 m
ol/
s.
Th
eref
ore
, v
apo
r gen
erat
ed i
n r
ebo
iler
= 0
.85
5(1
00
)
= 8
5.5
mo
l/s.
S
ince
th
e fe
ed i
s a
satu
rate
d l
iqu
id,
this
vap
or
rate
co
nti
nu
es u
p t
he
colu
mn
to
th
e
con
den
ser.
L
/V =
0.5
, w
hic
h i
s th
e sl
op
e o
f th
e o
per
atin
g l
ine.
T
her
efo
re,
L =
0.5
(85
.5)
= 4
2.7
5
mo
l/s.
T
her
efo
re,
the
dis
till
ate
rate
= 8
5.5
- 4
2.7
5 =
42
.75
mo
l/s.
P
assi
ng t
o t
he
reb
oil
er i
s a
liq
uid
rat
e o
f 4
2.7
5 +
10
0 =
14
2.7
5 m
ol/
s.
Th
e b
ott
om
s ra
te =
14
2.7
5 -
85
.5 =
57
.25
mo
l/s.
T
he
slo
pe
of
the
stri
pp
ing s
ecti
on
op
erat
ing l
ine
is L
V/=
14
2.7
5/8
5.5
= 1
.67
. T
he
q-l
ine
is a
ver
tica
l li
ne
bec
ause
th
e fe
ed i
s a
satu
rate
d l
iqu
id.
To
so
lve
for
the
com
po
siti
on
s o
f th
e d
isti
llat
e
and
bo
tto
ms
on
a M
cCab
e-T
hie
le d
iagra
m,
we
mu
st l
oca
te t
he
op
erat
ing l
ines
to
ob
tain
th
ree
equ
ilib
riu
m s
tages
th
at s
atis
fy a
n o
ver
all
ben
zen
e m
ater
ial
bal
ance
giv
en b
y,
x FF
= 5
4.4
= x
DD
+ x
BB
= 4
2.7
5x D
+ 5
7.2
5x B
(1
)
So
lvin
g E
q.
(1),
x B =
0.9
52
- 0
.74
67
xD
(2)
Th
eref
ore
, an
ap
pro
ach
to
so
lvin
g t
his
ex
erci
se i
s to
ass
um
e a
val
ue
of
x D a
nd
th
en c
om
pu
te t
he
val
ue
of
x B f
rom
Eq
. (2
).
Th
en c
on
stru
ct t
he
McC
abe-
Th
iele
dia
gra
m w
ith
th
e ab
ov
e o
per
atin
g
lin
es a
nd
q-l
ine
to s
ee i
f t
hre
e st
ages
are
req
uir
ed w
ith
th
e fe
ed t
o t
he
seco
nd
pla
te.
See
plo
t b
elo
w,
wh
ere
ben
zen
e m
ole
fra
ctio
ns
are
plo
tted
bec
ause
it
is t
he
mo
re v
ola
tile
com
po
nen
t.
It i
s se
en t
hat
fo
r b
enze
ne,
xD =
0.9
0 a
nd
xB =
0.2
8.
Ex
erci
se 7
.14
(c
on
tin
ued
)
M
cCa
be-
Th
iele
Dia
gra
m
Ex
erci
se 7
.15
Su
bje
ct:
E
ffec
t o
f lo
ss o
f p
late
s in
a d
isti
llat
ion
co
lum
n s
epar
atin
g a
ben
zen
e-to
luen
e m
ixtu
re.
Giv
en:
S
atu
rate
d v
apo
r fe
ed o
f 1
3,6
00
kg/h
of
40
wt%
ben
zen
e an
d 6
0 w
t% t
olu
ene.
C
olu
mn
wit
h 1
4 p
late
s ab
ov
e th
e fe
ed l
oca
tio
n.
Pla
te e
ffic
ien
cy i
s 5
0%
. R
eflu
x r
atio
is
3.5
. P
rev
iou
sly,
wit
h 1
0 p
late
s in
th
e st
rip
pin
g s
ecti
on
, co
lum
n c
ou
ld a
chie
ve
a d
isti
llat
e o
f 9
7 w
t% b
enze
ne
and
a
bo
tto
ms
of
98
wt%
to
luen
e.
Vap
or-
liq
uid
eq
uil
ibri
um
dat
a in
Ex
erci
se 7
.13
.
Ass
um
pti
on
s:
Co
nst
ant
mo
lar
ov
erfl
ow
. T
ota
l co
nd
ense
r an
d p
arti
al r
ebo
iler
.
Fin
d:
(a
) I
f co
lum
n w
ith
10
in
op
erab
le p
late
s ca
n y
ield
a d
isti
llat
e o
f 9
7 w
t% b
enze
ne,
assu
min
g t
hat
we
no
lo
nger
can
ach
iev
e th
e 9
8 w
t% b
ott
om
s p
rod
uct
.
(b
) T
he
dis
till
ate
flo
w r
ate.
(c
) T
he
com
po
siti
on
of
the
bo
tto
ms.
An
aly
sis:
(a)
Fir
st c
on
ver
t th
e fe
ed t
o k
mo
l/h
an
d m
ole
fra
ctio
ns,
usi
ng m
ole
cula
r w
eigh
ts o
f
78
.11
fo
r b
enze
ne
and
92
.13
. T
he
resu
lt i
s:
Co
mp
on
ent
km
ol/
h
Mo
le f
ract
ion
Ben
zen
e 6
9.6
5
0.4
4
To
luen
e 8
8.5
7
0.5
6
T
ota
l:
15
8.2
2
1.0
0
Fo
r a
dis
till
ate
of
97
wt%
ben
zen
e, t
he
mo
le f
ract
ion
fo
r b
enze
ne,
th
e m
ore
vo
lati
le o
f th
e tw
o
com
po
nen
ts,
is,
xD
=
+
=
97
78
11
97
78
11
3
92
13
09
74
.
..
.
Wit
h a
ref
lux
rat
io o
f 3
.5,
fro
m E
q.
(7-7
), t
he
slo
pe
of
the
rect
ifyin
g s
ecti
on
op
erat
ing l
ine
is,
L/V
= R
/(1
+ R
) =
3.5
/4.5
= 0
.77
8
Th
e q
-lin
e is
a h
ori
zon
tal
lin
e at
y =
0.4
4.
Fo
r 1
4 p
late
s w
ith
50
% e
ffic
ien
cy,
the
colu
mn
has
th
e
equ
ival
ent
of
7 e
qu
ilib
riu
m s
tages
+ 1
fo
r th
e p
arti
al r
ebo
iler
.
Th
e M
cCab
e-T
hie
le c
on
stru
ctio
n i
s sh
ow
n o
n t
he
nex
t p
age,
wh
ere
it i
s se
en t
hat
it
is p
oss
ible
to
ob
tain
th
e d
esir
ed d
isti
llat
e co
mp
osi
tio
n.
(b)
and
(c)
F
rom
th
e M
cCab
e-T
hie
le d
iagra
m,
the
mo
le f
ract
ion
of
ben
zen
e in
th
e b
ott
om
s is
x B =
0.2
4.
A
s a
wei
gh
t fr
acti
on
, th
is c
orr
esp
on
ds
to,
02
47
81
1
02
47
81
10
76
92
13
02
11
.(
.)
.(
.)
.(
.)
.+
=w
eigh
t fr
acti
on
or
21
.1 w
t% b
enze
ne
Co
mp
ute
th
e d
isti
llat
e ra
te b
y o
ver
all
mo
lar
mat
eria
l b
alan
ces.
Ov
eral
l to
tal
mas
s b
alan
ce:
1
58
.22
= D
+ B
(1)
Ov
eral
l b
enze
ne
mas
s b
alan
ce:
6
9.6
5 =
0.9
74
D +
0.2
40
B
(2)
So
lvin
g E
qs.
(1
) an
d (
2):
D
= 4
3.1
6 k
mo
l/h
B =
11
5.0
6 k
mo
l/h
By w
eigh
t, D
= 4
3.1
6[0
.97
4(7
8.1
1)
+ 0
.02
6(9
2.1
3)]
= 3
,38
7 k
g/h
Ex
erci
se 7
.15
(c
on
tin
ued
) A
na
lysi
s:
(a)
(co
nti
nu
ed)
McC
ab
e-T
hie
le D
iag
ram
Ex
erci
se 7
.16
S
ub
ject
: E
ffec
t o
n t
he
sep
arat
ion
of
A f
rom
B b
y d
isti
llat
ion
wh
en 3
of
7 t
heo
reti
cal
pla
tes
rust
an
d d
rop
to
th
e b
ott
om
of
the
colu
mn
.
Giv
en:
. C
olu
mn
has
7 t
heo
reti
cal
pla
tes
+ p
arti
al r
ebo
iler
.
Sat
ura
ted
liq
uid
fee
d o
f 1
00
km
ol/
h
of
50
mo
l% A
is
sen
t to
pla
te 5
fro
m t
he
top
. D
isti
llat
e co
nta
ins
90
mo
l% A
. T
he
L/V
= 0
.75
in
the
rect
ifyin
g s
ecti
on
. V
apo
r-li
qu
id e
qu
ilib
riu
m d
ata.
Ass
um
pti
on
s:
C
on
stan
t m
ola
r o
ver
flo
w.
To
tal
con
den
ser.
Fin
d:
Cas
e 1
: C
olu
mn
bef
ore
th
e 3
pla
tes
rust
an
d d
rop
.
(a)
Co
mp
osi
tio
n o
f th
e b
ott
om
s p
rod
uct
.
(b)
Th
e L
/V i
n t
he
stri
pp
ing s
ecti
on
.
(c)
Th
e k
mo
l/h
of
bo
tto
ms
pro
du
ct.
Cas
e 2
:
If p
late
s 5
, 6
, an
d 7
co
un
ted
do
wn
fro
m t
he
top
are
lo
st:
(a)
Co
mp
osi
tio
n o
f b
ott
om
s p
rod
uct
.
Cas
e 3
:
Sam
e as
Cas
e 2
, ex
cep
t re
pla
ce r
eflu
x w
ith
th
e sa
me
mo
lar
flo
w r
ate
of
pro
du
ct
con
tain
ing 8
0 m
ol%
A:
(a)
Co
mp
osi
tio
n o
f d
isti
llat
e.
(b)
Co
mp
osi
tio
n o
f b
ott
om
s.
An
aly
sis:
C
ase
1:
Ap
ply
th
e M
cCab
e-T
hie
le m
eth
od
in
ter
ms
of
com
po
nen
t A
, w
hic
h i
s
mo
re v
ola
tile
th
an B
. T
he
rect
ifyin
g s
ecti
on
op
erat
ing l
ine
pas
ses
thro
ugh
[0
.90
, 0
.90
] w
ith
a
slo
pe
of
0.7
5.
Th
e q
-lin
e is
ver
tica
l th
rou
gh
x =
0.5
0.
Ste
p o
ff 4
sta
ges
in
th
e re
ctif
yin
g s
ecti
on
.
Th
en,
by t
rial
an
d e
rro
r, f
ind
an
xB w
ith
a c
orr
esp
on
din
g s
trip
pin
g s
ecti
on
op
erat
ing l
ine
that
giv
es 4
eq
uil
ibri
um
sta
ges
in
th
e st
rip
pin
g s
ecti
on
. T
he
resu
lt i
s sh
ow
n o
n t
he
foll
ow
ing p
age,
wh
ere:
(a
) B
ott
om
s co
nta
ins
7 m
ol%
A a
nd
93
mo
l% B
.
(b
) T
he
slo
pe
of
the
stri
pp
ing s
ecti
on
op
erat
ing l
ine
fro
m t
he
coo
rdin
ates
of
the
lin
e is
:
{[0
.90
0.7
5(0
.90
0.5
0]
0.0
7}/(
0.5
0/
1.2
00
7)
3.
=−
−−
−=
LV
(c
) B
y m
ater
ial
bal
ance
s, F
= D
+ B
an
d
Fx F
= 5
0 =
0.9
D +
0.0
7B
. S
olv
ing t
hes
e tw
o
equ
atio
ns,
d
isti
llat
e fl
ow
rat
e =
51
.8 k
mo
l/h
an
d b
ott
om
s fl
ow
rat
e =
48
.2 k
mo
l/h
C
ase
2:
W
e n
ow
hav
e 4
eq
uil
ibri
um
sta
ges
an
d a
par
tial
reb
oil
er,
wit
h t
he
feed
bei
ng
sen
t to
th
e re
bo
iler
. A
ssu
me
that
uti
lity
rat
es a
re s
uch
th
at L
/V a
nd
L
V/ar
e th
e sa
me
as i
n C
ase
1.
Th
en,
on
th
e M
cCab
e-T
hie
le d
iagra
m,
the
val
ues
of
x D a
nd
xB m
ust
sh
ift
so t
hat
5 s
tages
are
step
ped
off
, w
ith
th
e fi
fth
, w
hic
h i
s th
e re
bo
iler
, in
ters
ecti
ng t
he
stri
pp
ing s
ecti
on
op
erat
ing l
ine
at t
he
45
o l
ine.
T
his
is
sho
wn
on
th
e M
cCab
e-T
hie
le d
iagra
m o
n t
he
foll
ow
ing p
age.
(a)
Fro
m t
his
dia
gra
m,
the
mo
le f
ract
ion
s o
f b
enze
ne
in t
he
dis
till
ate
and
bo
tto
ms
are
0.8
0 a
nd
0.2
1,
resp
ecti
vel
y.
Cas
e 3
:
Sin
ce t
he
dis
till
ate
com
po
siti
on
in
Cas
e 2
is
80
mo
l% b
enze
ne,
th
e re
sult
s w
ou
ld b
e th
e
sam
e as
Cas
e 2
if
an 8
0 m
ol%
ben
zen
e st
ream
fro
m a
no
ther
co
lum
n w
ere
use
d a
s re
flu
x.
Ex
erci
se 7
.16
(c
on
tin
ued
)
A
na
lysi
s:
Cas
e 1
(c
on
tin
ued
)
Ex
erci
se 7
.16
(c
on
tin
ued
)
A
na
lysi
s:
Cas
e 2
(c
on
tin
ued
)
Ex
erci
se 7
.17
S
ub
ject
: D
isti
llat
ion
of
a m
ixtu
re o
f b
enze
ne
and
to
luen
e w
ith
dif
fere
nt
feed
co
nd
itio
ns.
Giv
en:
C
olu
mn
wit
h 7
eq
uil
ibri
um
pla
tes,
to
tal
con
den
ser,
an
d p
arti
al r
ebo
iler
. F
eed
is
50
mo
l% b
enze
ne
and
50
mo
l% t
olu
ene.
O
per
atio
n a
t 1
01
kP
a to
pro
du
ce a
dis
till
ate
of
96
mo
l%
ben
zen
e.
Eq
uil
ibri
um
dat
a fr
om
Ex
erci
se 7
.13
.
Ass
um
pti
on
s:
Co
nst
ant
mo
lar
ov
erfl
ow
. U
se a
bas
is o
f 1
00
mo
l/s
for
the
feed
.
Fin
d:
(a
) F
or
a sa
tura
ted
liq
uid
fee
d s
ent
to t
ray 5
fro
m t
he
top
, (1
) m
inim
um
ref
lux
rat
io,
R =
L/D
, (2
) b
ott
om
s co
mp
osi
tio
n f
or
twic
e th
e m
inim
um
ref
lux
rat
io,
and
(3
) m
ole
s o
f p
rod
uct
s p
er
10
0 m
ole
s o
f fe
ed.
(b
) S
ame
as (
a) e
xce
pt
feed
is
satu
rate
d v
apo
r to
tra
y 5
fro
m t
he
top
.
(c
) F
or
a sa
tura
ted
vap
or
feed
to
th
e re
bo
iler
an
d a
ref
lux
rat
io,
L/V
, o
f 0
.9,
det
erm
ine,
(1
)
bo
tto
ms
com
po
siti
on
an
d (
2)
mo
les
of
pro
du
cts
per
10
0 m
ole
s o
f fe
ed.
An
aly
sis:
(a
)
(1)
Fo
r a
satu
rate
d l
iqu
id f
eed
, m
inim
um
ref
lux
co
rres
po
nd
s to
a p
inch
po
int
loca
ted
at
the
inte
rsec
tio
n o
f a
ver
tica
l q
-lin
e p
assi
ng t
hro
ugh
xF =
0.5
an
d t
he
equ
ilib
riu
m c
urv
e.
Fro
m t
he
equ
ilib
riu
m d
ata,
th
is i
nte
rsec
tio
n i
s at
y =
0.7
2 a
nd
x =
0.5
. T
hen
, th
e sl
op
e o
f th
e re
ctif
yin
g
sect
ion
op
erat
ing l
ine,
(L
/V) m
in i
s (0
.96
- 0
.72
)/(0
.96
- 0
.50
) =
0.5
22
. F
rom
a r
earr
angem
ent
of
Eq
. (7
-7),
Rm
in =
(L
/V) m
in /
[1 -
(L
/V) m
in ]
= 0
.52
2/(
1 -
0.5
22
) =
1.0
92
.
(2)
Ref
lux
rat
io =
2(1
.09
2)
= 2
.18
. F
rom
Eq
. (7
-7),
th
e sl
op
e o
f th
e re
ctif
yin
g s
ecti
on
op
erat
ing l
ine
= L
/V =
R/(
1 +
R)
= 2
.18
/3.1
8 =
0.6
86
. T
o d
eter
min
e th
e b
ott
om
s co
mp
osi
tio
n,
use
a M
cCab
e-T
hie
le d
iagra
m i
n t
erm
s o
f b
enze
ne,
th
e m
ore
vo
lati
le c
om
po
nen
t.
Th
e q
-lin
e an
d
the
rect
ifyin
g s
ecti
on
op
erat
ing l
ine
are
fix
ed a
nd
4 t
rays
are
step
ped
off
fro
m t
he
top
, st
arti
ng a
t
the
dis
till
ate
mo
le f
ract
ion
fo
r b
enze
ne,
xD ,
of
0.9
6.
Th
en,
the
stri
pp
ing s
ecti
on
op
erat
ing l
ine
is
po
siti
on
ed b
y t
rial
an
d e
rro
r so
th
at 3
mo
re s
tages
plu
s th
e re
bo
iler
sta
ge
are
step
ped
off
to
arr
ive
at t
he
po
int
wh
ere
the
assu
med
lo
cati
on
of
the
stri
pp
ing s
ecti
on
op
erat
ing l
ine
inte
rsec
ts t
he
45
o
lin
e.
Th
e re
sult
is
sho
wn
on
th
e n
ext
pag
e w
her
e it
is
seen
th
at x
B =
0.1
8.
(3)
Th
e p
rod
uct
s ar
e n
ow
co
mp
ute
d b
y o
ver
all
mat
eria
l b
alan
ces:
F
= 1
00
= D
+ B
an
d
50
= x
DD
+ x
BB
= 0
.96
D +
0.1
8B
. S
olv
ing t
hes
e tw
o e
qu
atio
ns,
D =
4
1.0
mo
l/1
00
mo
l fe
ed a
nd
B =
59
.0 m
ol/
10
0 m
ol
feed
.
Ex
erci
se 7
.17
(c
on
tin
ued
) A
na
lysi
s:
(a)
(co
nti
nu
ed)
(b
)
(
1)
Fo
r a
satu
rate
d v
apo
r fe
ed,
min
imu
m r
eflu
x c
orr
esp
on
ds
to a
pin
ch p
oin
t lo
cate
d a
t
the
inte
rsec
tio
n o
f a
ho
rizo
nta
l q
-lin
e p
assi
ng t
hro
ugh
xF =
y =
0.5
an
d t
he
equ
ilib
riu
m c
urv
e.
Fro
m t
he
equ
ilib
riu
m d
ata,
th
is i
nte
rsec
tio
n i
s at
y =
0.5
0 a
nd
x =
0.2
93
. T
hen
, th
e sl
op
e o
f th
e
rect
ifyin
g s
ecti
on
op
erat
ing l
ine,
(L
/V) m
in i
s (0
.96
- 0
.50
)/(0
.96
- 0
.29
3)
= 0
.69
0.
Fro
m a
rear
ran
gem
ent
of
Eq
. (7
-7),
Rm
in =
(L
/V) m
in /
[1 -
(L
/V) m
in ]
= 0
.69
/(1
- 0
.69
) =
2.2
3.
(2)
Ref
lux
rat
io =
2(2
.23
) =
4.4
6.
Fro
m E
q.
(7-7
), t
he
slo
pe
of
the
rect
ifyin
g s
ecti
on
op
erat
ing l
ine
= L
/V =
R/(
1 +
R)
= 4
.46
/5.4
6 =
0.8
17
. T
o d
eter
min
e th
e b
ott
om
s co
mp
osi
tio
n,
use
a M
cCab
e-T
hie
le d
iagra
m i
n t
erm
s o
f b
enze
ne,
th
e m
ore
vo
lati
le c
om
po
nen
t.
Th
e q
-lin
e an
d
the
rect
ifyin
g s
ecti
on
op
erat
ing l
ine
are
fix
ed a
nd
4 t
rays
are
step
ped
off
fro
m t
he
top
, st
arti
ng a
t
the
dis
till
ate
mo
le f
ract
ion
fo
r b
enze
ne,
xD ,
of
0.9
6.
Th
en,
the
stri
pp
ing s
ecti
on
op
erat
ing l
ine
is
po
siti
on
ed b
y t
rial
an
d e
rro
r so
th
at 3
mo
re s
tages
plu
s th
e re
bo
iler
sta
ge
are
step
ped
off
to
arr
ive
at t
he
po
int
wh
ere
the
assu
med
lo
cati
on
of
the
stri
pp
ing s
ecti
on
op
erat
ing l
ine
inte
rsec
ts t
he
45
o
lin
e.
Th
e re
sult
is
sho
wn
bel
ow
, w
her
e it
is
seen
th
at x
B =
0.0
8.
Ex
erci
se 7
.17
(c
on
tin
ued
) A
na
lysi
s:
(b)
(co
nti
nu
ed
(3
) T
he
pro
du
cts
are
no
w c
om
pu
ted
by o
ver
all
mat
eria
l b
alan
ces:
F
= 1
00
= D
+ B
an
d
50
= x
DD
+ x
BB
= 0
.96
D +
0.0
8B
. S
olv
ing t
hes
e tw
o e
qu
atio
ns,
D =
4
7.7
mo
l/1
00
mo
l fe
ed a
nd
B =
52
.3 m
ol/
10
0 m
ol
feed
.
Ex
erci
se 7
.17
(c
on
tin
ued
) A
na
lysi
s:
(co
nti
nu
ed)
(c)
(
1)
A s
atu
rate
d v
apo
r fe
ed i
s fe
d t
o t
he
reb
oil
er.
Th
e sl
op
e o
f th
e re
ctif
yin
g s
ecti
on
op
erat
ing l
ine,
(L
/V),
is
0.9
. T
o d
eter
min
e th
e b
ott
om
s co
mp
osi
tio
n,
use
a M
cCab
e-T
hie
le
dia
gra
m i
n t
erm
s o
f b
enze
ne,
th
e m
ore
vo
lati
le c
om
po
nen
t.
Th
e q
-lin
e an
d t
he
rect
ifyin
g s
ecti
on
op
erat
ing l
ine
are
fix
ed a
nd
7 t
rays
are
step
ped
off
fro
m t
he
top
, s
tart
ing a
t th
e d
isti
llat
e m
ole
frac
tio
n f
or
ben
zen
e, x
D ,
of
0.9
6.
Th
en,
the
stri
pp
ing s
ecti
on
op
erat
ing l
ine
is p
osi
tio
ned
by t
rial
and
err
or
so t
hat
th
e re
bo
iler
sta
ge
is s
tep
ped
off
to
arr
ive
at t
he
po
int
wh
ere
the
assu
med
lo
cati
on
of
the
stri
pp
ing s
ecti
on
op
erat
ing l
ine
inte
rsec
ts t
he
45
o l
ine.
T
he
resu
lt i
s sh
ow
n b
elo
w,
wh
ere
it
is s
een
th
at x
B =
0.0
7.
(2)
Th
e p
rod
uct
s ar
e n
ow
co
mp
ute
d b
y o
ver
all
mat
eria
l b
alan
ces:
F
= 1
00
= D
+ B
an
d
50
= x
DD
+ x
BB
= 0
.96
D +
0.0
7B
. S
olv
ing t
hes
e tw
o e
qu
atio
ns,
D =
4
8.3
mo
l/1
00
mo
l fe
ed a
nd
B =
51
.7 m
ol/
10
0 m
ol
feed
.
Ex
erci
se 7
.18
S
ub
ject
: C
on
ver
sio
n o
f a
dis
till
atio
n c
olu
mn
to
a r
ebo
iled
str
ipp
er t
o o
bta
in v
ery p
ure
tolu
ene
fro
m a
mix
ture
of
ben
zen
e an
d t
olu
ene
at 1
01
kP
a.
Giv
en:
A
co
lum
n w
ith
8 t
heo
reti
cal
pla
tes,
a t
ota
l co
nd
ense
r, a
nd
a p
arti
al r
ebo
iler
. F
eed
con
tain
s 3
6 m
ol%
ben
zen
e an
d 6
4 m
ol%
to
luen
e.
Reb
oil
er p
rod
uce
s 1
00
km
ol/
h o
f v
apo
r.
To
ob
tain
nea
rly p
ure
to
luen
e b
ott
om
s, f
eed
is
intr
od
uce
d t
o t
he
top
pla
te a
s a
satu
rate
d l
iqu
id,
wit
h
no
ref
lux
. V
apo
r-li
qu
id e
qu
ilib
riu
m d
ata
are
in E
xer
cise
7.1
3.
Ass
um
pti
on
s:
Co
nst
ant
mo
lar
ov
erfl
ow
.
Fin
d:
(a)
Min
imu
m f
eed
rat
e an
d c
orr
esp
on
din
g b
ott
om
s co
mp
osi
tio
n.
(b)
Bo
tto
ms
rate
an
d c
om
po
siti
on
fo
r a
feed
rat
e 2
5%
ab
ov
e th
e m
inim
um
.
An
aly
sis:
(a
)
T
he
min
imu
m f
eed
rat
e co
rres
po
nd
s to
a r
ate
equ
al t
o t
he
bo
ilu
p r
ate
so a
s to
giv
e an
LV/
= 1
.0.
Th
us,
th
e m
inim
um
fee
d r
ate
= 1
00
km
ol/
h.
Un
der
th
ese
con
dit
ion
s, n
o b
ott
om
s
pro
du
ct i
s w
ith
dra
wn
an
d t
he
reb
oil
er p
erfo
rms
as a
to
tal
reb
oil
er.
Th
e v
apo
r le
avin
g t
he
top
of
the
colu
mn
has
th
e sa
me
com
po
siti
on
as
the
feed
. T
her
efo
re,
we
con
sid
er o
nly
a t
ota
l o
f 8
equ
ilib
riu
m s
tages
.
In
th
e M
cCab
e-T
hie
le d
iagra
m b
elo
w,
the
stri
pp
ing s
ecti
on
op
erat
ing l
ine
is c
oin
cid
ent
wit
h t
he
45
o l
ine.
T
he
8 s
tages
are
ste
pp
ed o
ff f
rom
th
e to
p a
t y
= 0
.36
an
d x
= 0
.36
. T
he
mo
le
frac
tio
n o
f b
enze
ne
in t
he
reb
oil
er i
s fo
un
d t
o b
e 0
.00
8 f
rom
th
e lo
w c
on
cen
trat
ion
reg
ion
plo
t.
Th
eref
ore
, th
e co
rres
po
nd
ing t
olu
ene
mo
le f
ract
ion
= 0
.99
2,
wh
ich
is
qu
ite
pu
re.
No
te t
hat
2 d
iagra
ms
bel
ow
are
use
d,
wit
h t
he
seco
nd
, c
ov
erin
g t
he
stag
es a
t th
e b
ott
om
of
the
colu
mn
in
th
e lo
w c
on
cen
trat
ion
reg
ion
. T
o o
bta
in a
ccu
racy
in
th
is l
ow
-en
d r
egio
n,
the
vap
or-
liq
uid
eq
uil
ibri
um
dat
a fo
r x
= 0
.1 a
nd
x =
0.2
wer
e fi
tted
to
a q
uad
rati
c eq
uat
ion
pas
sin
g t
hro
ugh
the
ori
gin
, w
ith
th
e re
sult
, y
= 2
.35
x -
2.5
x2 .
Ex
erci
se 7
.18
(c
on
tin
ued
) A
na
lysi
s:
(a)
(c
on
tin
ued
)
Ex
erci
se 7
.18
(c
on
tin
ued
) A
na
lysi
s:
(co
nti
nu
ed)
(b)
F =
Fee
d r
ate
= L
= 1
.25
(10
0)
= 1
25
km
ol/
h.
V=
Vap
or
rate
= 1
00
km
ol/
h.
Th
eref
ore
,
wit
h n
o c
on
den
ser
and
co
nst
ant
mo
lar
ov
erfl
ow
, B
= F
-V
= 1
25
- 1
00
= 2
5 k
mo
l/h
. T
he
slo
pe
of
the
stri
pp
ing s
ecti
on
op
erat
ing l
ine
= L
/V=
12
5/1
00
= 1
.25
. T
he
q-l
ine
is v
erti
cal
for
a
satu
rate
d l
iqu
id f
eed
, p
assi
ng t
hro
ugh
xF =
0.3
6.
Th
e st
rip
pin
g s
ecti
on
op
erat
ing l
ine
is
po
siti
on
ed b
y t
rial
an
d e
rro
r so
th
at 8
+ 1
eq
uil
ibri
um
sta
ges
wil
l b
e st
epp
ed o
ff.
Bec
ause
par
t (a
)
sho
ws
that
a v
ery l
ow
mo
le f
ract
ion
of
ben
zen
e is
ob
tain
ed i
n t
he
bo
tto
ms,
it
is s
usp
ecte
d t
hat
th
e
op
erat
ing l
ine
wil
l in
ters
ect
the
45
o l
ine
alm
ost
at
the
ori
gin
. I
f th
is w
ere
tru
e, t
hen
th
e o
per
atin
g
lin
e, w
ith
a s
lop
e o
f 1
.25
, w
ou
ld i
nte
rsec
t th
e v
erti
cal
q-l
ine
at 1
.25
(0.3
6)
= 0
.45
. U
se t
his
as
a
firs
t ap
pro
xim
atio
n a
nd
ad
just
it
do
wn
war
d u
nti
l o
nly
9 s
tages
can
be
step
ped
off
. T
he
fin
al
resu
lt i
s sh
ow
n i
n t
he
two
plo
ts o
n t
he
nex
t p
age,
wh
ere
the
seco
nd
plo
t is
fo
r th
e lo
w
con
cen
trat
ion
reg
ion
. A
s se
en,
the
mo
le p
erce
nt
of
ben
zen
e in
th
e b
ott
om
s =
0.0
04
, giv
ing 9
9.6
mo
l% t
olu
ene
in t
he
bo
tto
ms.
T
he
ov
erh
ead
vap
or
con
tain
s 0
.44
9 m
ole
fra
ctio
n b
enze
ne.
B
y
mat
eria
l b
alan
ces,
F =
12
5 =
D +
B
and
0.3
6F
= 0
.44
9D
+ 0
.00
4B
, D
= 1
00
.0 a
nd
B
= 2
5.0
km
ol/
h.
Ex
erci
se 7
.18
(c
on
tin
ued
) A
na
lysi
s:
(b
) (
con
tin
ued
)
Lo
w-c
on
cen
tra
tio
n R
egio
n
Ex
erci
se 7
.19
S
ub
ject
: N
orm
al a
nd
ab
no
rmal
op
erat
ion
of
a d
isti
llat
ion
co
lum
n s
epar
atin
g a
met
han
ol
-
wat
er m
ixtu
re a
t 1
01
kP
a.
Giv
en:
C
olu
mn
wit
h 7
th
eore
tica
l p
late
s, a
to
tal
con
den
ser,
an
d a
par
tial
reb
oil
er.
A f
eed
of
10
0 k
mo
l/h
of
50
mo
l% m
eth
ano
l in
wat
er i
s se
nt
to p
late
3 f
rom
th
e b
ott
om
. D
uri
ng n
orm
al
op
erat
ion
, d
isti
llat
e is
90
mo
l% m
eth
ano
l an
d b
ott
om
s is
5 m
ol%
met
han
ol,
wit
h a
ref
lux
rat
e o
f
1 m
ole
per
mo
le d
isti
llat
e.
Du
rin
g a
bn
orm
al o
per
atio
n,
the
foll
ow
ing d
ata
are
ob
tain
ed:
Str
eam
k
mo
l/h
m
ol%
met
ha
no
l
Fee
d
10
0
51
Bo
tto
ms
62
1
2
Dis
till
ate
53
8
0
Ref
lux
9
4
-
Vap
or-
liq
uid
eq
uil
ibri
um
dat
a ar
e giv
en a
t 1
01
kP
a, w
her
e m
eth
ano
l is
th
e m
ore
vo
lati
le s
pec
ies.
Ass
um
pti
on
s:
Co
nst
ant
mo
lar
ov
erfl
ow
.
Fin
d:
M
ost
pro
bab
le c
ause
fo
r ab
no
rmal
op
erat
ion
.
R
eco
mm
end
ed f
urt
her
tes
ts.
If
9
0 m
ol%
met
han
ol
dis
till
ate
cou
ld b
e o
bta
ined
by i
ncr
easi
ng t
he
refl
ux
rat
io f
or
a
con
stan
t v
apo
r ra
te.
An
aly
sis:
F
irst
det
erm
ine
wh
eth
er t
he
no
rmal
op
erat
ion
can
be
ver
ifie
d b
y t
he
McC
abe-
Th
iele
met
ho
d.
Wit
h L
/D =
R =
1,
fro
m E
q.
(7-7
), t
he
slo
pe
of
the
rect
ifyin
g o
per
atin
g l
ine
= L
/V =
R/(
1 +
R)
= 1
/2 =
0.5
. A
lso
, x F
= 0
.5,
x D =
0.9
0,
and
xB =
0.0
5.
W
hat
is
no
t k
no
wn
is
the
ph
ase
con
dit
ion
of
the
feed
. I
f a
satu
rate
d l
iqu
id f
eed
is
assu
med
, giv
ing a
ver
tica
l q
-lin
e as
sh
ow
n i
n t
he
plo
t b
elo
w,
ste
pp
ing s
tages
up
fro
m t
he
bo
tto
m,
wit
h t
he
feed
sta
ge
to p
late
3 f
rom
th
e b
ott
om
, le
ss t
han
2 t
heo
reti
cal
pla
tes
are
nee
ded
in
th
e
rect
ifyin
g s
ecti
on
, w
hil
e 4
are
pre
sen
t.
Th
e co
nst
ruct
ion
is
sho
wn
on
th
e n
ext
pag
e.
Th
eref
ore
, it
ap
pea
rs t
hat
th
e fe
ed i
s n
ot
a sa
tura
ted
liq
uid
, b
ut
is p
arti
ally
vap
ori
zed
.
Ex
erci
se 7
.19
(c
on
tin
ued
) A
na
lysi
s:
No
rmal
Op
erat
ion
(co
nti
nu
ed)
B
y t
rial
an
d e
rro
r, u
sin
g q
-lin
es o
f v
ario
us
slo
pes
, th
e fo
llo
win
g M
cCab
e-T
hie
le d
iagra
m i
s
con
sist
ent
wit
h t
he
giv
en d
ata.
It
sh
ow
s a
q-l
ine
wit
h a
slo
pe
of
-0.3
4.
s
lop
e =
/(
1)
T
her
efo
re,
slo
pe/
(slo
pe-
1)=
-0
m
.34
/(-0
.34
-1.0
)=0
.25
Fro
m E
q.
(7-1
9o
lar
frac
tio
n v
apo
rize
),
= 1
d0
.7.
51
02
5
−
=
−=
−=
q
q
Ex
erci
se 7
.19
(c
on
tin
ued
) A
na
lysi
s:
No
rmal
op
erat
ion
(c
on
tin
ued
)
T
he
mat
eria
l b
alan
ce f
or
the
no
rmal
op
erat
ion
is
as f
oll
ow
s, u
sin
g t
he
ov
eral
l b
alan
ces,
F =
10
0 =
D +
B
and
0
.5F
= 0
.5(1
00
) =
50
= x
DD
+ x
BB
= 0
.90
D +
0.0
5B
.
Str
eam
k
mo
l/h
m
ol%
met
ha
no
l
Fee
d
10
0
50
Bo
tto
ms
47
.06
5
Dis
till
ate
52
.94
9
0
Ref
lux
5
2.9
4
90
Ex
erci
se 7
.19
(c
on
tin
ued
) A
na
lysi
s:
Ab
no
rmal
op
erat
ion
F
or
the
abn
orm
al o
per
atio
n,
firs
t ch
eck
th
e o
ver
all
tota
l m
ater
ial
bal
ance
usi
ng t
he
giv
en
dat
a.
F =
10
0 k
mo
l/h
.
D +
B =
53
+ 6
2 =
11
5 k
mo
l/h
. T
her
efo
re,
it a
pp
ears
th
at w
e h
ave
11
5 -
10
0 =
15
km
ol/
h m
ore
flo
w o
ut
of
the
dis
till
atio
n s
yst
em.
No
w c
hec
k t
he
met
han
ol
ov
eral
l
mat
eria
l b
alan
ce u
sin
g t
he
giv
en d
ata.
M
eth
ano
l fl
ow
rat
e in
= 0
.51
(10
0)
= 5
1 k
mo
l/h
. M
eth
ano
l
flo
w r
ate
ou
t =
0.8
0(5
3)
+ 0
.12
(62
) =
49
.84
km
ol/
h.
Th
eref
ore
, th
e m
eth
ano
l b
alan
ce i
s cl
ose
,
wit
h o
nly
ab
ou
t a
2%
dis
crep
ancy
. N
ow
ch
eck
th
e w
ater
ov
eral
l m
ater
ial
bal
ance
usi
ng t
he
giv
en
dat
a.
Wat
er f
low
in
= 0
.49
(10
0)
= 4
9 k
mo
l/h
. W
ater
flo
w o
ut
= 0
.20
(53
) +
0.8
8(6
2)
= 6
5.1
6
km
ol/
h.
Th
eref
ore
, w
e h
ave
65
.16
- 4
9 =
16
.16
km
ol/
h m
ore
wat
er o
ut
than
in
. T
his
is
a
sign
ific
ant
dis
crep
ancy
. I
t ap
pea
rs c
erta
in t
hat
wat
er i
s le
akin
g i
nto
th
e d
isti
llat
ion
syst
em.
Tw
o
po
ssib
ilit
ies
are:
(1
) le
akag
e o
f co
nd
ense
r co
oli
ng w
ater
in
to t
he
con
den
sate
, o
r (2
) le
akag
e o
f
reb
oil
er s
team
in
to t
he
bo
ilu
p v
apo
r.
A r
ebo
iler
ste
am l
eak
may
no
t b
e se
rio
us
bec
ause
th
e st
eam
mig
ht
no
t get
to
th
e to
p o
f th
e co
lum
n t
o d
ilu
te t
he
met
han
ol
pro
du
ct.
A c
on
den
ser
coo
lin
g w
ater
leak
co
uld
be
ver
y s
erio
us
bec
ause
par
t o
f it
wo
uld
en
d u
p i
n t
he
dis
till
ate,
th
ereb
y d
ilu
tin
g t
he
met
han
ol
pro
du
ct.
Bec
ause
of
the
imp
ure
met
han
ol
dis
till
ate
for
the
abn
orm
al o
per
atio
n,
it
app
ears
th
at a
co
nd
ense
r co
oli
ng w
ater
lea
k i
s th
e fa
ult
. C
hec
k t
his
nex
t.
W
e n
ote
th
at t
he
dis
till
ate
flo
w r
ate
for
the
abn
orm
al o
per
atio
n i
s al
mo
st e
xac
tly t
he
sam
e
as t
hat
fo
r th
e n
orm
al o
per
atio
n.
A f
low
rat
e eq
ual
to
th
at o
f h
e le
akag
e p
asse
s o
ut
the
bo
tto
m o
f
the
colu
mn
. I
n n
orm
al o
per
atio
n,
the
wat
er p
assi
ng o
ut
in t
he
dis
till
ate
= 0
.1(5
3)
= 5
.3 k
mo
l/h
,
wh
ile
for
the
abn
orm
al o
per
atio
n,
the
wat
er p
assi
ng o
ut
in t
he
dis
till
ate
= 0
.2(5
3)
= 1
0.6
km
ol/
h.
Th
us,
an
ad
dit
ion
al 5
.3 k
mo
l/h
of
wat
er l
eav
es i
n t
he
dis
till
ate.
F
or
the
abn
orm
al o
per
atio
n,
the
ov
erh
ead
vap
or
rate
= 5
3 +
94
= 1
47
km
ol/
h a
nd
, th
eref
ore
, 5
3/1
47
x 1
00
% =
36
% o
f th
e
ov
erh
ead
vap
or
(to
tal
con
den
sate
) is
dis
till
ate.
T
hu
s, i
f 1
5 k
mo
l/h
of
wat
er l
eak
ed i
nto
th
e
ov
erh
ead
vap
or,
th
en,
we
wo
uld
ex
pec
t 0
.36
(15
) =
5.4
km
ol/
h w
ou
ld b
e ex
pec
ted
to
lea
ve
wit
h
the
dis
till
ate.
T
his
co
mp
ares
ver
y w
ell
wit
h t
he
5.3
km
ol/
h a
dd
itio
nal
wat
er c
alcu
late
d a
bo
ve
by
mat
eria
l b
alan
ce.
If
the
deg
ree
of
frac
tio
nat
ion
wit
hin
th
e co
lum
n i
s ab
ou
t th
e sa
me
as f
or
the
no
rmal
op
erat
ion
, it
co
uld
be
con
clu
ded
th
at a
co
nd
ense
r co
oli
ng w
ater
lea
k i
s to
bla
me.
T
o c
hec
k t
he
coo
lin
g w
ater
lea
k,
cou
ld m
eter
th
e co
oli
ng w
ater
in
an
d o
ut
of
the
con
den
ser
and
see
if
ther
e is
a d
iffe
ren
ce.
If
th
e v
apo
r ra
te i
s k
ept
con
stan
t an
d t
he
refl
ux
rat
e is
in
crea
sed
, th
en t
he
dis
till
ate
rate
mu
st b
e d
ecre
ased
. A
ssu
me
a v
apo
r ra
te o
f 1
47
km
ol/
h,
wit
h 3
0 k
mo
l/h
to
dis
till
ate
and
11
7
km
ol/
h t
o r
eflu
x.
Th
en,
30
/11
7 x
10
0%
= 2
5.6
% o
f th
e o
ver
hea
d v
apo
r is
dis
till
ate.
T
her
efo
re,
the
wat
er l
eak
to
th
e d
isti
llat
e w
ou
ld b
e 0
.25
6(1
5)
= 3
.84
km
ol/
h.
If
the
frac
tio
nat
ion
wer
e
oth
erw
ise
the
sam
e as
fo
r n
orm
al o
per
atio
n s
o t
hat
th
e o
ver
hea
d v
apo
r w
as 9
0 m
ol%
met
han
ol,
the
dil
uti
on
wit
h l
eak
age
wo
uld
res
ult
in
0.1
(30
- 3
.84
) +
3.8
4 =
6.4
6 k
mo
l/h
of
wat
er i
n 3
0
km
ol/
h.
Th
us,
met
han
ol
pu
rity
= (
30
- 6
.46
)/3
0 x
10
0%
= 7
8.5
mo
l%.
Ho
wev
er,
the
hig
her
refl
ux
rat
io w
ou
ld i
ncr
ease
th
e fr
acti
on
atio
n,
so a
s to
in
crea
se t
he
pu
rity
ab
ov
e th
is v
alu
e.
A
furt
her
in
crea
se i
n f
ract
ion
atio
n c
ou
ld b
e ac
hie
ved
, if
th
e fe
ed w
ere
con
den
sed
to
a s
atu
rate
d
liq
uid
an
d a
dd
itio
nal
hea
t w
as t
ran
sfer
red
in
th
e re
bo
iler
. B
ut,
ev
en i
f a
pu
re m
eth
ano
l o
ver
hea
d
vap
or
wer
e ac
hie
ved
, th
e m
eth
ano
l p
uri
ty a
fter
dil
uti
on
wit
h t
he
wat
er l
eak
age
wo
uld
be
:
(30
- 3
.84
)/3
0 x
10
0%
= 8
7.2
mo
l% m
eth
ano
l.
Mu
st e
lim
inat
e th
e le
ak.
Ex
erci
se 7
.20
S
ub
ject
: E
ffec
t o
n r
eflu
x a
nd
bo
ilu
p c
om
po
siti
on
s o
f re
du
cin
g t
he
feed
rat
e to
a d
isti
llat
ion
colu
mn
wh
en t
he
refl
ux
an
d b
oil
up
rat
e ar
e h
eld
co
nst
ant
Giv
en:
C
olu
mn
wit
h 3
th
eore
tica
l p
late
s, a
to
tal
con
den
ser,
an
d a
par
tial
reb
oil
er.
Fee
d i
s a
satu
rate
d l
iqu
id o
f 5
0 m
ol%
A a
nd
50
mo
l% B
, fe
d t
o t
he
bo
tto
m t
ray.
A
t a
feed
rat
e o
f 1
00
km
ol/
h,
des
ired
pro
du
cts
of
dis
till
ate
wit
h 9
0 m
ol%
A a
nd
bo
tto
ms
of
20
mo
l% A
can
be
ach
iev
ed,
wh
en a
ref
lux
co
rres
po
nd
ing t
o L
/V =
0.7
5 i
s u
sed
. R
elat
ive
vo
lati
lity
of
A t
o B
is
con
stan
t at
3.0
.
Ass
um
pti
on
s:
Co
nst
ant
mo
lar
ov
erfl
ow
.
Sat
ura
ted
liq
uid
ref
lux
.
Fin
d:
C
om
po
siti
on
s o
f re
flu
x a
nd
bo
ilu
p w
hen
fee
d r
ate
is i
nad
ver
ten
tly r
edu
ced
to
25
km
ol/
h,
wh
ile
kee
pin
g t
he
refl
ux
an
d b
oil
up
flo
w r
ates
co
nst
ant.
An
aly
sis:
F
irst
, v
erif
y t
he
sep
arat
ion
fo
r a
feed
rat
e o
f 1
00
km
ol/
h.
Th
is i
s sh
ow
n i
n t
he
McC
abe-
Th
iele
plo
t b
elo
w i
n t
erm
s o
f m
ole
fra
ctio
ns
of
A,
the
mo
re v
ola
tile
co
mp
on
ent.
T
he
equ
ilib
riu
m c
urv
e is
co
mp
ute
d f
rom
Eq
. (7
-3),
yx
x
x
x=
+−
=+
α α1
1
3
12
()
Th
e giv
en m
ole
fra
ctio
ns
are:
x F
= 0
.50
x D
= 0
.90
x B
= 0
.20
Th
e re
ctif
icat
ion
sec
tio
n o
per
atin
g l
ine
has
a s
lop
e o
f 0
.75
an
d p
asse
s th
rou
gh
po
int
{0
.9,
0.9
}.
Th
e q
-lin
e is
ver
tica
l at
x =
0.5
. T
he
plo
t sh
ow
s al
mo
st p
erfe
ct a
gre
emen
t w
ith
th
e d
esir
ed
sep
arat
ion
fo
r a
feed
rat
e o
f 1
00
km
ol/
h.
Ex
erci
se 7
.20
(c
on
tin
ued
) A
na
lysi
s:
(co
nti
nu
ed)
Fo
r th
e b
ase
case
of
F =
10
0 k
mo
l/h
, th
e m
ater
ial
bal
ance
eq
uat
ion
s ar
e
F =
D +
B
and
x
FF
= 5
0 =
xDD
+ x
BB
= 0
.90
D +
0.2
0B
. S
olv
ing,
thes
e eq
uat
ion
s, a
lon
g w
ith
V =
L +
D,
V/L
= 0
.75
, V
VL
LF
==
+,
and
, g
ives
th
e fo
llo
win
g r
esu
lts:
Str
eam
F
low
ra
te,
km
ol/
h
Mo
l% A
M
ol%
B
Fee
d
10
0.0
0
50
5
0
Dis
till
ate
4
2.8
6
90
1
0
Bo
tto
ms
5
7.1
4
20
8
0
Ref
lux
, L
1
28
.58
Ov
erh
ead
vap
or,
V
17
1.4
4
Liq
uid
to
reb
oil
er,
L
22
8.5
8
Vap
or
fro
m r
ebo
iler
, V
1
71
.44
W
hen
th
e fe
ed r
ate
is r
edu
ced
to
25
km
ol/
h,
the
refl
ux
rat
e, L
, is
mai
nta
ined
at
12
8.5
8
km
ol/
h a
nd
th
e b
oil
up
, V
, is
mai
nta
ined
at
17
1.4
4 k
mo
l/h
. T
her
efo
re b
y m
ater
ial
bal
ance
s,
L=
L +
F =
12
8.5
8 +
25
= 1
53
.58
an
d B
= L
-V=
15
3.5
8 -
17
1.4
4 =
-1
7.8
6 k
mo
l/h
. T
his
is
imp
oss
ible
. T
her
efo
re,
the
colu
mn
can
no
t b
e o
per
ated
wit
h t
he
sam
e b
oil
up
rat
e.
Th
at r
ate
wo
uld
hav
e to
be
red
uce
d t
o a
chie
ve
a d
esir
ed b
ott
om
s ra
te,
e. g
. th
e 5
7.1
4 %
of
the
feed
, as
in
the
bas
e ca
se o
r 0
.57
14
(25
) =
14
.29
km
ol/
h.
If
this
wer
e d
on
e, w
e w
ou
ld n
ow
hav
e, V
=L
- B
=
15
3.5
8 -
14
.29
= 1
39
.29
km
ol/
h =
V.
Th
us,
in
th
e re
ctif
yin
g s
ecti
on
, L
/V =
12
8.5
8/1
39
.29
=
0.9
23
an
d i
n t
he
stri
pp
ing s
ecti
on
, L
/V=
15
3.5
8/1
39
.29
= 1
.10
3.
Th
e re
sult
ing d
isti
llat
e an
d
bo
tto
ms
com
po
siti
on
s ar
e d
eter
min
ed b
y p
osi
tio
nin
g t
he
op
erat
ing l
ines
so
th
at 3
sta
ges
+ a
reb
oil
er c
an b
e st
epp
ed o
ff.
Th
e re
sult
is
sho
wn
bel
ow
, w
her
e th
e m
ole
fra
ctio
ns
of
A a
re 0
.93
in
the
dis
till
ate
and
ref
lux
, 0
.18
in
th
e b
ott
om
s, a
nd
0.3
8 i
n t
he
reb
oil
er v
apo
r.
Ex
erci
se 7
.20
(c
on
tin
ued
) A
na
lysi
s:
(co
nti
nu
ed)
Ex
erci
se 7
.21
Su
bje
ct:
Dis
till
atio
n o
f a
satu
rate
d v
apo
r o
f m
alei
c an
hyd
rid
e (A
) an
d b
enzo
ic a
cid
(B
)
un
der
vac
uu
m a
t 1
3.3
kP
a.
Giv
en:
F
eed
co
nta
ins
90
mo
l% A
an
d 1
0 m
ol%
B.
Dis
till
ate
to c
on
tain
99
.5 m
ol%
an
hyd
rid
e
and
bo
tto
ms
to c
on
tain
0.5
mo
l% a
cid
. V
apo
r p
ress
ure
dat
a.
Ass
um
pti
on
s:
Rao
ult
's l
aw t
o c
om
pu
te K
-val
ues
fro
m v
apo
r p
ress
ure
dat
a.
Co
nst
ant
mo
lar
ov
erfl
ow
.
Fin
d:
N
um
ber
of
theo
reti
cal
pla
tes
nee
ded
if
a re
flu
x r
atio
, L
/D =
1.6
tim
es m
inim
um
.
An
aly
sis:
F
irst
co
mp
ute
an
eq
uil
ibri
um
y,
x cu
rve
usi
ng R
aou
lt's
law
wit
h t
he
vap
or
pre
ssu
re
dat
a.
Eq
. (2
-44
) a
pp
lies
, as
wel
l as
th
e su
m o
f th
e m
ole
fra
ctio
ns
in t
he
ph
ases
in
eq
uil
ibri
um
.
Th
us,
Ky x
PT
PK
y x
PT
P
yy
xx
ss
AA A
A
BB B
B
AB
AB
,
(1
, 2
)
,
(3
, 4
)
==
==
+=
+=
��
��
11
E
qu
atio
ns
(1)
to (
4)
can
be
red
uce
d t
o t
he
foll
ow
ing e
qu
atio
ns
for
the
mo
le f
ract
ion
s o
f
mal
eic
anh
yd
rid
e (A
) in
ter
ms
of
the
K-v
alu
es:
xK
KK
yK
xA
B
AB
AA
A
,
=− −
=1
(5,
6)
If t
he
giv
en v
apo
r p
ress
ure
dat
a ar
e fi
tted
to
An
toin
e eq
uat
ion
s, w
e o
bta
in:
PT
PT
s sA B
(
7)
(8
)
=−
+
� ��� ��
=−
+
� ��� ��
exp
.. .
exp
.. .
16
65
41
40
88
12
20
39
24
23
01
55
93
36
97
32
14
34
Wh
ere
vap
or
pre
ssu
re i
s in
to
rr a
nd
tem
per
atu
re i
s in
oC
. S
olv
ing,
Eq
s. (
1)
to (
8),
In s
olv
ing t
he
equ
atio
ns,
P =
13
.3 k
Pa
or
99
.8 t
orr
. T
he
resu
lts
are
tab
ula
ted
on
th
e n
ext
pag
e.
Bel
ow
th
e ta
ble
is
a M
cCab
e-T
hie
le p
lot
of
y A v
ersu
s x A
fo
r d
eter
min
ing t
he
min
imu
m r
eflu
x f
or
x D =
0.9
95
an
d a
ho
rizo
nta
l q
-lin
e at
y =
0.9
0,
wh
ich
in
ters
ects
th
e eq
uil
ibri
um
cu
rve
at
x =
0.5
72
. T
her
efo
re,
the
slo
pe
of
the
rect
ifyin
g s
ecti
on
op
erat
ing l
ine
at m
inim
um
ref
lux
is
(L/V
) min
= (
0.9
95
- 0
.90
)/(0
.99
5 -
0.5
72
) =
0.2
25
. F
rom
a r
earr
angem
ent
of
Eq
. (7
-7),
Rm
in =
(L
/V) m
in/[
1 -
(L
/V) m
in]
= 0
.22
5/(
1-0
.22
5)
= 0
.29
0.
Th
eref
ore
, th
e re
flu
x r
atio
fo
r o
per
atio
n
= 1
.6R
min
= 1
.6(0
.29
0)
= 0
.46
4.
Ex
erci
se 7
.21
(c
on
tin
ued
) A
na
lysi
s:
(c
on
tin
ued
)
T,
oC
P
s of
A,
torr
Ps o
f B
, to
rr
KA
K
B
xA
y A
13
5.3
99
.8
13
.1
1.0
00
0
.13
1
1.0
00
1
.00
0
13
6.5
10
4.1
1
3.8
1
.04
3
0.1
38
0
.95
3
0.9
93
1
37
.8
1
08
.9
14
.6
1.0
92
0
.14
7
0.9
03
0
.98
6
14
0.3
11
8.8
1
6.3
1
.19
1
0.1
64
0
.81
4
0.9
70
1
42
.8
1
29
.5
18
.2
1.2
97
0
.18
3
0.7
33
0
.95
1
14
5.3
14
0.9
2
0.3
1
.41
1
0.2
03
0
.65
9
0.9
31
1
47
.8
1
53
.1
22
.6
1.5
34
0
.22
6
0.5
92
0
.90
8
15
0.3
16
6.2
2
5.1
1
.66
5
0.2
51
0
.53
0
0.8
82
1
52
.8
1
80
.2
27
.9
1.8
05
0
.27
9
0.4
72
0
.85
3
15
7.8
21
1.1
3
4.2
2
.11
5
0.3
43
0
.37
1
0.7
84
1
60
.3
2
28
.1
37
.8
2.2
86
0
.37
9
0.3
26
0
.74
4
16
2.8
24
6.3
4
1.8
2
.46
8
0.4
19
0
.28
4
0.7
00
1
65
.3
2
65
.6
46
.2
2.6
61
0
.46
3
0.2
44
0
.65
0
16
7.8
28
6.1
5
0.9
2
.86
7
0.5
10
0
.20
8
0.5
96
1
70
.3
3
07
.9
56
.1
3.0
85
0
.56
2
0.1
73
0
.53
5
17
2.8
33
1.1
6
1.8
3
.31
7
0.6
19
0
.14
1
0.4
68
1
75
.3
3
55
.6
68
.0
3.5
63
0
.68
1
0.1
11
0
.39
5
17
7.8
38
1.6
7
4.7
3
.82
4
0.7
48
0
.08
2
0.3
13
1
80
.3
4
09
.2
81
.9
4.1
00
0
.82
1
0.0
55
0
.22
4
18
2.8
43
8.3
8
9.9
4
.39
2
0.9
01
0
.02
8
0.1
25
1
85
.3
4
69
.1
98
.5
4.7
01
0
.98
7
0.0
04
0
.01
7
18
5.7
47
4.2
9
9.9
4
.75
1
1.0
01
0
.00
0
0.0
00
Ex
erci
se 7
.21
(c
on
tin
ued
) A
na
lysi
s:
(c
on
tin
ued
)
Ex
erci
se 7
.21
(c
on
tin
ued
)
A
na
lysi
s:
(c
on
tin
ued
)
N
ow
det
erm
ine
the
tray
req
uir
emen
ts f
or
actu
al o
per
atio
n.
Usi
ng E
q.
(7-7
), w
ith
th
e
op
erat
ing r
eflu
x r
atio
of
0.4
64
, L
/V =
R/(
1 +
R)
= 0
.46
4/(
1 +
0.4
64
) =
0.3
17
. B
ecau
se s
uch
hig
h
pu
rity
dis
till
ate
and
bo
tto
ms
pro
du
cts
are
to o
bta
ined
, u
se 3
McC
abe-
Th
iele
dia
gra
ms.
T
he
firs
t
dia
gra
m i
s fo
r th
e h
igh
pu
rity
reg
ion
of
com
po
nen
t A
fro
m y
an
d x
= 0
.9 t
o 1
.0.
Th
e o
per
atin
g
lin
e fo
r th
e re
ctif
yin
g s
ecti
on
beg
ins
at {
0.9
95
, 0
.99
5} a
nd
, w
ith
a s
lop
e o
f 0
.31
7,
inte
rsec
ts t
he
ver
tica
l ax
is f
or
x =
0.9
0 a
t y
= 0
.96
5.
Th
e en
tire
reg
ion
is
cov
ered
in
th
e se
con
d d
iagra
m,
the
feed
sta
ge
is l
oca
ted
op
tim
ally
. T
he
low
co
nce
ntr
atio
n r
egio
n i
s co
ver
ed i
n t
he
thir
d d
iagra
m.
Fro
m t
hes
e th
ree
dia
gra
ms,
it
is s
een
th
at 8
th
eore
tica
l p
late
s p
lus
a p
arti
al r
ebo
iler
are
nee
ded
.
Th
e fe
ed i
s se
nt
to p
late
4 f
rom
th
e to
p.
Ex
erci
se 7
.21
(c
on
tin
ued
) A
na
lysi
s:
(c
on
tin
ued
)
Ex
erci
se 7
.21
(c
on
tin
ued
) A
na
lysi
s:
(c
on
tin
ued
)
Ex
erci
se 7
.22
S
ub
ject
: D
isti
llat
ion
of
a m
ixtu
re o
f A
an
d B
bas
ed o
n b
oil
up
, ra
ther
th
an r
eflu
x,
req
uir
emen
ts.
Giv
en:
A
bu
bb
le-p
oin
t fe
ed m
ixtu
re o
f 5
mo
l% A
an
d 9
5 m
ol%
B.
Dis
till
ate
to c
on
tain
35
mo
l% A
an
d a
bo
tto
ms
to c
on
tain
0.2
mo
l% A
. R
elat
ive
vo
lati
lity
, α
A,B
= 6
= a
co
nst
ant.
Co
lum
n e
qu
ipp
ed w
ith
par
tial
co
nd
ense
r an
d p
arti
al r
ebo
iler
.
Ass
um
pti
on
s:
C
on
stan
t m
ola
r o
ver
flo
w.
Fin
d:
U
sin
g a
lgeb
raic
met
ho
ds,
(a)
Min
imu
m n
um
ber
of
equ
ilib
riu
m s
tages
.
(b
) M
inim
um
bo
ilu
p r
atio
, V
B =
VB
/.
(c
) N
um
ber
of
equ
ilib
riu
m s
tages
fo
r a
bo
ilu
p r
atio
= 1
.2 t
imes
min
imu
m.
An
aly
sis:
F
rom
a r
earr
angem
ent
of
the
equ
ilib
riu
m e
qu
atio
n,
Eq
. (7
-3),
xy
yy
y
y=
+−
=−
α(
)1
65
(1
)
(a
) F
or
min
imu
m s
tages
, h
ave
tota
l re
flu
x,
so t
hat
y =
x f
or
pas
sin
g s
trea
ms.
B
egin
calc
ula
tio
ns
fro
m t
he
top
. y
D =
y1 =
0.3
5.
Fro
m E
q.
(1),
x1 =
0.3
5/[
6 -
5(0
.35
)] =
0.0
82
4.
Th
eref
ore
, y 2
= x
1 =
0.0
82
4.
Fro
m E
q.
(1),
x2 =
0.0
82
4/[
6-5
(0.0
82
4)]
= 0
.01
47
. T
her
efo
re,
y 3 =
x2 =
0.0
14
7.
Fro
m E
q.
(1),
x3 =
0.0
14
7/[
6-5
(0.0
14
7)]
= 0
.00
25
. T
his
is
clo
se t
o b
ut
no
t
qu
ite
equ
al t
o t
he
des
ired
val
ue
of
0.0
02
. T
hu
s, w
e n
eed
ju
st s
ligh
tly m
ore
th
an 3
min
imu
m
equ
ilib
riu
m s
tages
.
(b)
Fo
r m
inim
um
bo
ilu
p r
atio
, th
e st
rip
pin
g s
ecti
on
op
erat
ing l
ine
con
nec
ts t
he
two
po
ints
fo
r {y,
x} o
f {0
.00
2,
0.0
02
} a
nd
{y
in e
qu
ilib
riu
m w
ith
x =
0.0
5}.
Fro
m a
rea
rran
gem
ent
of
Eq
. (1
), t
he
y in
eq
uil
ibri
um
wit
h x
= 0
.05
is:
y
= α
x/[1
+
x(α
− 1
)] =
6(0
.05
)/[1
+ 0
.05
(6 −
1)]
= 0
.24
. T
he
slo
pe
of
the
op
erat
ing l
ine
= (
LV/
) =
(0
.24
-
0.0
02
)/(0
.05
- 0
.00
2)
= 4
.96
. F
rom
a r
earr
angem
ent
of
Eq
. (7
-12
), (
VB) m
in =
1/
[(L
V/)
- 1
] =
1/(
4.9
6 -
1)
= 0
.25
3.
(c)
Th
e b
oil
up
rat
io =
VB =
1.2
(0.2
53
) =
0.3
03
6.
Fro
m E
q.
(7-1
2),
th
e sl
op
e o
f th
e
stri
pp
ing s
ecti
on
op
erat
ing l
ine
= L
V/=
(V
B +
1)/
VB =
(0
.30
36
+ 1
)/0
.30
36
= 4
.29
4.
Th
is l
ine
inte
rsec
ts t
he
ver
tica
l q
-lin
e (x
F
= 0
.05
) at
0.0
02
+ 4
.29
4(0
.05
- 0
.00
2)
= 0
.20
81
. T
her
efo
re,
the
slo
pe
of
the
rect
ifyin
g l
ine
= L
/V =
(0
.35
- 0
.20
81
)/(0
.35
- 0
.05
) =
0.4
73
0.
Fro
m a
rea
rran
gem
ent
of
Eq
. (7
-8),
R =
(L
/V)/
[1 -
(L
/V)]
= 0
.47
3/(
1 -
0.4
73
) =
0.8
97
5.
Th
e eq
uat
ion
fo
r th
e re
ctif
yin
g
sect
ion
op
erat
ing l
ine,
usi
ng E
q.
((7
-9),
wit
h a
mo
dif
icat
ion
fo
r a
par
tial
co
nd
ense
r as
det
erm
ined
fro
m F
ig.
7.1
8,
is,
y
R
Rx
Ry
xn
nD
n+
=+
� ��� ��
++
� ��� ��
=+
11
1
10
47
30
18
4.
.5
(2)
Ex
erci
se 7
.22
(c
on
tin
ued
) A
na
lysi
s:
(c)
(c
on
tin
ued
)
Th
e eq
uat
ion
fo
r th
e st
rip
pin
g s
ecti
on
op
erat
ing l
ine,
usi
ng E
q.
(7-1
2)
is,
y
V
Vx
Vx
xm
B
B
m
B
Bm
+=
+� ��� ��
−� ��� ��
=−
1
11
42
94
00
06
59
..
(3)
We
can
no
w c
alcu
late
sta
ge
by s
tage
do
wn
fro
m t
he
top
, st
arti
ng f
rom
yD =
0.3
5,
alte
rnat
ing
bet
wee
n t
he
equ
ilib
riu
m c
urv
e, E
q.
(1)
and
th
e ap
pro
pri
ate
op
erat
ing l
ine,
Eq
. (2
) o
r (3
).
We
beg
in u
sin
g E
q.
(2),
bu
t sw
itch
to
Eq
. (3
), w
hen
x <
xF =
0.0
5.
Th
e ca
lcu
lati
on
s ar
e te
rmin
ated
wh
en x
< x
B =
0.0
02
. T
he
calc
ula
tio
ns
can
be
do
ne
wit
h a
sp
read
shee
t, w
ith
th
e fo
llo
win
g
resu
lts,
giv
en a
s m
ole
fra
ctio
ns
of
A l
eav
ing a
n e
qu
ilib
riu
m s
tage.
T
he
op
tim
al f
eed
sta
ge
is t
he
top
pla
te.
Eq
uil
ibri
um
sta
ge
y A
xA
Par
tial
co
nd
ense
r 0
.35
0
0.0
82
4
1
0.2
23
0
.04
58
2
0.1
90
0
.03
76
3
0.1
55
0
.02
96
4
0.1
21
0
.02
24
5
0
.08
94
0
.01
61
6
0
.06
26
0
.01
10
7
0
.04
07
0.0
07
01
8
0
.02
35
0.0
04
00
Par
tial
reb
oil
er
0
.01
06
0.0
01
78
Th
e ca
lcu
lati
on
s sh
ow
th
at b
esid
es t
he
par
tial
co
nd
ense
r an
d p
arti
al r
ebo
iler
, 8
eq
uil
ibri
um
sta
ges
are
nee
ded
in
th
e co
lum
n.
Ex
erci
se 7
.23
S
ub
ject
: D
isti
llat
ion
of
a m
ixtu
re o
f m
eth
ano
l an
d w
ater
wit
h a
su
bco
ole
d l
iqu
id f
eed
.
Giv
en:
L
iqu
id f
eed
of
14
,46
0 k
g/h
met
han
ol
and
10
,44
0 k
g/h
wat
er a
t q
= 1
.12
. D
isti
llat
e o
f 9
9
mo
l% m
eth
ano
l an
d a
bo
tto
ms
of
99
mo
l% w
ater
are
des
ired
. C
olu
mn
has
a t
ota
l co
nd
ense
r an
d
a p
arti
al r
ebo
iler
. O
per
atio
n a
t 1
atm
wit
h a
ref
lux
rat
io o
f L
/D =
R =
1.0
. V
apo
r-li
qu
id
equ
ilib
riu
m d
ata
in E
xer
cise
of
7.1
9.
Ass
um
pti
on
s:
Co
nst
ant
mo
lar
ov
erfl
ow
.
Fin
d:
F
eed
sta
ge
loca
tio
n a
nd
nu
mb
er o
f eq
uil
ibri
um
sta
ges
.
An
aly
sis:
F
irst
, d
eter
min
e fe
ed c
om
po
siti
on
in
mo
l%.
Usi
ng m
ole
cula
r w
eigh
ts o
f 3
2.0
4 f
or
met
han
ol
and
18
.02
fo
r w
ater
,
Co
mp
on
ent
kg
/h
km
ol/
h
Mo
l%
Met
han
ol
14
,46
0
4
51
.3
4
3.7
9
Wat
er
10
,44
0
5
79
.4
5
6.2
1
T
ota
l:
24
,90
0
1,0
30
.7
10
0.0
0
Usi
ng t
he
vap
or-
liq
uid
eq
uil
ibri
um
dat
a, a
y-x
plo
t fo
r th
e M
cCab
e-T
hie
le m
eth
od
is
mad
e an
d
smo
oth
ed w
ith
a s
pre
adsh
eet,
no
tin
g t
hat
met
han
ol
is t
he
mo
re v
ola
tile
. T
her
efo
re,
x F =
0.4
37
9,
x D =
0.9
9,
xB =
0.0
1.
Fro
m E
q.
(7-2
6),
slo
pe
of
q-l
ine
= q
/(q
- 1
) =
1.1
2/(
1.1
2 -
1)
= 9
.33
3.
Th
eref
ore
, o
n t
he
McC
abe-
Th
iele
dia
gra
m,
a li
ne
is d
raw
n w
ith
a s
lop
e o
f 9
.33
3 t
hat
in
ters
ects
th
e p
oin
t {0
.43
8,0
.43
8}.
Fro
m E
q.
(7-7
), t
he
slo
pe
of
the
rect
ifyin
g s
ecti
on
op
erat
ing l
ine
= L
/V =
R/(
R +
1)
= 1
/(1
+ 1
) =
0.5
. T
his
lin
e is
dra
wn
on
th
e M
cCab
e-T
hie
le d
iagra
m w
ith
a s
lop
e o
f 0
.5 t
hat
in
ters
ects
th
e
po
int
{0
.99
,0.9
9}.
Th
e st
rip
pin
g s
ecti
on
op
erat
ing l
ine
is d
raw
n t
o i
nte
rsec
t th
e p
oin
t
{0
.01
,0.0
1} a
nd
th
e p
oin
t w
her
e th
e q
-lin
e in
ters
ects
th
e re
ctif
yin
g s
ecti
on
op
erat
ing l
ine.
In t
he
McC
abe-
Th
iele
gra
ph
s b
elo
w,
the
firs
t fo
r th
e h
igh
mo
le-f
ract
ion
reg
ion
, it
is
seen
th
at t
he
spec
ifie
d r
eflu
x r
atio
is,
fo
rtu
nat
ely,
abo
ve
the
min
imu
m v
alu
e fo
r th
e sp
ecif
ied
dis
till
ate
mo
le
frac
tio
n.
Fro
m t
he
plo
ts,
it i
s se
en t
hat
20
th
eore
tica
l st
ages
plu
s a
par
tial
reb
oil
er a
re n
eed
ed.
Th
e o
pti
mal
feed
sta
ge
is n
um
ber
17
do
wn
fro
m t
he
top
.
Ex
erci
se 7
.23
(c
on
tin
ued
) A
na
lysi
s:
(co
nti
nu
ed)
Ex
erci
se 7
.23
(c
on
tin
ued
) A
na
lysi
s:
(co
nti
nu
ed)
Ex
erci
se 7
.24
S
ub
ject
: P
arti
al s
epar
atio
n o
f a
ben
zen
e-to
luen
e m
ixtu
re w
ith
a p
arti
al r
ebo
iler
an
d a
par
tial
con
den
ser.
Giv
en:
S
atu
rate
d l
iqu
id f
eed
of
69
.4 m
ol%
ben
zen
e (B
) in
to
luen
e (T
) fe
d t
o a
par
tial
reb
oil
er.
Vap
or
fro
m t
he
reb
oil
er p
asse
s to
a p
arti
al c
on
den
ser.
V
apo
r fr
om
th
e p
arti
al c
on
den
ser
pas
ses
to
a to
tal
con
den
ser.
R
eflu
x f
rom
th
e p
arti
al c
on
den
ser
is s
ent
to t
he
par
tial
reb
oil
er.
Dis
till
ate
is t
o
con
tain
90
mo
l% b
enze
ne
(yD =
0.9
) at
a r
ate
of
25
mo
les
per
10
0 m
ole
s o
f fe
ed.
Th
e re
lati
ve
vo
lati
lity
of
ben
zen
e w
ith
res
pec
t to
to
luen
e =
α =
2.5
.
Fin
d:
M
ole
s o
f v
apo
r gen
erat
ed i
n t
he
reb
oil
er p
er 1
00
mo
les
of
feed
by a
nal
yti
cal
and
gra
ph
ical
met
ho
ds.
An
aly
sis:
F
irst
co
mp
ute
ov
eral
l m
ater
ial
bal
ance
. T
he
tota
l co
nd
ense
r n
eed
no
t b
e co
nsi
der
ed.
Bas
is:
10
0 m
ole
s o
f fe
ed.
Ov
eral
l to
tal
mat
eria
l b
alan
ce:
F
= 1
00
= D
+ B
= 2
5 +
B
(1)
So
lvin
g E
q.
(1),
B =
75
mo
les
Ov
eral
l b
enze
ne
mat
eria
l b
alan
ce:
F
x F =
69
.4 =
Dy D
+ B
x B
= 2
5(0
.9)
+ 7
5x B
(2
)
So
lvin
g E
q.
(2),
xB =
0.6
25
An
aly
tica
l M
eth
od
:
W
rite
mat
eria
l b
alan
ces
aro
un
d t
he
par
tial
reb
oil
er a
nd
par
tial
co
nd
ense
r, u
sin
g s
ub
scri
pts
B f
or
stre
ams
leav
ing t
he
reb
oil
er a
nd
D f
or
stre
ams
leav
ing t
he
par
tial
co
nd
ense
r.
Par
tial
reb
oil
er:
T
ota
l m
ater
ial
bal
ance
: F
+ L
D =
B +
VB
or
10
0 +
LD =
75
+ V
B
(3)
B
enze
ne
mat
eria
l b
alan
ce:
Fx F
+ L
Dx D
= B
x B +
VBy B
o
r 6
9.4
+ L
Dx D
= 7
5(0
.62
5)
+ V
By B
= 4
6.9
+ V
By B
(4
)
Par
tial
co
nd
ense
r:
T
ota
l m
ater
ial
bal
ance
: V
B =
D +
LD =
75
+ L
D
(5)
B
enze
ne
mat
eria
l b
alan
ce:
VBy B
= D
y D +
LDx D
= 7
5(0
.9)
+ L
Dx D
= 6
7.5
+ L
Dx D
(
6)
Ass
um
e eq
uil
ibri
um
in
th
e p
arti
al c
on
den
ser
and
par
tial
reb
oil
er.
Usi
ng t
he
giv
en α
wit
h i
ts
def
init
ion
in
Eq
. (7
-2).
F
or
the
par
tial
co
nd
ense
r,
α =
2.5
= y
D (
1 -
xD)/
x D(1
- y
D)
= 0
.9(1
- x
D)/
x D(1
-0
.9)
= 9
(1 -
xD)/
x D
(7)
So
lvin
g E
q.
(7),
xD =
0.7
83
Fo
r th
e p
arti
al r
ebo
iler
,
α =
2.5
= y
B (
1 -
xB)/
x B(1
- y
B)
= y
B (
1 -
0.6
25
)/0
.62
5(1
- y
B)
= 0
.6 y
B/(
1 -
yB)
(8)
So
lvin
g E
q.
(8),
yB =
0.8
06
Eq
s. (
3)
thro
ugh
(6
), a
re 4
eq
uat
ion
s in
2 u
nk
no
wn
s, V
B a
nd
LD.
We
on
ly n
eed
2 o
f th
e 4
equ
atio
ns.
U
sin
g E
qs.
(3
) an
d (
4),
10
0 +
LD =
75
+ V
B
(3
)
6
9.4
+ L
D(0
.78
3)
= 4
6.9
+ V
B(0
.80
6)
(9)
So
lvin
g E
qs.
(3
) an
d (
9),
LD =
98
mo
les
/10
0 m
ole
s o
f fe
ed a
nd
V
B =
12
3 m
ole
s/1
00
mo
les
of
feed
E
xer
cise
7.2
4 (c
on
tin
ued
) A
na
lysi
s:
(co
nti
nu
ed)
Gra
ph
ica
l M
eth
od
:
O
n t
he
McC
abe-
Th
iele
dia
gra
m b
elo
w,
the
equ
ilib
riu
m c
urv
e is
ob
tain
ed f
rom
Eq
. (7
-3),
yx
x
x
x=
+−
=+
α
α1
1
25
11
5(
)
.
.
Th
e re
ctif
icat
ion
sec
tio
n o
per
atin
g l
ine
is l
oca
ted
, as
sh
ow
n,
so t
hat
tw
o e
qu
ilib
riu
m s
tep
s, o
ne
for
the
par
tial
co
nd
ense
r an
d o
ne
for
the
par
tial
reb
oil
er,
are
step
ped
off
bet
wee
n x
C =
0.9
(fr
om
the
tota
l co
nd
ense
r) a
nd
xB =
0.6
25
. T
he
mea
sure
d s
lop
e o
f th
e o
per
atin
g l
ine
= L
D/V
B =
0.8
.
Co
mb
inin
g t
his
wit
h E
q.
(3),
V
B =
12
5 m
ole
s/1
00
mo
les
of
feed
, w
hic
h i
s cl
ose
to
th
e an
alyti
cal
val
ue.
Ex
erci
se 7
.25
S
ub
ject
: R
ecti
fica
tio
n o
f a
mix
ture
of
ben
zen
e an
d c
hlo
rob
enze
ne
at t
ota
l re
flu
x.
Giv
en:
F
eed
of
10
0 k
mo
l o
f 2
0 m
ol%
ben
zen
e an
d 8
0 m
ol%
ch
loro
ben
zen
e.
Co
lum
n h
as 4
theo
reti
cal
pla
tes,
a t
ota
l co
nd
ense
r, a
ref
lux
dru
m,
and
a s
till
to
vap
ori
ze t
he
feed
. A
t an
op
erat
ing p
ress
ure
of
1 a
tm,
rela
tiv
e v
ola
tili
ty o
f b
enze
ne
wit
h r
esp
ect
to c
hlo
rob
enze
ne
= α
=
4.1
3.
Op
erat
e at
to
tal
refl
ux
wit
h h
old
up
s o
nly
in
th
e re
flu
x d
rum
an
d t
he
stil
l.
Wan
t li
qu
id i
n
the
stil
l w
ith
0.1
mo
l% b
enze
ne.
Ass
um
pti
on
s:
Per
fect
mix
ing t
o g
ive
un
ifo
rm c
om
po
siti
on
s in
th
e re
flu
x d
rum
an
d t
he
stil
l.
Fin
d:
M
ole
s o
f li
qu
id i
n t
he
stil
l at
ste
ady s
tate
.
An
aly
sis:
T
his
ex
erci
se c
an b
e so
lved
an
alyti
call
y o
r gra
ph
ical
ly.
Sin
ce b
enze
ne
is t
he
mo
re
vo
lati
le c
om
po
nen
t, E
q.
(7-3
) giv
es t
he
equ
ilib
riu
m r
elat
ion
at
the
stil
l o
r an
y o
f th
e 4
pla
tes,
n,
as,
yx
x
x
xn
n
n
n
n
=+
−=
+
α
α1
1
41
3
13
13
()
.
.
(1
)
At
tota
l re
flu
x,
nu
mb
erin
g s
tages
up
fro
m t
he
bo
tto
m,
x n
+1
= y
n
(2)
An
aly
tica
l M
eth
od
:
S
tart
at
the
bo
tto
m,
stag
e 1
, w
ith
x1 =
0.0
01
. S
olv
e fo
r y 1
(v
apo
r le
avin
g t
he
stil
l) w
ith
Eq
. (1
).
Th
en,
fro
m E
q.
(2),
x2 =
y1.
Co
nti
nu
e in
th
is m
ann
er,
solv
ing a
lter
nat
ely E
q.
(1)
and
then
Eq
. (2
), u
nti
l y 5
(v
apo
r le
avin
g t
he
top
pla
te)
is r
each
ed.
Th
en,
x in
th
e re
flu
x d
rum
= y
5.
Th
e re
sult
s fr
om
a s
pre
adsh
eet
are,
Eq
uil
bri
um
sta
ge
x
y
1 (
stil
l)
0.0
01
00
0
.00
41
2
2 (
bo
tto
m p
late
0
.00
41
2
0.0
16
79
3
0.0
16
79
0
.06
58
7
4
0.0
65
87
0
.22
55
4
5 (
top
pla
te)
0.2
25
54
0
.54
60
3
refl
ux
dru
m
0.5
46
03
By o
ver
all
tota
l m
ater
ial
bal
ance
, F
= 1
00
= D
+ B
(3)
By o
ver
all
ben
zen
e m
ater
ial
bal
ance
,
Fx F
= (
10
0)(
0.2
0)
= 2
0 =
Dx D
+ B
x B =
D(0
.54
60
3)
+ B
(0.0
01
)
(4)
So
lvin
g E
qs.
(3
) an
d (
4),
D =
dis
till
ate
in r
eflu
x d
rum
= 3
6.5
1 k
mo
les
B
= b
ott
om
s in
sti
ll =
63
.49
km
ole
s
Ex
erci
se 7
.25
(co
nti
nu
ed)
Gra
ph
ica
l M
eth
od
:
O
n t
he
McC
abe-
Th
iele
plo
t o
n t
he
nex
t p
age,
th
e eq
uil
ibri
um
cu
rve
is c
om
pu
ted
fro
m E
q.
(1).
T
he
rect
ific
atio
n s
ecti
on
op
erat
ing l
ine
is t
he
45
o l
ine.
F
ive
stag
es a
re s
tep
ped
off
fro
m t
he
bo
tto
ms
of
x B =
0.0
01
. T
he
resu
ltin
g y
5 is
ess
enti
ally
th
e sa
me
as t
hat
fo
r th
e an
alyti
cal
met
ho
d.
Th
us,
agai
n,
B
= b
ott
om
s in
sti
ll =
63
.49
km
ole
s.
Ex
erci
se 7
.25
(c
on
tin
ued
) A
na
lysi
s:
Gra
ph
ical
met
ho
d
(co
nti
nu
ed)
Ex
erci
se 7
.26
S
ub
ject
: D
isti
llat
ion
of
ace
ton
e an
d i
sop
rop
ano
l, t
akin
g i
nto
acc
ou
nt
tray
eff
icie
ncy
.
Giv
en:
S
atu
rate
d l
iqu
id f
eed
of
50
mo
l% a
ceto
ne
and
50
mo
l% i
sop
rop
ano
l.
Co
lum
n i
s
equ
ipp
ed w
ith
a t
ota
l co
nd
ense
r, a
nd
a p
arti
al r
ebo
iler
. R
eflu
x r
atio
, L
/D,
is 0
.5.
Mu
rph
ree
vap
or
effi
cien
cy =
50
%.
Vap
or-
liq
uid
eq
uil
ibri
um
dat
a at
1 a
tm a
re g
iven
, w
ith
ace
ton
e b
ein
g t
he
mo
re
vo
lati
le c
om
po
nen
t.
Ass
um
pti
on
s:
Co
nst
ant
mo
lar
ov
erfl
ow
.
Fin
d:
N
um
ber
of
actu
al t
rays
req
uir
ed t
o a
chie
ve
a d
isti
llat
e o
f 8
0 m
ol%
ace
ton
e an
d a
bo
tto
ms
of
25
mo
l% a
ceto
ne,
in
sert
ing t
he
feed
at
the
op
tim
al l
oca
tio
n.
An
aly
sis:
I
n t
he
McC
abe-
Th
iele
dia
gra
m b
elo
w,
the
equ
ilib
riu
m c
urv
e is
plo
tted
fro
m t
he
giv
en
dat
a.
Th
e q
-lin
e is
ver
tica
l, p
assi
ng t
hro
ugh
x =
0.5
. T
he
rect
ific
atio
n o
per
atin
g l
ine
has
a s
lop
e,
L/V
, fr
om
Eq
. (7
-9),
of
R/(
R +
1)
= 0
.5/1
.5 =
0.3
33
. T
his
op
erat
ing l
ine
pas
ses
thro
ugh
th
e p
oin
t,
y =
0.8
, x
= 0
.8.
Fro
m E
q.
7-9
), t
he
equ
atio
n f
or
the
rect
ifyin
g s
ecti
on
op
erat
ing l
ine
is,
yR
Rx
Rx
xx
D=
+
� ��� ��
++
� ��� ��
=+
=+
1
1
10
33
30
66
70
80
33
30
53
3.
.(
.)
..
Fro
m t
his
eq
uat
ion
, th
e in
ters
ecti
on
of
the
rect
ifyin
g s
ecti
on
op
erat
ing l
ine
and
th
e v
erti
cal
q-l
ine
is a
t y
= 0
.33
3(0
.5)
+ 0
.53
3 =
0.7
0.
Th
e st
rip
pin
g s
ecti
on
op
erat
ing l
ine
pas
ses
thro
ugh
th
e {y,
x}
po
ints
{0
.70
, 0
.50
} a
nd
{0
.25
, 0
.25
},
giv
ing i
t th
e eq
uat
ion
, y
= 1
.80
x-0
.20
.
Ex
cep
t fo
r th
e re
bo
iler
sta
ge,
th
e st
ages
are
ste
pp
ed o
ff f
rom
an
eff
icie
ncy
lin
e, w
hic
h f
or
a
Mu
rph
ree
vap
or
effi
cien
cy o
f 0
.5 i
s p
osi
tio
ned
ver
tica
lly h
alf
way
bet
wee
n t
he
equ
ilib
riu
m c
urv
e
and
th
e o
per
atin
g l
ine,
as
go
ver
ned
by E
q.
(7-4
1),
E
MV =
0.5
= (
y n -
yn
+1)/
(yn*
- y
n+
1),
wh
ere
y n+
1
is t
he
loca
tio
n o
n t
he
op
erat
ing l
ine,
yn i
s th
e lo
cati
on
on
th
e ef
fici
ency
lin
e, a
nd
yn*
is
the
loca
tio
n o
n t
he
equ
ilib
riu
m l
ine.
H
ow
ever
, th
e re
bo
iler
is
assu
med
to
hav
e a
10
0%
eff
icie
ncy
.
As
seen
in
th
e p
lot,
ju
st o
ver
8 t
rays
are
req
uir
ed p
lus
the
par
tial
reb
oil
er.
Th
e fe
ed p
late
is
4
fro
m t
he
top
.
Ex
erci
se 7
.26
(c
on
tin
ued
) A
na
lysi
s (
con
tin
ued
)
Ex
erci
se 7
.27
S
ub
ject
: D
isti
llat
ion
of
carb
on
dis
ulf
ide
and
car
bo
n t
etra
chlo
rid
e.
Giv
en:
P
arti
ally
vap
ori
zed
fee
d (
q =
0.5
) o
f 4
0 m
ol%
CS
2.
Op
erat
ion
wit
h a
ref
lux
rat
io,
L/D
,
of
4 a
nd
a M
urp
hre
e v
apo
r ef
fici
ency
of
80
%.
P
arti
al r
ebo
iler
an
d t
ota
l co
nd
ense
r.
Vap
or-
liq
uid
equ
ilib
riu
m d
ata.
Ass
um
pti
on
s:
Co
nst
ant
mo
lar
ov
erfl
ow
.
Fin
d:
F
or
a d
isti
llat
e o
f 9
5 m
ol%
CS
2 a
nd
a b
ott
om
s o
f 5
mo
l% C
S2,
det
erm
ine:
(a
) M
inim
um
ref
lux
rat
io,
min
imu
m b
oil
up
rat
io,
and
min
imu
m n
um
ber
of
stag
es.
(b
) N
um
ber
of
tray
s.
An
aly
sis:
(
a) I
n t
he
McC
abe-
Th
iele
plo
t o
n t
he
nex
t p
age,
rec
tify
ing s
ecti
on
an
d s
trip
pin
g
sect
ion
op
erat
ing l
ines
are
sh
ow
n f
or
det
erm
inin
g m
inim
um
ref
lux
an
d b
oil
up
rat
ios.
N
ote
th
at
the
q-l
ine
has
a s
lop
e giv
en i
n E
q.
(7-2
6)
as q
/(q
- 1
) =
0.5
/(0
.5 -
1)
= -
1 a
nd
in
ters
ects
th
e p
oin
t
{0
.4,
0.4
}.
Th
e re
ctif
yin
g s
ecti
on
op
erat
ing l
ine
inte
rsec
ts t
he
po
int
{0
.95
, 0
.95
} a
nd
th
e p
oin
t
wh
ere
the
equ
ilib
riu
m c
urv
e an
d t
he
q-l
ine
inte
rsec
t.
Th
e sl
op
e o
f th
at l
ine
is m
easu
red
to
be
L/V
= 0
.64
2.
Fro
m E
q.
(7-9
), L
/V =
R/(
R +
1).
R
earr
angin
g,
Rm
in =
(L
/V)/
[1 -
(L
/V)]
= 0
.64
2/(
1 -
0.6
42
) =
1.7
9
Th
e st
rip
pin
g s
ecti
on
op
erat
ing l
ine
inte
rsec
ts t
he
po
int
{0
.05
, 0
.05
} a
nd
th
e p
oin
t w
her
e th
e
equ
ilib
riu
m c
urv
e an
d t
he
q-l
ine
inte
rsec
t.
Th
e sl
op
e o
f th
at l
ine
is m
easu
red
to
be
LV/
=
2.0
43
. F
rom
Eq
. (7
-14
), L
V/=
(V
B +
1)/
VB.
Rea
rran
gin
g,
()
()
mn
min
i
10
.95
1
2.0
43
1/
19
��
==
=�
�−
�=
−�
B
V BL
VV
Th
e M
cCab
e-T
hie
le p
lot
for
min
imu
m s
tages
at
tota
l re
flu
x i
s al
so s
ho
wn
on
th
e n
ext
pag
e.
Th
e
op
erat
ing l
ines
are
co
inci
den
t w
ith
th
e 4
5o l
ine.
It
is
seen
th
at 6
eq
uil
ibri
um
sta
ges
are
nee
ded
.
(b
) F
or
a re
flu
x r
atio
, R
= L
/D,
of
4,
the
slo
pe
of
the
rect
ifyin
g s
ecti
on
op
erat
ing l
ine
fro
m E
q.
(7-9
) is
L/V
= R
/(R
+ 1
) =
4/5
= 0
.8.
Th
is l
ine
and
th
e st
rip
pin
g s
ecti
on
op
erat
ing l
ine
are
sho
wn
on
th
e th
ird
McC
abe-
Th
iele
dia
gra
m b
elo
w.
E
xce
pt
for
the
reb
oil
er s
tage,
th
e st
ages
are
step
ped
off
fro
m a
n e
ffic
ien
cy l
ine,
wh
ich
fo
r a
Mu
rph
ree
vap
or
effi
cien
cy o
f 0
.8 i
s
po
siti
on
ed 8
0%
of
the
ver
tica
l d
ista
nce
fro
m t
he
op
erat
ing l
ine
to t
he
equ
ilib
riu
m c
urv
e, a
s
go
ver
ned
by E
q.
(7-4
1),
E
MV =
0.8
= (
y n -
yn
+1)/
(yn*
- y
n+
1),
wh
ere
y n+
1 i
s th
e lo
cati
on
on
th
e
op
erat
ing l
ine,
yn i
s th
e lo
cati
on
on
th
e ef
fici
ency
lin
e, a
nd
yn*
is
the
loca
tio
n o
n t
he
equ
ilib
riu
m
lin
e.
Ho
wev
er,
the
reb
oil
er i
s as
sum
ed t
o h
ave
a 1
00
% e
ffic
ien
cy.
As
seen
in
th
e p
lot,
ju
st o
ver
9 t
rays
are
req
uir
ed p
lus
the
par
tial
reb
oil
er.
Cal
l it
10
tra
ys
plu
s th
e re
bo
iler
. T
he
feed
pla
te i
s 7
fro
m t
he
top
.
Ex
erci
se 7
.27
(c
on
tin
ued
) A
na
lysi
s:
(a)
(co
nti
nu
ed)
Ex
erci
se 7
.27
(c
on
tin
ued
) A
na
lysi
s:
(a)
(co
nti
nu
ed)
Ex
erci
se 7
.27
(c
on
tin
ued
) A
na
lysi
s:
(b)
(co
nti
nu
ed)
Ex
erci
se 7
.28
S
ub
ject
: P
reli
min
ary d
esig
n c
alcu
lati
on
s fo
r th
e d
isti
llat
ion
of
a b
enze
ne-
tolu
ene
mix
ture
.
Giv
en:
B
ub
ble
-po
int
feed
of
50
mo
l% b
enze
ne
and
50
mo
l% t
olu
ene.
E
qu
ipm
ent
to i
ncl
ud
e a
par
tial
reb
oil
er,
tota
l co
nd
ense
r, a
nd
a b
ub
ble
-cap
tra
y c
olu
mn
wit
h a
n o
ver
all
pla
te e
ffic
ien
cy o
f
65
%.
Co
lum
n t
o o
per
ate
at 1
atm
to
pro
du
ce a
dis
till
ate
of
95
mo
l% b
enze
ne
and
a b
ott
om
s o
f
95
mo
l% t
olu
ene.
V
apo
r-li
qu
id e
qu
ilib
riu
m d
ata
fro
m E
xer
cise
7.1
3.
En
thal
py d
ata
fo
r re
bo
iler
.
Ass
um
pti
on
s:
Co
nst
ant
mo
lar
ov
erfl
ow
an
d s
atu
rate
d l
iqu
id r
eflu
x.
Fin
d:
(a)
Min
imu
m r
eflu
x r
atio
(in
fin
ite
stag
es).
(b
) M
inim
um
nu
mb
er o
f ac
tual
pla
tes
(to
tal
refl
ux
).
(c
) N
um
ber
of
actu
al p
late
s fo
r R
= 1
.5 R
min
.
(d
) K
ilo
gra
ms
per
ho
ur
of
pro
du
cts
for
a fe
ed o
f 9
07
.3 k
g/h
.
(e
) K
g/h
of
satu
rate
d s
team
at
27
3.7
kP
a fo
r re
bo
iler
hea
t d
uty
usi
ng g
iven
en
thal
py d
ata.
(f
) R
igo
rou
s en
thal
py b
alan
ce a
rou
nd
th
e re
bo
iler
.
An
aly
sis:
M
cCab
e-T
hie
le p
lots
are
mad
e in
ter
ms
of
ben
zen
e m
ole
fra
ctio
ns,
sin
ce b
enze
ne
is
the
mo
re v
ola
tile
co
mp
on
ent.
T
he
equ
ilib
riu
m c
urv
e is
plo
tted
fro
m t
he
dat
a in
Ex
erci
se 7
.13
.
(a)
Fo
r a
satu
rate
d l
iqu
id f
eed
, m
inim
um
ref
lux
co
rres
po
nd
s to
a p
inch
po
int
loca
ted
at
the
inte
rsec
tio
n o
f a
ver
tica
l q
-lin
e p
assi
ng t
hro
ugh
xF =
0.5
an
d t
he
equ
ilib
riu
m c
urv
e as
sh
ow
n
in t
he
McC
abe-
Th
iele
dia
gra
m b
elo
w.
Fro
m t
he
equ
ilib
riu
m d
ata,
th
is i
nte
rsec
tio
n i
s at
y =
0.7
2
and
x =
0.5
. T
hen
, th
e sl
op
e o
f th
e re
ctif
yin
g s
ecti
on
op
erat
ing l
ine,
(L
/V) m
in i
s (0
.95
- 0
.72
)/(0
.95
- 0
.50
) =
0.5
11
. F
rom
a r
earr
angem
ent
of
Eq
. (7
-7),
Rm
in =
(L
/V) m
in /
[1 -
(L
/V) m
in ]
= 0
.51
1/(
1 -
0.5
11
) =
1.0
45
.
(b
) T
he
McC
abe-
Th
iele
plo
t fo
r m
inim
um
sta
ges
at
tota
l re
flu
x i
s sh
ow
n b
elo
w.
Th
e
op
erat
ing l
ines
are
co
inci
den
t w
ith
th
e 4
5o l
ine.
E
qu
ilib
riu
m s
tages
are
ste
pp
ed o
ff s
tart
ing f
rom
x B =
0.0
5 t
o x
D =
0.9
5.
It
is s
een
th
at j
ust
les
s th
an 7
eq
uil
ibri
um
sta
ges
are
nee
ded
. C
all
it N
t = 7
.
Fro
m E
q.
(6-2
1),
fo
r an
ov
eral
l p
late
eff
icie
ncy
of
65
%,
i.e.
Eo =
0.6
5,
the
actu
al m
inim
um
nu
mb
er o
f p
late
s =
Na =
Nt /
Eo =
7/0
.65
= 1
0.8
.
(c
) O
per
atin
g r
eflu
x r
atio
= R
= 1
.5 R
min
= 1
.5(1
.04
5)
= 1
.57
. F
rom
Eq
. (7
-7),
th
e sl
op
e
of
the
op
erat
ing l
ine
for
the
rect
ifyin
g s
ecti
on
= L
/V =
R/(
1 +
R)
= 1
.57
(1 +
1.5
7)
= 0
.61
1.
On
the
McC
abe-
Th
iele
dia
gra
m o
n t
he
nex
t p
age,
th
e re
ctif
yin
g s
ecti
on
op
erat
ing l
ine
has
th
is s
lop
e
and
pas
ses
thro
ugh
th
e p
oin
t, y
=0
.95
, x=
0.9
5.
th
e st
rip
pin
g s
ecti
on
op
erat
ing l
ine
pas
ses
thro
ugh
the
po
int,
y=
0.0
5,
x=0
.05
an
d i
nte
rsec
ts t
he
ver
tica
l q
-lin
e at
th
e p
oin
t w
her
e th
e re
ctif
yin
g
sect
ion
op
erat
ing l
ine
inte
rsec
ts t
he
q-l
ine.
A
s se
en,
the
equ
ilib
riu
m s
tages
are
ste
pp
ed o
ff
star
tin
g a
t th
e to
p,
wit
h a
sw
itch
fro
m t
he
rect
ifyin
g s
ecti
on
to
th
e st
rip
pin
g s
ecti
on
to
min
imiz
e
the
nu
mb
er o
f st
ages
an
d,
thu
s, l
oca
tin
g t
he
op
tim
al f
eed
sta
ge.
T
he
resu
lt i
s ju
st o
ver
10
equ
ilib
riu
m s
tages
plu
s a
par
tial
reb
oil
er.
Cal
l it
11
eq
uil
ibri
um
sta
ges
plu
s a
par
tial
reb
oil
er.
Ap
ply
ing E
q.
(6-2
1),
Na =
11
/0.6
5 =
16
.9 o
r 1
7 a
ctu
al p
late
s p
lus
the
par
tial
reb
oil
er.
Ex
erci
se 7
.28
(co
nti
nu
ed)
An
aly
sis:
(c
on
tin
ued
)
Ex
erci
se 7
.28
(co
nti
nu
ed)
An
aly
sis:
(c
on
tin
ued
)
Ex
erci
se 7
.28
(co
nti
nu
ed)
An
aly
sis:
(c
on
tin
ued
)
Ex
erci
se 7
.28
(co
nti
nu
ed)
An
aly
sis:
(c
on
tin
ued
)
(d
)
MW
of
ben
zen
e =
78
.11
. M
W o
f to
luen
e =
92
.14
.
Let
F =
km
ol/
h o
f fe
ed.
Th
en b
y m
ass
mat
eria
l b
alan
ce w
ith
an
eq
uim
ola
r fe
ed,
0.5
F (
78
.11
) +
0.5
F(9
2.1
4)
= 9
07
.3
So
lvin
g,
F =
10
.66
km
ol/
h.
Fo
r th
e eq
uim
ola
r fe
ed,
the
com
po
nen
t fl
ow
rat
es i
n t
he
feed
are
:
5.3
3 k
mo
l/h
eac
h f
or
ben
zen
e an
d t
olu
ene
Nex
t ca
lcu
late
th
e d
isti
llat
e an
d b
ott
om
s fl
ow
rat
es f
rom
,
ov
eral
l to
tal
mo
le b
alan
ce:
F =
nF =
10
.66
= D
+ B
(1)
ov
eral
l b
enze
ne
mo
le b
alan
ce:
Fx F
= 5
.33
= 0
.95
D +
0.0
5B
(2)
So
lvin
g E
qs.
(1
) an
d (
2),
D =
5.3
3 k
mo
l/h
an
d B
= 5
.33
km
ol/
h
Th
eref
ore
in
ter
ms
of
mas
s fl
ow
rat
es,
tota
l to
tal
dis
till
ate
rate
is,
mD =
0.9
5(5
.33
)(7
8.1
1)
+ 0
.05
(5.3
3)(
92
.14
) =
42
0.1
kg/h
Th
eref
ore
th
e b
ott
om
s ra
te =
mB =
90
7.3
- 4
20
.1 =
48
7.2
kg/h
(
e)
Fir
st c
om
pu
te t
he
km
ol/
h o
f v
apo
r le
avin
g t
he
reb
oil
er,
usi
ng t
he
assu
mp
tio
n o
f
con
stan
t m
ola
r o
ver
flo
w.
Fro
m p
art
(c),
th
e re
flu
x r
atio
= 1
.57
. T
her
efo
re,
the
refl
ux
rat
e =
1.5
7(5
.33
) =
8.3
7 k
mo
l/h
. B
elo
w t
he
feed
sta
ge,
th
e li
qu
id r
ate
= 8
.37
+ 1
0.6
6 =
19
.03
km
ol/
h.
Th
e v
apo
r ra
te l
eav
ing t
he
reb
oil
er =
19
.03
- 5
.33
= 1
3.7
0 k
mo
l/h
. F
rom
th
e p
lot
abo
ve,
th
e
com
po
siti
on
of
the
reb
oil
er v
apo
r =
12
mo
l% b
enze
ne.
N
egle
ctin
g t
he
sen
sib
le h
eat
and
usi
ng
the
enth
alp
y d
ata
giv
en,
afte
r co
nv
erti
ng f
rom
Btu
/lb
mo
l to
kJ/
km
ol,
th
e re
bo
iler
hea
t d
uty
is,
QR =
2.3
24
[0.1
2(1
3.7
)(1
8,1
30
- 4
,90
0)
+ 0
.88
(13
.7)(
21
,83
0 -
8,0
80
)] =
43
6,0
00
kJ/
km
ol.
Fro
m P
erry
's H
and
bo
ok
, la
ten
t h
eat
of
vap
ori
zati
on
of
stea
m a
t 2
73
.7 k
Pa
(40
4 K
) =
2,1
72
kJ/
kg
Th
eref
ore
, w
e n
eed
43
6,0
00
/2,1
72
= 2
00
.7 k
mo
l/h
or
3,6
16
kg/h
.
(f
) A
rig
oro
us
enth
alp
y b
alan
ce a
rou
nd
th
e re
bo
iler
tak
es i
nto
acc
ou
nt
the
sen
sib
le h
eat
effe
ct s
ince
th
e te
mp
erat
ure
of
the
liq
uid
en
teri
ng t
he
reb
oil
er i
s n
ot
the
sam
e as
th
e te
mp
erat
ure
s
of
the
equ
ilib
riu
m l
iqu
id a
nd
vap
or
leav
ing t
he
reb
oil
er.
Let
N =
co
nd
itio
ns
leav
ing t
he
reb
oil
er
and
N-1
be
the
con
dit
ion
s le
avin
g t
he
stag
e ab
ov
e th
e re
bo
iler
. T
hen
,
QV
HL
HL
HR
NV
NL
NL
NN
N=
+−
−−
11
No
te t
hat
in
th
e si
mp
lifi
ed e
nth
alp
y b
alan
ce o
f p
art
(e),
th
e fo
llo
win
g e
qu
atio
n w
as
app
lied
,
QV
HH
RN
VL
NN
=−
Sin
ce,
VL
LN
NN
=−
−1,
this
is
equ
ival
ent
to a
ssu
min
g H
HL
LN
N=
−1
Ex
erci
se 7
.29
S
ub
ject
: P
reli
min
ary d
esig
n f
or
the
dis
till
atio
n o
f a
mix
ture
of
eth
ano
l an
d w
ater
at
1 a
tm.
Giv
en:
B
ub
ble
-po
int
feed
co
nta
inin
g 2
0 m
ol%
eth
ano
l in
wat
er.
Un
it c
on
sist
ing o
f a
per
fora
ted
-tra
y c
olu
mn
, p
arti
al r
ebo
iler
, an
d t
ota
l co
nd
ense
r.
Dis
till
ate
to c
on
tain
85
mo
l%
alco
ho
l an
d a
97
% r
eco
ver
y o
f al
coh
ol.
V
apo
r-li
qu
id e
qu
ilib
riu
m d
ata.
Ass
um
pti
on
s:
Co
nst
ant
mo
lar
ov
erfl
ow
.
Fin
d:
(a)
M
ola
r co
nce
ntr
atio
ns
in t
he
bo
tto
ms
pro
du
ct.
(b
) M
inim
um
val
ues
of
L/V
, L
/D,
an
d V
B/B
.
(c
) M
inim
um
nu
mb
er o
f eq
uil
ibri
um
sta
ges
an
d a
ctu
al p
late
s fo
r E
o =
0.5
5.
(d
) N
um
ber
of
actu
al p
late
s fo
r L
/V =
0.8
0.
An
aly
sis:
F
rom
th
e v
apo
r-li
qu
id e
qu
ilib
riu
m d
ata
for
1 a
tm.,
it
is s
een
th
at e
than
ol
is m
ore
vo
lati
le t
han
wat
er f
or
eth
ano
l m
ole
fra
ctio
ns
in t
he
liq
uid
fro
m 0
to
0.8
94
3,
wh
ich
is
the
azeo
tro
pe
con
cen
trat
ion
. T
he
dis
till
ate
com
po
siti
on
is
wit
hin
th
is r
egio
n.
(a
) T
ake
a b
asis
of
F =
10
0 k
mo
l/h
.
Ov
eral
l to
tal
mat
eria
l b
alan
ce:
F =
10
0 =
D +
B
(1
)
Eth
ano
l re
cov
ery:
0
.97
Fx F
= 0
.97
(10
0)(
0.2
0)
= 1
9.4
= D
x D =
0.8
5D
(2
)
So
lvin
g E
q.
(2),
D =
22
.82
km
ol/
h.
Fro
m E
q.
(1),
B =
10
0 -
22
.82
= 7
7.1
8 k
mo
l/h
Eth
ano
l in
bo
tto
ms
= 2
0 -
19
.4 =
0.6
km
ol/
h
Th
eref
ore
, et
han
ol
mo
le f
ract
ion
in
bo
tto
ms
= 0
.6/7
7.1
8 =
0.0
07
77
Wat
er m
ole
fra
ctio
n i
n b
ott
om
s =
1.0
- 0
.00
77
7 =
0.9
92
23
(b)
In
th
e M
cCab
e-T
hie
le d
iagra
m o
n t
he
nex
t p
age,
th
e giv
en e
qu
ilib
riu
m d
ata
are
plo
tted
. F
or
a b
ub
ble
-po
int
liq
uid
fee
d,
the
q-l
ine
is v
erti
cal
at x
F =
0.2
. T
he
min
imu
m r
eflu
x i
n
term
s o
f L
/V i
s o
bta
ined
fro
m t
he
slo
pe
of
the
rect
ifyin
g s
ecti
on
op
erat
ing l
ine,
wh
ich
pas
ses
thro
ugh
th
e p
oin
t, y
= x
D =
0.8
5 a
nd
is
tan
gen
t to
th
e eq
uil
ibri
um
cu
rve,
rat
her
th
an b
ein
g d
raw
n
thro
ugh
th
e in
ters
ecti
on
of
the
q-l
ine
and
th
e eq
uil
ibri
um
cu
rve
bec
ause
th
at w
ou
ld c
ause
th
e
op
erat
ing l
ine
to m
ista
ken
ly c
ross
ov
er t
he
equ
ilib
riu
m c
urv
e.
Th
e sl
op
e o
f th
e o
per
atin
g l
ine
= (
L/V
) min
= 0
.65
.
Fro
m E
q.
(7-2
7),
Rm
in =
(L
/D) m
in =
0.6
5/(
1-0
.65
) =
1.8
6.
Th
e li
qu
id r
ate
in t
he
rect
ifyin
g s
ecti
on
= L
= 1
.86
D =
1.8
6(2
2.8
2)
= 4
2.4
4 k
mo
l/h
.
Bel
ow
th
e fe
ed p
late
, L
= L
+ F
= 4
2.4
4 +
10
0 =
14
2.4
4 k
mo
l/h
.
Vap
or
rate
fro
m t
he
reb
oil
er =
VB =
L
- B
= 1
42
.44
- 7
7.1
8 =
65
.26
km
ol/
h.
Th
eref
ore
, b
oil
up
rat
io =
V
B/B
= 6
5.2
6/7
7.1
8 =
0.8
46
.
(c)
In
th
e se
con
d M
cCab
e-T
hie
le d
iagra
m o
n t
he
nex
t p
age,
th
e m
inim
um
nu
mb
er o
f
stag
es i
s d
eter
min
ed b
y s
tep
pin
g o
ff s
tages
bet
wee
n t
he
equ
ilib
riu
m c
urv
e an
d t
he
45
o li
ne
(to
tal
refl
ux
) fr
om
th
e p
oin
ts 0
.85
an
d 0
.00
77
7 o
n t
he
45
o l
ine.
Th
e re
sult
is
app
rox
imat
ely 1
0
min
imu
m e
qu
ilib
riu
m s
tages
. F
or
a st
age
effi
cien
cy o
f 0
.55
, u
sin
g E
q.
(6-2
1),
N
a =
Nt/E
o =
10
/0.5
5 =
18
.2 m
inim
um
pla
tes.
Ex
erci
se 7
.29
(c
on
tin
ued
) A
na
lysi
s:
(b a
nd
c)
(co
nti
nu
ed)
Ex
erci
se 7
.29
(c
on
tin
ued
) A
na
lysi
s:
(b a
nd
c)
(co
nti
nu
ed)
Ex
erci
se 7
.29
(c
on
tin
ued
) A
na
lysi
s:
(co
nti
nu
ed)
(d)
Fo
r an
op
erat
ing r
eflu
x r
atio
= L
/V =
0.8
, th
e re
flu
x r
atio
, R
= L
/D =
0.8
/(1
-0.8
) =
4.
On
th
e
McC
abe-
Th
iele
dia
gra
m b
elo
w,
the
rect
ifyin
g s
ecti
on
op
erat
ing l
ine
has
a s
lop
e o
f 0
.8 a
nd
pas
ses
thro
ugh
th
e p
oin
t, y
=0
.85
, x=
0.8
5.
th
e st
rip
pin
g s
ecti
on
op
erat
ing l
ine
pas
ses
thro
ugh
th
e p
oin
t,
y=0
.00
77
7,
x=0
.07
77
an
d i
nte
rsec
ts t
he
ver
tica
l q
-lin
e at
th
e p
oin
t w
her
e th
e re
ctif
yin
g s
ecti
on
op
erat
ing l
ine
inte
rsec
ts t
he
q-l
ine.
A
s se
en,
the
equ
ilib
riu
m s
tages
are
ste
pp
ed o
ff s
tart
ing a
t th
e
top
, w
ith
a s
wit
ch f
rom
th
e re
ctif
yin
g s
ecti
on
to
th
e st
rip
pin
g s
ecti
on
to
min
imiz
e th
e n
um
ber
of
stag
es a
nd
, th
us,
lo
cati
ng t
he
op
tim
al f
eed
sta
ge.
T
he
resu
lt i
s ju
st l
ess
than
15
eq
uil
ibri
um
stag
es.
Cal
l it
14
eq
uil
ibri
um
sta
ges
plu
s a
par
tial
reb
oil
er.
Ap
ply
ing E
q.
(6-2
1),
Na =
14
/0.5
5 =
25
.5 o
r 2
6 a
ctu
al p
late
s p
lus
the
par
tial
reb
oil
er a
s an
eq
uil
ibri
um
sta
ge.
Ex
erci
se 7
.30
S
ub
ject
: R
eco
ver
y b
y d
isti
llat
ion
wit
h o
pen
ste
am o
f so
lven
t A
fro
m w
ater
in
tw
o f
eed
s.
Giv
en:
T
wo
sat
ura
ted
liq
uid
fee
ds,
eac
h c
on
tain
ing 5
0 k
mo
l/h
of
A.
Fee
d 1
co
nta
ins
40
mo
l%
A a
nd
Fee
d 2
co
nta
ins
60
mo
l% A
. U
nit
co
nsi
sts
of
a co
lum
n a
nd
a t
ota
l co
nd
ense
r.
Op
en s
team
is u
sed
in
lie
u o
f a
par
tial
reb
oil
er.
Rel
ativ
e v
ola
tili
ty =
3.0
fo
r A
wit
h r
esp
ect
to w
ater
.
Dis
till
ate
is t
o c
on
tain
95
mo
l% A
wit
h a
95
% r
eco
ver
y.
Ass
um
pti
on
s:
Co
nst
ant
mo
lar
ov
erfl
ow
. O
pen
ste
am e
nte
rs b
ott
om
sta
ge
as s
atu
rate
d v
apo
r.
Bo
th f
eed
s en
ter
at o
pti
mal
lo
cati
on
s.
Fin
d:
F
or
an o
ver
all
pla
te e
ffic
ien
cy o
f 7
0%
an
d a
n R
= L
/D =
1.3
3 t
imes
min
imu
m,
det
erm
ine
the
nu
mb
er o
f ac
tual
pla
tes.
C
om
pu
te t
he
bo
tto
ms
com
po
siti
on
. D
eter
min
e an
alyti
call
y t
he
loca
tio
n o
f al
l th
ree
op
erat
iin
g l
ines
.
An
aly
sis:
T
he
tota
l fl
ow
rat
e o
f F
eed
1 =
50
/0.4
= 1
25
km
ol/
h.
Th
e to
tal
feed
rat
e o
f F
eed
2 =
50
/0.6
= 8
3.3
km
ol/
h.
Th
e to
tal
feed
rat
e o
f A
= 5
0 +
50
= 1
00
km
ol/
h.
Fo
r a
reco
ver
y o
f 9
5%
of
A i
n t
he
dis
till
ate,
th
e fl
ow
rat
e o
f A
in
th
e d
isti
llat
e =
0.9
5(1
00
) =
95
km
ol/
h.
Wit
h a
mo
le
frac
tio
n o
f 0
.95
fo
r A
in
th
e d
isti
llat
e, t
he
tota
l fl
ow
rat
e o
f th
e d
isti
llat
e =
95
/0.9
5 =
10
0 k
mo
l/h
.
Fro
m E
q.
(7-3
) fo
r α
= 3
, th
e eq
uil
ibri
um
mo
le f
ract
ion
s o
f A
are
rel
ated
by,
yx
x
x
x=
+−
=+
α α1
1
3
12
()
(1
)
Eq
uat
ion
(1
) is
plo
tted
in
th
e M
cCab
e-T
hie
le d
iagra
m o
n t
he
nex
t p
age.
B
ecau
se F
eed
2 i
s ri
cher
in A
th
an F
eed
1,
Fee
d 2
en
ters
th
e co
lum
n a
bo
ve
Fee
d 1
. A
t m
inim
um
ref
lux
, th
e p
inch
con
dit
ion
wil
l o
ccu
r at
eit
her
Fee
d 1
or
Fee
d 2
. A
ssu
me
that
th
e p
inch
occ
urs
at
Fee
d 2
. F
or
a
satu
rate
d l
iqu
id f
eed
, u
sin
g E
q.
(1),
th
e u
pp
er s
ecti
on
op
erat
ing l
ine
wil
l in
ters
ect
the
equ
ilib
riu
m
curv
e fo
r x F
= 0
.6 a
t y
= 3
(0.6
)/[1
+ 2
(0.6
)] =
0.8
18
. T
her
efo
re,
the
slo
pe
of
this
op
erat
ing l
ine
is,
(L/V
) min
= (
0.9
5 -
0.8
18
)/(0
.95
0 -
0.6
) =
0.3
77
Co
rres
po
nd
ingly
, u
sin
g E
q.
(7-1
7),
R =
L/D
= (
L/V
) min
/[1
- (
L/V
) min
] =
0.3
77
/(1
- 0
.37
7)
= 0
.60
5
and
Lm
in =
0.6
05
(10
0)
= 6
0.5
km
ol/
h.
No
w c
hec
k t
he
mid
dle
sec
tio
n t
o s
ee i
f th
e o
per
atin
g l
ine
ther
e is
bel
ow
th
e eq
uil
ibri
um
cu
rve.
Th
e li
qu
id r
ate
in t
he
mid
dle
sec
tio
n =
L' =
L +
F2 =
60
.5 +
83
.3 =
14
3.8
km
ol/
h.
Th
e v
apo
r ra
te i
n t
he
mid
dle
sec
tio
n =
V' =
V =
L +
D =
60
.5 +
10
0 =
16
0.5
km
ol/
h.
Th
eref
ore
th
e sl
op
e o
f th
e o
per
atin
g l
ine
in t
he
mid
dle
sec
tio
n =
L'/
V' =
14
3.8
/16
0.5
= 0
.89
6.
As
seen
in
th
e M
cCab
e-T
hie
le d
iagra
m o
n t
he
nex
t p
age,
th
is o
per
atin
g l
ine
do
es n
ot
cro
ss o
ver
the
equ
ilib
riu
m c
urv
e.
Th
eref
ore
, th
e p
inch
do
es o
ccu
r at
Fee
d 2
(th
e u
pp
er f
eed
).
Fo
r an
op
erat
ing r
eflu
x r
atio
of
1.3
3 t
imes
min
imu
m,
L =
1.3
3(6
0.5
) =
80
.5 k
mo
l/h
.
Th
e v
apo
r ra
te i
n t
he
up
per
sec
tio
n =
L +
D =
80
.5 +
10
0 =
18
0.5
km
ol/
h.
Ex
erci
se 7
.30
(c
on
tin
ued
) A
na
lysi
s:
(co
nti
nu
ed)
T
her
efo
re t
he
up
per
sec
tio
n o
per
atin
g l
ine
has
a s
lop
e, L
/V =
80
.5/1
80
.5 =
0.4
46
an
d p
asse
s
thro
ugh
th
e p
oin
t y
= x
= 0
.95
. I
t in
ters
ects
th
e v
erti
cal
q-l
ine
at x
= 0
.6 a
nd
fo
r th
e sl
op
e o
f
0.4
46
= (
0.9
5 -
y)/
(0.9
5 -
0.6
), y
= 0
.79
4.
Fo
r th
e m
idd
le s
ecti
on
, L
' =
L +
F2
= 8
0.5
+ 8
3.3
= 1
63
.8 k
mo
l/h
an
d V
' =
V =
18
0.5
km
ol/
h
Th
eref
ore
, th
e m
idd
le s
ecti
on
op
erat
ing l
ine
has
a s
lop
e o
f L
'/V
' =
16
3.8
/18
0.5
= 0
.90
8 a
nd
inte
rsec
ts t
he
q-l
ine
for
x =
0.6
at
y =
0.7
94
. I
t in
ters
ects
th
e v
erti
cal
q-l
ine
at x
= 0
.4 a
nd
fo
r th
e
slo
pe
of
0.9
08
= (
0.7
94
- y
)/(0
.6 -
0.4
), y
= 0
.61
3.
Fo
r th
e lo
wer
sec
tio
n,
L"
= L
' +
F1 =
16
3.8
+ 1
25
= 2
88
.8 k
mo
l/h
an
d V
"=V
' =
18
0.5
km
ol/
h
Th
eref
ore
, th
e lo
wer
sec
tio
n o
per
atin
g l
ine
has
a s
lop
e o
f L
"/V
" =
28
8.8
/18
0.5
= 1
.60
an
d
inte
rsec
ts t
he
q-l
ine
for
x =
0.4
an
d y
= 0
.61
3.
As
seen
in
Fig
. 7
.27
(c),
th
e m
ole
fra
ctio
n o
f A
in
the
bo
tto
ms,
xB ,
is
det
erm
ined
fro
m t
he
inte
rsec
tio
n o
f th
e o
per
atin
g l
ine
for
the
low
er s
ecti
on
wit
h t
he
y-ax
is.
Th
us,
1
.60
= (
0.6
13
- 0
)/(0
.4 -
xB).
S
olv
ing,
x B =
0.0
16
9 f
or
com
po
nen
t A
.
Sin
ce t
he
bo
tto
ms
con
tain
s 5
km
ol/
h o
f A
, th
e b
ott
om
s ra
te =
B =
5/0
.01
69
= 2
95
.9 k
mo
l/h
.
Th
us,
th
e b
ott
om
s co
nta
ins
29
0.9
km
ol/
h o
f w
ater
. B
ut,
th
e fl
ow
rat
e o
f w
ater
en
teri
ng i
n t
he
two
feed
s =
12
5 +
83
.3 -
10
0 =
10
8.3
km
ol/
h.
Th
eref
ore
, th
e o
pen
ste
am f
low
rat
e =
29
0.9
+ 5
- 1
08
.3 =
18
7.6
km
ol/
h
In t
he
McC
abe-
Th
iele
dia
gra
m o
n t
he
nex
t p
age,
th
e th
ree
op
erat
ing l
ines
are
dra
wn
an
d t
he
equ
ilib
riu
m s
tages
are
ste
pp
ed o
ff s
o a
s to
pla
ce t
he
two
fee
ds
at t
hei
r o
pti
mal
lo
cati
on
s.
As
seen
, th
e n
um
ber
of
equ
ilib
riu
m s
tages
req
uir
ed =
Nt =
14
. F
rom
Eq
. (6
-21
), f
or
a p
late
effi
cien
cy o
f 7
0%
, th
e ac
tual
nu
mb
er o
f tr
ays
= N
a =
Nt /
Eo =
14
/0.7
= 2
0 p
late
s.
Ex
erci
se 7
.30
(c
on
tin
ued
) A
na
lysi
s:
(co
nti
nu
ed)
Ex
erci
se 7
.31
S
ub
ject
: D
isti
llat
ion
of
a m
ixtu
re o
f n
-hex
ane
and
n-o
ctan
e in
a c
olu
mn
wit
h a
n
inte
rco
ole
r.
Giv
en:
S
atu
rate
d l
iqu
id f
eed
of
40
mo
l% h
exan
e in
oct
ane.
In
terc
oo
ler
at s
eco
nd
sta
ge
fro
m t
he
top
rem
ov
es h
eat
so a
s to
co
nd
ense
50
mo
l% o
f th
e v
apo
r ri
sin
g f
rom
th
e th
ird
. D
isti
llat
e is
to
con
tain
95
mo
l% o
f h
exan
e an
d b
ott
om
s is
to
co
nta
in 5
mo
l% o
f h
exan
e.
Ref
lux
rat
io,
L/D
, at
the
top
, is
eq
ual
to
0.5
. V
apo
r-li
qu
id e
qu
ilib
riu
m d
ata
for
1 a
tm i
s p
lott
ed i
n F
ig.
4.4
.
Ass
um
pti
on
s:
Co
nst
ant
mo
lar
ov
erfl
ow
. T
ota
l co
nd
ense
r an
d p
arti
al r
ebo
iler
. O
per
atin
g
pre
ssu
re o
f 1
atm
.
Fin
d:
(a
) E
qu
atio
ns
to l
oca
te o
per
atin
g l
ines
.
(b
) N
um
ber
of
equ
ilib
riu
m s
tages
if
op
tim
al f
eed
sta
ge
loca
tio
n i
s u
sed
.
An
aly
sis:
F
irst
co
mp
ute
ov
eral
l m
ater
ial
bal
ance
. T
ake
a b
asis
of
F =
10
0 k
mo
l/h
.
O
ver
all
tota
l m
ole
bal
ance
:
F
= 1
00
= D
+ B
(1)
O
ver
all
hex
ane
mo
le b
alan
ce:
F
x F =
40
= D
x D +
Bx B
= 0
.95
D +
0.0
5B
(2
)
So
lvin
g E
qs.
(1
) an
d (
2),
D
= 3
8.9
km
ol/
h
and
B
= 6
1.1
km
ol/
h
(a
) F
or
a re
flu
x r
atio
of
0.5
, in
th
e se
ctio
n a
bo
ve
the
inte
rco
ole
r, L
= 0
.5D
= 1
9.4
5
km
ol/
h.
Th
e o
ver
hea
d v
apo
r ra
te i
s V
= L
+ D
=
19
.45
+ 3
8.9
= 5
8.3
5 k
mo
l/h
. T
he
slo
pe
of
the
op
erat
ing l
ine
= L
/V =
19
.45
/58
.35
= 0
.33
3.
Usi
ng E
q.
(7-6
), t
he
equ
atio
n f
or
the
op
erat
ing l
ine
is,
y
= 0
.33
3x
+ D
x D/V
=
0.3
33
x +
(3
8.9
)(0
.95
)/(5
8.3
5)
= 0
.33
3x
+ 0
.63
3
(3)
No
w c
on
sid
er t
he
sect
ion
of
stag
es b
etw
een
th
e in
terc
oo
ler
at s
tage
2 f
rom
th
e to
p a
nd
th
e fe
ed
stag
e.
Bec
ause
50
mo
l% o
f th
e v
apo
r fr
om
th
is s
ecti
on
is
con
den
sed
at
stag
e 2
by t
he
inte
rco
ole
r,
the
vap
or
rate
in
th
is s
ecti
on
= V
' =
2V
= 2
(58
.35
) =
11
6.7
km
ol/
h.
Th
e li
qu
id r
ate
in t
his
sec
tio
n
is L
' =
V' -
D =
11
6.7
- 3
8.9
= 7
7.8
km
ol/
h.
Th
e sl
op
e o
f th
e o
per
atin
g l
ine
= L
'/V
' =
77
.8/1
16
.7
= 0
.66
7.
In
th
is s
ecti
on
, b
y h
exan
e m
ater
ial
bal
ance
, yV
' =
xL
' +
xDD
o
r,
y
= (
L'/
V')
x +
Dx D
/V' =
0.6
67
x +
(3
8.9
)(0
.95
)/1
16
.7 =
0.6
67
x +
0.3
17
(4
)
In t
he
sect
ion
bel
ow
th
e fe
ed s
tage,
fo
r a
satu
rate
d l
iqu
id f
eed
, L
"= L
' +
F =
7
7.8
+ 1
00
= 1
77
.8
km
ol/
h.
Th
e v
apo
r ra
te =
V"
= V
' =
11
6.7
km
ol/
h.
Th
e sl
op
e o
f th
e o
per
atin
g l
ine
= L
"/V
" =
17
7.8
/11
6.7
= 1
.52
4.
Fro
m E
q.
(7-1
1),
y
= (
L"/
V")
x -
Bx B
/V”
= 1
.52
4x
- (6
1.1
)(0
.05
)/1
16
.7 =
1.5
24
x -
0.0
26
(5
)
(b)
A M
cCab
e-T
hie
le d
iagra
m i
n t
erm
s o
f h
exan
e, t
he
mo
re v
ola
tile
co
mp
on
ent,
is
sho
wn
on
th
e n
ext
pag
e, w
her
e th
e eq
uil
ibri
um
cu
rve
is o
bta
ined
fro
m F
ig.
4.4
an
d t
he
op
erat
ing
lin
es f
or
the
thre
e se
ctio
ns
are
dra
wn
fro
m E
qs.
(3
), (
4),
an
d (
5).
T
he
q-l
ine
is v
erti
cal,
pas
sin
g
thro
ugh
x =
0.4
.
No
te t
hat
th
e u
pp
er a
nd
mid
dle
sec
tio
n o
per
atin
g l
ines
bo
th p
ass
thro
ugh
th
e
po
int
{0
.95
, 0
.95
}.
Th
e th
eore
tica
l st
ages
are
ste
pp
ed o
ff s
tart
ing f
rom
th
e to
p,
swit
chin
g t
o t
he
mid
dle
sec
tio
n o
per
atin
g l
ine
afte
r st
age
2,
and
sw
itch
ing t
o t
he
stri
pp
ing s
ecti
on
so
as
to l
oca
te
the
feed
sta
ge
op
tim
ally
. T
he
resu
lt i
s ju
st s
ligh
tly l
ess
than
5
eq
uil
ibri
um
sta
ges
or,
say
, 4
stag
es p
lus
a p
arti
al r
ebo
iler
.
Ex
erci
se 7
.31
(co
nti
nu
ed)
An
aly
sis:
(co
nti
nu
ed)
Ex
erci
se 7
.32
S
ub
ject
: D
isti
llat
ion
of
a m
ixtu
re o
f et
hyl
alco
ho
l an
d w
ater
at
1 a
tm u
sin
g o
pen
ste
am
inst
ead
of
a re
bo
iler
.
Giv
en:
1
00
km
ol/
h o
f a
satu
rate
d l
iqu
id f
eed
co
nta
inin
g 1
2 m
ol%
eth
yl
alco
ho
l in
wat
er.
Dis
till
ate
to c
on
tain
85
mo
l% a
lco
ho
l w
ith
a r
eco
ver
y o
f 9
0%
. R
eflu
x r
atio
, L
/D =
3 w
ith
satu
rate
d l
iqu
id r
eflu
x.
Fee
d s
tage
loca
ted
op
tim
ally
. V
apo
r-li
qu
id e
qu
ilib
riu
m d
ata
in E
xer
cise
7.2
9.
Ass
um
pti
on
s:
C
on
stan
t m
ola
r o
ver
flo
w.
To
tal
con
den
ser.
Fin
d:
(a)
O
pen
ste
am r
equ
irem
ent,
km
ol/
h
(b
) N
um
ber
of
equ
ilib
riu
m s
tages
(c
) O
pti
mal
fee
d s
tage
loca
tio
n.
(d
) M
inim
um
ref
lux
rat
io.
An
aly
sis:
F
irst
co
mp
ute
mat
eria
l b
alan
ce.
Bec
ause
th
e et
han
ol
mo
le f
ract
ion
in
th
e d
isti
llat
e is
less
th
an t
hat
of
the
azeo
tro
pe
(89
.43
mo
l% i
n E
xer
cise
7.2
9),
th
e et
han
ol
is a
lway
s th
e m
ore
vo
lati
le c
om
po
nen
t.
Th
e fe
ed c
on
tain
s 1
2 k
mo
l/h
of
eth
ano
l an
d 8
8 k
mo
l/h
of
wat
er.
Fo
r a
90
%
reco
ver
y,
the
dis
till
ate
con
tain
s 0
.9(1
2)
= 1
0.8
km
ol/
h o
f et
han
ol.
S
ince
th
e d
isti
llat
e is
85
mo
l%
eth
ano
l, t
he
tota
l d
isti
llat
e ra
te =
D =
10
.8/0
.85
= 1
2.7
km
ol/
h.
Th
e b
ott
om
s co
nta
ins
12
- 1
0.8
=
1.2
km
ol/
h o
f et
han
ol.
T
he
dis
till
ate
con
tain
s 1
2.7
- 1
0.8
= 1
.9 k
mo
l/h
of
wat
er.
Th
e b
ott
om
s
con
tain
s 8
8 -
1.9
+ o
pen
ste
am =
89
.9 +
op
en s
team
in
km
ol/
h.
(a
) F
or
a re
flu
x r
atio
of
3,
L =
3D
= 3
(12
.7)
= 3
8.1
km
ol/
h.
Ov
erh
ead
vap
or
rate
= V
= L
+ D
= 3
8.1
+ 1
2.7
= 5
0.8
km
ol/
h.
Bel
ow
th
e fe
ed s
tage,
L' =
L +
F =
38
.1 +
10
0 =
13
8.1
km
ol/
h.
Bo
ilu
p r
ate
= V
' =
V =
50
.8 k
mo
l/h
= f
low
rat
e o
f o
pen
ste
am.
(b)
Th
e b
ott
om
s ra
te =
13
8.1
km
ol/
h.
Th
e b
ott
om
s co
nsi
sts
of
1.2
km
ol/
h o
f et
han
ol
and
13
8.1
- 1
.2 =
13
6.9
km
ol/
h o
f w
ater
. T
he
mo
le f
ract
ion
of
eth
ano
l in
th
e b
ott
om
s =
1.2
/13
8.1
=
0.0
08
7.
Th
e M
cCab
e-T
hie
le d
iagra
m i
s giv
en o
n t
he
nex
t p
age,
wh
ere
the
equ
ilib
riu
m c
urv
e is
ob
tain
ed f
rom
Ex
erci
se 7
.29
an
d t
he
q-l
ine
is v
erti
cal
at x
= 0
.12
. T
he
rect
ifyin
g s
ecti
on
op
erat
ing l
ine
pas
ses
thro
ugh
th
e p
oin
t {0
.85
, 0
.85
}an
d h
as a
slo
pe,
L/V
= 3
8.1
/50
.8 =
0.7
5.
Th
e
stri
pp
ing s
ecti
on
op
erat
ing l
ine
has
a s
lop
e, L
'/V
' =
13
8.1
/50
.8 =
2.7
2 a
nd
, as
sh
ow
n i
n F
ig.
7.2
7(c
), p
asse
s th
rou
gh
th
e p
oin
t x
= x
B =
0.0
08
7 a
t y
= 0
. B
ecau
se t
he
stag
es a
re s
o c
row
ded
at
the
hig
h m
ole
fra
ctio
n e
nd
, a
seco
nd
McC
abe-
Th
iele
dia
gra
m i
s sh
ow
n f
or
the
regio
n a
bo
ve
y =
x
= 0
.7.
As
sho
wn
, w
ith
th
e u
se o
f th
e tw
o d
iagra
ms,
ju
st l
ess
than
20
eq
uil
ibri
um
sta
ges
are
nee
ded
. (c)
Fro
m t
he
firs
t M
cCab
e-T
hie
le p
lot,
th
e o
pti
mal
fee
d s
tage
is S
tage
18
fro
m t
he
top
.
(d)
Fro
m t
he
thir
d M
cCab
e-T
hie
le d
iagra
m o
n t
he
nex
t p
age,
th
e m
inim
um
ref
lux
in
term
s o
f L
/V i
s o
bta
ined
fro
m t
he
slo
pe
of
the
rect
ifyin
g s
ecti
on
op
erat
ing l
ine,
wh
ich
pas
ses
thro
ugh
th
e p
oin
t, y
= x
D =
0.8
5 a
nd
is
tan
gen
t to
th
e eq
uil
ibri
um
cu
rve,
rat
her
th
an b
ein
g d
raw
n
thro
ugh
th
e in
ters
ecti
on
of
the
q-l
ine
and
th
e eq
uil
ibri
um
cu
rve
bec
ause
th
at w
ou
ld c
ause
th
e
op
erat
ing l
ine
to m
ista
ken
ly c
ross
ov
er t
he
equ
ilib
riu
m c
urv
e.
Th
e sl
op
e o
f th
e o
per
atin
g l
ine
=
(L/V
) min
= 0
.66
7.
F
rom
Eq
. (7
-27
), R
min
= (
L/D
) min
= 0
.66
7/(
1-0
.66
7)
= 2
.0.
Ex
erci
se 7
.32
(c
on
tin
ued
) A
na
lysi
s:
(b
, c,
an
d d
)
(co
nti
nu
ed)
Ex
erci
se 7
.32
(c
on
tin
ued
)
A
na
lysi
s:
(b
, c,
an
d d
)
(co
nti
nu
ed)
Ex
erci
se 7
.32
(c
on
tin
ued
)
A
na
lysi
s:
(b
, c,
an
d d
)
(co
nti
nu
ed)
Ex
erci
se 7
.33
S
ub
ject
: D
isti
llat
ion
of
a m
ixtu
re o
f is
op
rop
yl
alco
ho
l an
d w
ater
at
1 a
tm u
sin
g e
ith
er a
par
tial
reb
oil
er o
r o
pen
ste
am.
Giv
en:
B
ub
ble
-po
int
feed
co
nta
inin
g 1
0 m
ol%
iso
pro
pyl
alco
ho
l in
wat
er.
Dis
till
ate
to c
on
tain
67
.5 m
ol%
iso
pro
pyl
alco
ho
l w
ith
a 9
8%
rec
ov
ery.
Vap
or-
liq
uid
eq
uil
ibri
um
dat
a ,
wit
h a
n
azeo
tro
pe
at 6
8.5
4 m
ol%
alc
oh
ol.
Ass
um
pti
on
s:
Co
nst
ant
mo
lar
ov
erfl
ow
. T
ota
l co
nd
ense
r.
Fin
d:
F
or
a re
flu
x r
atio
, R
= L
/D =
1.5
tim
es m
inim
um
, d
eter
min
e n
um
ber
of
stag
es,
if:
(a
) P
arti
al r
ebo
iler
is
use
d.
(b
) O
pen
sat
ura
ted
st
eam
is
use
d.
and
(c
) M
inim
um
nu
mb
er o
f eq
uil
ibri
um
sta
ges
.
An
aly
sis:
In
th
e co
mp
osi
tio
n r
egio
n o
f o
per
atio
n,
the
alco
ho
l is
th
e m
ost
vo
lati
le c
om
po
nen
t.
Fir
st,
com
pu
te t
he
dis
trib
uti
on
of
the
alco
ho
l.
Tak
e a
bas
is o
f 1
00
km
ol/
h o
f fe
ed.
Th
en,
the
feed
co
nta
ins
10
km
ol/
h a
lco
ho
l an
d 9
0 k
mo
l/h
of
wat
er.
Fo
r a
reco
ver
y o
f 9
8 m
ol%
,
alco
ho
l, d
isti
llat
e co
nta
ins
9.8
km
ol/
h o
f al
coh
ol.
F
or
an a
lco
ho
l p
uri
ty o
f 6
7.5
mo
l%,
the
dis
till
ate
rate
= D
= 9
.8/0
.67
5 =
14
.52
km
ol/
h.
Wat
er i
n t
he
dis
till
ate
= 1
4.5
2 -
9.8
= 4
.72
km
ol/
h.
Alc
oh
ol
in t
he
bo
tto
ms
= 1
0 -
9.8
= 0
.2 k
mo
l/h
.
(a
) W
ith
a p
arti
al r
ebo
iler
, n
o o
ther
wat
er e
nte
rs t
he
syst
em.
Th
eref
ore
, w
ater
in
th
e
bo
tto
ms
= 9
0 -
4.7
2 =
85
.28
km
ol/
h.
To
tal
bo
tto
ms
rate
= B
= 8
5.2
8 +
0.2
= 8
5.4
8 k
mo
l/h
.
Mo
le f
ract
ion
of
alco
ho
l in
bo
tto
ms
= 0
.2/8
5.4
8 =
0.0
02
3.
Th
e m
inim
um
ref
lux
is
det
erm
ined
fro
m t
he
McC
abe-
Th
iele
dia
gra
m o
n t
he
nex
t p
age,
wh
ere
the
equ
ilib
riu
m c
urv
e is
dra
wn
fro
m t
he
giv
en d
ata
and
th
e q
-lin
e is
ver
tica
l, p
assi
ng t
hro
ugh
x =
0.1
0.
Th
e re
ctif
yin
g
sect
ion
op
erat
ing l
ine
for
min
imu
m r
eflu
x u
sual
ly i
s a
stra
igh
t li
ne
that
co
nn
ects
th
e d
isti
llat
e
mo
le f
ract
ion
on
th
e 4
5o l
ine
to t
he
inte
rsec
tio
n o
f th
e eq
uil
ibri
um
cu
rve
and
th
e q
-lin
e as
sh
ow
n
by t
he
das
hed
lin
e o
n t
he
dia
gra
m.
Ho
wev
er,
in t
his
cas
e th
e li
ne
mis
tak
enly
cro
sses
ov
er t
he
equ
ilib
riu
m c
urv
e.
Th
eref
ore
, in
stea
d,
the
op
erat
ing l
ine
is d
raw
n t
angen
t to
th
e eq
uil
ibri
um
curv
e fr
om
th
e p
oin
t x
= x
D =
0.6
75
as
sho
wn
on
th
e d
iagra
m b
y a
so
lid
lin
e.
Th
e sl
op
e o
f th
e
op
erat
ing l
ine
= L
/V =
0.4
67
.
Fro
m E
q.
(7-2
7),
Rm
in =
(L
/D) m
in =
0.4
67
/(1
-0.4
67
) =
0.8
76
.
Th
e o
per
atin
g r
eflu
x r
atio
= R
= 1
.5R
min
= 1
.5(0
.87
6)
= 1
.31
4.
Fro
m E
q.
(7-7
), L
/V =
R/(
1+
R)
=
1.3
14
/(1
+1
.31
4)
= 0
.56
8.
On
a s
et o
f th
ree
McC
abe-
Th
iele
dia
gra
ms
on
th
e n
ext
pag
e, t
he
rect
ifyin
g s
ecti
on
op
erat
ing l
ine
has
th
is s
lop
e an
d p
asse
s th
rou
gh
th
e p
oin
t, y
=0
.67
5,
x=0
.67
5.
the
stri
pp
ing s
ecti
on
op
erat
ing l
ine
pas
ses
thro
ugh
th
e p
oin
t, y
=0
.00
23
, x=
0.0
02
3 a
nd
in
ters
ects
the
ver
tica
l q
-lin
e at
th
e p
oin
t w
her
e th
e re
ctif
yin
g s
ecti
on
op
erat
ing l
ine
inte
rsec
ts t
he
q-l
ine.
A
s
seen
, th
e eq
uil
ibri
um
sta
ges
are
ste
pp
ed o
ff s
tart
ing a
t th
e to
p,
wit
h a
sw
itch
fro
m t
he
rect
ifyin
g
sect
ion
to
th
e st
rip
pin
g s
ecti
on
to
min
imiz
e th
e n
um
ber
of
stag
es a
nd
, th
us,
lo
cati
ng t
he
op
tim
al
feed
sta
ge.
T
o a
chie
ve
accu
racy
, o
ne
dia
gra
m c
ov
ers
the
hig
h-c
on
cen
trat
ion
reg
ion
, o
ne
the
mid
dle
re
gio
n,
and
o
ne
the
low
-co
nce
ntr
atio
n
regio
n.
T
he
resu
lt
is
bet
wee
n
14
an
d
15
equ
ilib
riu
m s
tages
. C
all
it 1
4 s
tages
plu
s a
par
tial
reb
oil
er.
Ex
erci
se 7
.33
(co
nti
nu
ed)
An
aly
sis:
(a
) (
con
tin
ued
)
Ex
erci
se 7
.33
(co
nti
nu
ed)
An
aly
sis:
(a
) (
con
tin
ued
)
Ex
erci
se 7
.33
(co
nti
nu
ed)
An
aly
sis:
(a
) (
con
tin
ued
)
Ex
erci
se 7
.33
(co
nti
nu
ed)
An
aly
sis:
(a
) (
con
tin
ued
)
Ex
erci
se 7
.33
(co
nti
nu
ed)
An
aly
sis:
(
con
tin
ued
)
(b
) W
hen
op
en (
liv
e) s
team
is
use
d w
ith
th
e sa
me
refl
ux
rat
io,
the
rect
ific
atio
n s
ecti
on
op
erat
ing l
ine
and
th
e q
-lin
e ar
e id
enti
cal
to p
art
(a)
for
a p
arti
al r
ebo
iler
. T
hu
s, t
he
par
t (a
)
McC
abe-
Th
iele
dia
gra
m f
or
the
hig
h c
on
cen
trat
ion
reg
ion
ap
pli
es f
or
op
en s
team
.
H
ow
ever
, th
e st
rip
pin
g s
ecti
on
op
erat
ing l
ine
and
th
e b
ott
om
s m
ole
fra
ctio
n c
han
ge
as
foll
ow
s.
Th
e li
qu
id r
ate
in t
he
rect
ific
atio
n s
ecti
on
= L
= 1
.31
4D
= 1
.31
4(1
4.5
2)
= 1
9.0
8 k
mo
l/h
.
Th
e v
apo
r ra
te i
n t
he
rect
ifyin
g s
ecti
on
= V
= L
+ D
= 1
9.0
8 +
14
.52
= 3
3.6
km
ol/
h.
Th
e li
qu
id
rate
bel
ow
th
e fe
ed s
tage
= L
' =
L +
F =
1
9.0
8 +
10
0 =
11
9.0
8 k
mo
l/h
. T
he
vap
or
rate
in
th
e
stri
pp
ing s
ecti
on
= V
' =
V =
33
.6 k
mo
l/h
= o
pen
ste
am f
low
rat
e.
Th
e b
ott
om
s ra
te =
B =
L' =
11
9.0
8 k
mo
l/h
. T
he
mo
le f
ract
ion
of
iso
pro
pan
ol
in t
he
bo
tto
ms
= 0
.2/1
19
.08
= 0
.00
16
8.
Th
e
chan
ge
to t
he
par
t (a
) M
cCab
e-T
hie
le d
iagra
ms
on
th
e p
rece
din
g p
age
for
the
mid
dle
con
cen
trat
ion
reg
ion
is
extr
emel
y s
mal
l b
ecau
se t
he
loca
tio
n o
f th
e st
rip
pin
g s
ecti
on
op
erat
ing
lin
e ch
anges
on
ly s
ligh
tly.
H
ow
ever
, th
e ch
ange
is i
mp
ort
ant
in t
he
low
-co
nce
ntr
atio
n r
egio
n.
Th
e n
ew M
cCab
e-
Th
iele
dia
gra
m f
or
the
low
co
nce
ntr
atio
n r
egio
n i
s sh
ow
n b
elo
w.
Th
e o
per
atin
g l
ine
for
the
stri
pp
ing s
ecti
on
has
a s
lop
e o
f L
'/V
' =
11
9.0
8/3
3.6
= 3
.54
an
d p
asse
s th
rou
gh
th
e p
oin
t {y
= 0
, x
= 0
.00
16
8}.
Th
e n
um
ber
of
stag
es r
emai
ns
abo
ut
the
sam
e as
fo
r p
art
(a).
T
hu
s, w
ith
ou
t a
reb
oil
er,
use
15
eq
uil
ibri
um
sta
ges
in
th
e co
lum
n.
Ex
erci
se 7
.33
(co
nti
nu
ed)
An
aly
sis:
(
c)
(co
nti
nu
ed)
(c
) T
he
min
imu
m n
um
ber
of
stag
es i
s d
eter
min
ed a
s sh
ow
n i
n t
he
McC
abe-
Th
iele
dia
gra
ms
on
th
e n
ext
pag
e b
y s
tep
pin
g o
ff
stag
es b
etw
een
th
e eq
uil
ibri
um
cu
rve
and
th
e 4
5o l
ine
fro
m
x B =
0.0
02
3 a
nd
xD =
0.6
75
. T
he
nu
mb
er o
f m
inim
um
eq
uil
ibri
um
sta
ges
= j
ust
mo
re t
han
8 e
qu
ilib
riu
m s
tages
.
Ex
erci
se 7
.33
(co
nti
nu
ed)
An
aly
sis:
(
c)
(co
nti
nu
ed)
Ex
erci
se 7
.33
(co
nti
nu
ed)
An
aly
sis:
(
c)
(co
nti
nu
ed)
Ex
erci
se 7
.34
S
ub
ject
: S
trip
pin
g o
f is
op
rop
yl
alco
ho
l fr
om
wat
er a
t 1
atm
usi
ng e
ith
er a
par
tial
reb
oil
er o
r
op
en (
liv
e) s
team
.
Giv
en:
B
ub
ble
-po
int
liq
uid
fee
d c
on
tain
ing 1
0 m
ol%
alc
oh
ol.
V
apo
r o
ver
hea
d t
o c
on
tain
40
mo
l% a
lco
ho
l.
Bo
ilu
p,
V/F
= 0
.24
6.
Vap
or-
liq
uid
eq
uil
ibri
um
dat
a fr
om
Ex
erci
se 7
.33
.
Ass
um
pti
on
s:
Co
nst
ant
mo
lar
ov
erfl
ow
.
Fin
d:
D
eter
min
e th
e n
um
ber
of
equ
ilib
riu
m s
tages
fo
r: (
1)
Par
tial
reb
oil
er,
(2)
Op
en s
team
.
An
aly
sis:
T
ake
a b
asis
of
F =
10
0 k
mo
l/h
. V
apo
r ra
te l
eav
ing t
op
of
colu
mn
= V
= 0
.24
6F
= D
=
0.2
46
(10
0)
= 2
4.6
km
ol/
h.
Alc
oh
ol
in o
ver
hea
d v
apo
r =
0.4
(24
.6)
= 9
.84
km
ol/
h.
Wat
er i
n t
he
ov
erh
ead
vap
or
= 2
4.6
- 9
.84
= 1
4.7
6 k
mo
l/h
.
(1)
W
ith
a p
arti
al r
ebo
iler
, b
ott
om
s ra
te =
B =
F -
D =
10
0 -
24
.6 =
75
.4 k
mo
l/h
. A
lco
ho
l in
bo
tto
ms
= 1
0 -
9.8
4 =
0.1
6 k
mo
l/h
. M
ole
fra
ctio
n o
f al
coh
ol
in b
ott
om
s =
xB =
0.1
6/7
5.4
=
0.0
02
1.
Wit
h i
sop
rop
ano
l as
th
e m
ost
vo
lati
le c
om
po
nen
t, t
he
McC
abe-
Th
iele
dia
gra
m i
s giv
en
bel
ow
, w
her
e th
e eq
uil
ibri
um
cu
rve
is o
bta
ined
fro
m t
he
dat
a in
Ex
erci
se 7
.33
an
d t
he
q-l
ine
is
ver
tica
l th
rou
gh
x =
0.1
0.
Th
e st
rip
pin
g s
ecti
on
op
erat
ing l
ine
pas
ses
thro
ugh
th
e p
oin
t
{x=
0.0
02
1,
y=0
.00
21
}w
ith
a s
lop
e =
L/V
= F
/V =
10
0/2
4.6
= 4
.06
5.
It
also
pas
ses
thro
ugh
th
e
po
int
{x=
0.1
, y=
0.4
}.
Fro
m t
he
plo
t, t
he
nu
mb
er o
f eq
uil
ibri
um
sta
ges
= j
ust
les
s th
an 3
. C
all
it
2 e
qu
ilib
riu
m s
tages
in
th
e co
lum
n +
par
tial
reb
oil
er.
(2)
T
he
op
en s
team
rat
e =
V =
24
.6 k
mo
l/h
. T
he
liq
uid
rat
e =
L =
10
0 k
mo
l/h
. T
her
efo
re,
the
slo
pe
of
the
stri
pp
ing s
ecti
on
op
erat
ing l
ine
is t
he
sam
e as
fo
r p
art
(1),
i.e
.
L./
V =
10
0/2
4.6
= 4
.06
5.
No
w t
he
mo
le f
ract
ion
of
alco
ho
l in
th
e b
ott
om
s =
xB =
0.1
6/1
00
=
0.0
01
6.
Th
us,
as
sho
wn
in
th
e M
cCab
e-T
hie
le d
iagra
m b
elo
w,
the
op
erat
ing l
ine
pas
ses
thro
ugh
the
po
ints
{x=
0.0
01
6,
y=0
}an
d {
x=0
.10
, y=
0.4
0},
wit
h t
he
slo
pe
of
4.0
65
. N
ow
, T
he
nu
mb
er
of
equ
ilib
riu
m s
tag
es i
s eq
ual
to
3,
all
of
them
in
th
e co
lum
n.
Ex
erci
se 7
.34
(c
on
tin
ued
)
A
na
lysi
s:
Par
tial
Reb
oil
er C
ase:
Ex
erci
se 7
.34
(c
on
tin
ued
)
A
na
lysi
s:
Op
en S
team
Cas
e:
E
xer
cise
7.3
5
Su
bje
ct:
Dis
till
atio
n o
f tw
o f
eed
s o
f m
ixtu
res
of
wat
er a
nd
ace
tic
acid
at
1 a
tm.
Giv
en:
F
eed
1 i
s a
bu
bb
le-p
oin
t li
qu
id o
f 1
00
km
ol/
h c
on
tain
ing 7
5 m
ol%
wat
er.
Fee
d 2
is
50
mo
l% v
apo
rize
d o
f 1
00
km
ol/
h c
on
tain
ing 5
0 m
ol%
wat
er.
Un
it c
on
sist
s o
f a
pla
te c
olu
mn
, to
tal
con
den
ser,
an
d p
arti
al r
ebo
iler
. D
isti
llat
e is
to
co
nta
in 9
8 m
ol%
wat
er.
Bo
tto
ms
is t
o c
on
tain
5
mo
l% w
ater
. R
eflu
x r
atio
, L
/D =
R =
1.2
tim
es m
inim
um
. V
apo
r-li
qu
id e
qu
ilib
riu
m d
ata.
Ass
um
pti
on
s:
C
on
stan
t m
ola
r o
ver
flo
w.
Fin
d:
O
pti
mal
fee
d s
tage
loca
tio
ns
and
nu
mb
er o
f eq
uil
ibri
um
sta
ges
.
An
aly
sis:
W
ater
is
the
mo
re v
ola
tile
co
mp
on
ent.
C
om
pu
te f
low
rat
es o
f d
isti
llat
e an
d b
ott
om
s.
Ov
eral
l to
tal
mat
eria
l b
alan
ce:
F
1 +
F2 =
10
0 +
10
0 =
20
0 =
D +
B
(1)
Ov
eral
l w
ater
bal
ance
: (
0.7
5)(
10
0)
+ 0
.5(1
00
) =
12
5 =
xDD
+ x
BB
= 0
.98
D +
0.0
5B
(2)
So
lvin
g E
qs.
(1
) an
d (
2),
D
= 1
23
.66
km
ol/
h
an
d
B
= 7
6.3
4 k
mo
l/h
.
Ass
um
e th
e m
inim
um
ref
lux
is
con
tro
lled
by t
he
up
per
fee
d.
Th
is i
s v
erif
ied
in
th
e
McC
abe-
Th
iele
dia
gra
m b
elo
w,
wh
ere
the
equ
ilib
riu
m c
urv
e is
plo
tted
fro
m t
he
dat
a, t
he
q-l
ine
for
Fee
d 1
is
ver
tica
l th
rou
gh
th
e p
oin
t, x
= 0
.75
, th
e q
-lin
e fo
r F
eed
2 h
as a
slo
pe
of
-1 s
tart
ing
fro
m x
= 0
.50
, an
d t
he
op
erat
ing l
ine
for
the
up
per
sec
tio
n b
etw
een
Fee
d 1
an
d t
he
con
den
ser
is
dra
wn
th
rou
gh
th
e tw
o p
oin
ts,
{x=
0.9
8,
y=0
.98
} a
nd
th
e in
ters
ecti
on
of
the
equ
ilib
riu
m c
urv
e an
d
the
q-l
ine
for
Fee
d 1
. F
rom
th
e p
lot,
fo
r th
e u
pp
er s
ecti
on
, L
/V =
(0
.98
-0.8
28
)/(0
.98
-0.7
5)
=
0.6
61
. F
rom
Eq
. (7
-27
), R
= L
/D =
(L
/V)/
[1 -
(L
/V)]
= 0
.66
1/(
1 -
0.6
61
) =
1.9
5.
Th
eref
ore
,
L =
1.9
5D
= 1
.95
(12
3.6
6)
= 2
41
.1 k
mo
l/h
an
d
V =
L +
D =
24
1.1
+ 1
23
.66
= 3
64
.8 k
mo
l/h
.
In t
he
mid
dle
sec
tio
n,
bet
wee
n t
he
two
fee
ds,
L' =
L +
F1 =
24
1.1
+ 1
00
= 3
41
.1 k
mo
l/h
an
d
V' =
V =
36
4.8
km
ol/
h.
Th
eref
ore
, th
e sl
op
e o
f th
e m
idd
le s
ecti
on
op
erat
ing l
ine
= L
'/V
' =
34
1.1
/36
4.8
= 0
.93
5.
As
seen
in
th
e d
iagra
m b
elo
w,
this
lin
e d
oes
no
t ca
use
a p
inch
ed r
egio
n a
t
Fee
d 2
. T
her
efo
re,
the
assu
mp
tio
n i
s co
rrec
t an
d R
min
= 1
.95
.
Fo
r an
op
erat
ing r
eflu
x r
atio
of
1.2
tim
es m
inim
um
, L
= 1
.2(2
41
.1)
= 2
89
.3 k
mo
l/h
.
Th
e v
apo
r ra
te i
n t
he
up
per
sec
tio
n =
V =
L +
D =
28
9.3
+ 1
23
.66
= 4
13
km
ol/
h.
Th
eref
ore
th
e u
pp
er s
ecti
on
op
erat
ing l
ine
has
a s
lop
e, L
/V =
28
9.3
/41
3 =
0.7
00
an
d p
asse
s
thro
ugh
th
e p
oin
t y
= x
= 0
.98
. I
t in
ters
ects
th
e v
erti
cal
q-l
ine
at x
= 0
.75
an
d,
for
the
slo
pe
of
0.7
00
= (
0.9
8 -
y)/
(0.9
8 -
0.7
5),
at
y =
0.8
19
.
Fo
r th
e m
idd
le s
ecti
on
, L
' =
L +
F1
=
28
9.3
+1
00
= 3
89
.3 k
mo
l/h
an
d V
' =
V =
41
3
km
ol/
h.
Th
eref
ore
, th
e m
idd
le s
ecti
on
op
erat
ing l
ine
has
a s
lop
e o
f L
'/V
' =
38
9.3
/41
3 =
0.9
43
and
in
ters
ects
th
e q
-lin
e fo
r x
= 0
.75
at
y =
0.8
19
. I
t in
ters
ects
th
e q
-lin
e fo
r F
eed
2 a
t y
= 0
.54
3.
Fo
r th
e lo
wer
sec
tio
n,
L"
= L
' +
0.5
F2 =
38
9.3
+ 5
0 =
43
9.3
km
ol/
h
and
V"=
V' -
0.5
F2=
41
3 -
50
= 3
63
km
ol/
h.
Th
eref
ore
, th
e lo
wer
sec
tio
n o
per
atin
g l
ine
has
a s
lop
e o
f L
"/V
" =
43
9.3
/36
3 =
1.2
10
an
d i
nte
rsec
ts t
he
q-l
ine
for
Fee
d 2
at
y =
0.5
43
an
d t
he
45
o l
ine
at x
B =
0.0
5.
In t
he
McC
abe-
Th
iele
dia
gra
ms
bel
ow
an
d o
n t
he
nex
t p
age
for
the
hig
h,
mid
dle
, an
d l
ow
mo
le
frac
tio
n r
egio
ns,
th
e th
ree
op
erat
ing l
ines
are
dra
wn
an
d t
he
equ
ilib
riu
m s
tages
are
ste
pp
ed o
ff s
o
as t
o p
lace
th
e tw
o f
eed
s at
th
eir
op
tim
al l
oca
tio
ns.
A
s se
en,
the
nu
mb
er o
f eq
uil
ibri
um
sta
ges
req
uir
ed =
ju
st l
ess
than
33
eq
uil
ibri
um
sta
ges
. C
all
it 3
2 e
qu
ilib
riu
m s
tages
in
th
e co
lum
n a
nd
a
par
tial
reb
oil
er.
Op
tim
al f
eed
sta
ges
are
lo
cate
d a
t S
tages
17
an
d 2
7 f
rom
th
e to
p.
Ex
erci
se 7
.35
(co
nti
nu
ed)
An
aly
sis:
(c
on
tin
ued
)
Ex
erci
se 7
.35
(c
on
tin
ued
) A
na
lysi
s:
(co
nti
nu
ed)
Ex
erci
se 7
.35
(c
on
tin
ued
) A
na
lysi
s:
(co
nti
nu
ed)
Ex
erci
se 7
.35
(c
on
tin
ued
) A
na
lysi
s:
(co
nti
nu
ed)
Ex
erci
se 7
.36
S
ub
ject
: D
isti
llat
ion
at
1 a
tm o
f a
mix
ture
of
met
han
ol
(M)
and
eth
ano
l (E
) to
ob
tain
a
dis
till
ate,
bo
tto
ms,
an
d a
liq
uid
sid
estr
eam
.
Giv
en:
10
0 k
mo
l/h
of
a 2
5 m
ol%
vap
ori
zed
mix
ture
of
75
mo
l% m
eth
ano
l in
eth
ano
l.
Dis
till
ate
is 9
6 m
ol%
met
han
ol
and
bo
tto
ms
is 5
mo
l% m
eth
ano
l.
Un
it c
on
sist
s o
f a
tota
l
con
den
ser,
pla
te c
olu
mn
, an
d p
arti
al r
ebo
iler
. S
ides
trea
m i
s 1
5 k
mo
l/h
of
20
mo
l% m
eth
ano
l.
Ref
lux
rat
io,
R =
1.2
tim
es m
inim
um
.
Ass
um
pti
on
s:
C
on
stan
t m
ola
r o
ver
flo
w.
Rao
ult
's l
aw K
-val
ues
.
Fin
d:
N
um
ber
of
theo
reti
cal
stag
es a
nd
op
tim
al l
oca
tio
ns
of
feed
an
d s
ides
trea
m.
An
aly
sis:
F
irst
co
mp
ute
th
e m
ater
ial
bal
ance
.
Ov
eral
l to
tal
mat
eria
l b
alan
ce:
F
= 1
00
= D
+ B
+ S
= D
+ B
+ 1
5
(1
)
Ov
eral
l m
eth
ano
l m
ater
ial
bal
ance
: 7
5 =
0.9
6D
+ 0
.05
B +
0.2
0(1
5)
(2
)
So
lvin
g E
qs.
(1
) an
d (
2),
D
= 7
4.4
5 k
mo
l/h
an
d
B =
10
.55
km
ol/
h
N
ow
det
erm
ine
the
equ
ilib
riu
m c
urv
e.
At
1 a
tm (
14
.69
6 p
sia)
, m
eth
ano
l b
oil
s at
64
.7oC
and
eth
ano
l b
oil
s at
78
.4oC
. F
rom
Fig
. 2
.4,
the
vap
or
pre
ssu
re o
f et
han
ol
at 6
4.7
oC
= 8
.2 p
sia.
Th
e v
apo
r p
ress
ure
of
met
han
ol
at 7
8.4
oC
= 2
5 p
sia.
F
or
the
Rao
ult
's l
aw K
-val
ue,
Eq
. (2
-44
)
app
lies
. C
om
bin
ing t
his
eq
uat
ion
wit
h t
he
def
init
ion
of
the
rela
tiv
e v
ola
tili
ty o
f E
q.
(2-2
1),
giv
es,
for
met
han
ol
wit
h r
esp
ect
to t
he
less
vo
lati
le e
than
ol,
αΜ
,Ε =
(P
s ) M/
(Ps ) E
.
At
64
.7oC
, α
Μ,Ε
= 1
4.6
96
/8.2
= 1
.79
. A
t 7
8.4
oC
, α
Μ,Ε
= 2
5/1
4.6
96
= 1
.70
. S
ince
th
ese
val
ues
are
clo
se (
wit
hin
abo
ut
5%
), u
se a
n e
qu
ilib
riu
m c
urv
e b
ased
on
a c
on
stan
t α
= (
1.7
0 +
1.7
9)/
2 =
1.7
45
. F
rom
Eq
.
(7-3
), t
he
curv
e is
co
mp
ute
d f
rom
,
y =
αx/
[1 +
x(α
-1)]
= 1
.74
5x/
(1+
0.7
45
x)
(3)
Th
e M
cCab
e-T
hie
le d
iagra
m o
n t
he
nex
t p
age
sho
ws
the
op
erat
ing l
ines
fo
r d
eter
min
ing t
he
min
imu
m r
eflu
x r
atio
. I
t as
sum
es t
hat
th
e p
inch
reg
ion
occ
urs
at
the
feed
sta
ge
and
no
t at
th
e
sid
estr
eam
sta
ge.
F
rom
Eq
. (7
-18
), q
fo
r 2
5 m
ol%
vap
ori
zed
= 0
.75
. F
rom
Eq
. (7
-26
), t
he
slo
pe
of
the
q-l
ine
= q
/(q
-1)
= 0
.75
/(0
.75
-1)
= -
3.
Th
e u
pp
er s
ecti
on
op
erat
ing l
ine
inte
rsec
ts t
he
q-l
ine
and
eq
uil
ibri
um
cu
rve
at y
=0
.82
3 a
nd
x=
0.7
27
.
Th
us,
slo
pe
of
the
up
per
sec
tio
n o
per
atin
g l
ine
=
L/V
= (
0.9
6-0
.82
3)/
(0.9
6-0
.72
7)
= 0
.58
8.
Fro
m E
q.
(7-2
7),
Rm
in =
(L
/V)/
[1 -
(L
/V)]
= 0
.58
8/(
1-
0.5
88
) =
1.4
27
. T
her
efo
re,
L =
1.4
27
(74
.45
) =
10
6.3
km
ol/
h
and
V
= L
+ D
= 1
06
.3 +
74
.45
=
18
0.7
5 k
mo
l/h
. I
n t
he
mid
dle
sec
tio
n b
etw
een
th
e fe
ed s
tage
and
sid
estr
eam
sta
ge,
fo
r 2
5 m
ol%
vap
ori
zati
on
, L
' =
L +
0.7
5(1
00
) =
10
6.3
+ 7
5 =
18
1.3
km
ol/
h
and
V
' =
V -
0.2
5(1
00
) =
18
0.7
5 -
25
= 1
55
.75
km
ol/
h.
Th
us,
L'/
V' =
18
1.3
/15
5.7
5 =
1.1
64
. T
he
mid
dle
sec
tio
n o
per
atin
g l
ine
has
this
slo
pe
and
pas
ses
thro
ugh
y=
0.8
23
an
d x
=0
.72
7.
In
th
e lo
wer
sec
tio
n o
per
atin
g l
ine
bel
ow
th
e
sid
estr
eam
, fo
r a
liq
uid
sid
estr
eam
flo
w r
ate
of
15
km
ol/
h,
L"
= L
' -
S =
18
1.3
- 1
5 =
16
6.3
km
ol/
h
and
V
" =
V' =
15
5.7
5 k
mo
l/h
.
Th
us,
L"/
V"
= 1
66
.3/1
55
.75
= 1
.06
8.
Th
is l
ine
pas
ses
thro
ugh
th
e p
oin
t y=
0.0
5 a
nd
x =
0.0
5 w
ith
th
e sl
op
e o
f 1
.06
8.
It
also
in
ters
ects
th
e m
idd
le
sect
ion
op
erat
ing l
ine
at t
he
sid
estr
eam
co
mp
osi
tio
n,
x s =
0.2
0.
Th
ese
thre
e o
per
atin
g l
ines
are
dra
wn
in
th
e M
cCab
e-T
hie
le d
iagra
m,
sho
win
g t
hat
th
e m
idd
le s
ecti
on
op
erat
ing l
ine
lies
bel
ow
Ex
erci
se 7
.36
(co
nti
nu
ed)
An
aly
sis:
(co
nti
nu
ed)
the
equ
ilib
riu
m c
urv
e.
Th
eref
ore
, th
e as
sum
pti
on
th
at t
he
min
imu
m r
eflu
x i
s co
ntr
oll
ed b
y t
he
feed
sta
ge
is v
erif
ied
an
d t
he
min
imu
m r
eflu
x r
atio
is
1.4
27
.
Fo
r ac
tual
op
erat
ion
, re
flu
x r
atio
= 1
.2R
min
= 1
.2(1
.42
7)
= 1
.71
2.
Ref
lux
rat
e in
up
per
sect
ion
= L
= 1
.2L
min
= 1
.2(1
06
.3)
= 1
27
.6 k
mo
l/h
. V
apo
r ra
te =
V
= L
+ D
= 1
27
.6 +
74
.45
=
20
2.0
5 k
mo
l/h
. S
lop
e o
f u
pp
er s
ecti
on
op
erat
ing l
ine
= L
/V =
12
7.6
/20
2.0
5 =
0.6
32
. F
or
con
stan
t m
ola
r o
ver
flo
w,
the
flo
w r
ates
in
th
e o
ther
sec
tio
ns
are:
Mid
dle
sec
tio
n:
L' =
20
2.6
km
ol/
h
V' =
17
7.0
5 k
mo
l/h
L
'/V
' =
1.1
44
Lo
wer
sec
tio
n:
L"
= 1
87
.6 k
mo
l/h
V
" =
17
7.0
5 k
mo
l/h
L
"/V
" =
1.0
60
Ex
erci
se 7
.36
(co
nti
nu
ed)
An
aly
sis:
(co
nti
nu
ed)
In t
he
McC
abe-
Th
iele
dia
gra
ms
bel
ow
, u
pp
er,
mid
dle
, an
d l
ow
er o
per
atin
g l
ines
are
bas
ed o
n t
hes
e v
alu
es s
tart
ing f
rom
th
e u
pp
er l
ine,
wh
ich
pas
ses
thro
ugh
th
e p
oin
t x
= 0
.96
on
th
e
45
o l
ine.
E
qu
ilib
riu
m s
tages
are
ste
pp
ed o
ff s
tart
ing f
rom
th
e d
isti
llat
e co
mp
osi
tio
n a
nd
swit
chin
g o
per
atin
g l
ines
at
the
app
rop
riat
e ti
mes
to
det
erm
ine
the
op
tim
al f
eed
sta
ge
and
sid
estr
eam
sta
ge
loca
tio
ns.
A
sep
arat
e M
cCab
e-T
hie
le d
iagra
m i
s u
sed
fo
r th
e u
pp
er s
ecti
on
to
ach
iev
e b
ette
r ac
cura
cy.
As
seen
19
eq
uil
ibri
um
sta
ges
plu
s a
par
tial
reb
oil
er a
re r
equ
ired
. T
he
op
tim
al f
eed
sta
ge
is 9
fro
m t
he
top
an
d t
he
op
tim
al s
ides
trea
m s
tage
is 1
7 f
rom
th
e to
p.
Ex
erci
se 7
.36
(co
nti
nu
ed)
An
aly
sis:
(co
nti
nu
ed)
Ex
erci
se 7
.37
S
ub
ject
: D
isti
llat
ion
at
1 a
tm o
f a
mix
ture
of
tolu
ene
and
ph
eno
l fo
r a
giv
en b
oil
up
rat
io,
wit
h a
n a
lter
nat
ive
usi
ng a
n i
nte
rreb
oil
er.
Giv
en:
1
,00
0 k
mo
l/h
of
a sa
tura
ted
liq
uid
fee
d o
f 2
5 m
ol%
to
luen
e.
Dis
till
ate
is 9
8 m
ol%
tolu
ene
and
bo
tto
ms
is 2
mo
l% t
olu
ene.
T
he
bas
e u
nit
co
nsi
sts
of
a to
tal
con
den
ser,
a p
late
colu
mn
, an
d a
par
tial
reb
oil
er,
wit
h a
bo
ilu
p r
atio
, V
B =
VB
/=
1.1
5 t
imes
min
imu
m.
Th
e
alte
rnat
ive
un
it a
dd
s an
in
terr
ebo
iler
mid
way
in
th
e st
rip
pin
g s
ecti
on
to
pro
vid
e 5
0%
of
the
bo
ilu
p.
A t
able
of
T
-y-x
p
has
e eq
uil
ibri
um
dat
a
Ass
um
pti
on
s:
C
on
stan
t m
ola
r o
ver
flo
w.
Fin
d:
F
or
each
un
it,
det
erm
ine
the
nu
mb
er o
f th
eore
tica
l st
ages
. F
or
the
alte
rnat
ive
un
it,
det
erm
ine
the
tem
per
atu
re o
f th
e in
terr
ebo
iler
sta
ge.
An
aly
sis:
To
luen
e is
th
e m
ore
vo
lati
le u
nit
.
Ba
se u
nit
:
F
rom
th
e M
cCab
e-T
hie
le d
iagra
m b
elo
w,
the
min
imu
m b
oil
up
rat
io i
s d
eter
min
ed f
rom
the
slo
pe
of
the
stri
pp
ing s
ecti
on
op
erat
ing l
ine
that
in
ters
ects
th
e eq
uil
ibri
um
cu
rve
at t
he
feed
com
po
siti
on
of
x F =
0.2
5.
() m
in
0.8
15
0.0
2/
3.4
6
0.2
50
.02
−=
=−
LV
Fro
m E
q.
(7-2
8),
()
()
min
min
11
0.4
07
3.4
61
/1
==
=−
−B
VL
V
Ex
erci
se 7
.37
(co
nti
nu
ed)
An
aly
sis:
B
ase
Ca
se (
con
tin
ued
)
Fo
r co
lum
n o
per
atio
n,
VB =
1.1
5(V
B) m
in =
1.1
5(0
.40
7)
= 0
.46
8
Fro
m E
q.
(7-1
2),
th
e sl
op
e o
f th
e st
rip
pin
g s
ecti
on
op
erat
ing l
ine
is,
LV
V
VB
B
/.
..
=+
=+
=1
04
68
1
04
68
31
4
As
sho
wn
in
th
e M
cCab
e-T
hie
le d
iagra
m,
bel
ow
, a
lin
e o
f th
is s
lop
e is
dra
wn
th
rou
gh
th
e p
oin
t
x =
y =
0.0
2 u
nti
l it
in
ters
ects
th
e q
-lin
e.
Eq
uil
ibri
um
sta
ges
are
ste
pp
ed o
ff,
star
tin
g f
rom
th
e
dis
till
ate
po
int
at y
= x
= 0
.98
. T
he
op
tim
al f
eed
sta
ge
loca
tio
n i
s lo
cate
d a
s sh
ow
n a
t st
age
5
fro
m t
he
top
. T
he
tota
l n
um
ber
of
stag
es r
equ
ired
is
just
les
s th
an 8
, w
ith
on
e o
f th
ose
sta
ges
bei
ng t
he
par
tial
reb
oil
er.
Ex
erci
se 7
.37
(co
nti
nu
ed)
An
aly
sis:
B
ase
Ca
se (
con
tin
ued
)
Ex
erci
se 7
.37
(co
nti
nu
ed)
An
aly
sis:
(
con
tin
ued
)
Alt
ern
ati
ve
un
it w
ith
In
terr
ebo
iler
:
F
or
colu
mn
op
erat
ion
wit
h a
n i
nte
rreb
oil
er t
hat
pro
vid
es 5
0%
of
the
reb
oil
er d
uty
, th
e
op
erat
ing b
oil
up
rat
io b
etw
een
th
e re
bo
iler
an
d t
he
inte
rreb
oil
er i
s 5
0%
of
0.4
68
or
0.2
34
.
Fro
m E
q.
(7-1
2),
th
e sl
op
e o
f th
e o
per
atin
g l
ine
in t
his
reg
ion
is:
LV
V
VB
B
/.
..
=+
=+
=1
02
34
1
02
34
52
7
Bet
wee
n t
he
inte
rreb
oil
er a
nd
th
e fe
ed s
tage,
th
e sl
op
e o
f th
e o
per
atin
g l
ine
rem
ain
s at
3.1
4,
bas
ed o
n a
mat
eria
l b
alan
ce a
rou
nd
th
e co
lum
n s
ecti
on
fro
m t
he
bo
tto
ms
to t
he
regio
n b
etw
een
the
inte
rreb
oil
er a
nd
th
e fe
ed s
tage.
T
hes
e tw
o o
per
atin
g l
ines
are
sh
ow
n i
n t
he
McC
abe-
Th
iele
dia
gra
m b
elo
w,
wh
ere
bo
th p
ass
thro
ugh
th
e p
oin
t y
= x
= 0
.02
. S
tep
pin
g o
ff s
tages
fro
m t
he
bo
tto
m,
it i
s se
en t
hat
3 s
tages
are
nee
ded
bel
ow
th
e fe
ed s
tage.
T
he
firs
t st
age
is t
he
par
tial
reb
oil
er.
Th
e in
terr
ebo
iler
is
loca
ted
at
the
seco
nd
eq
uil
ibri
um
sta
ge.
A
to
tal
of
8 e
qu
ilib
riu
m
stag
es i
s re
qu
ired
, ju
st s
ligh
tly m
ore
th
an t
hat
wh
en a
ll o
f th
e h
eat
inp
ut
is t
o t
he
par
tial
reb
oil
er
at t
he
bo
tto
m o
f th
e co
lum
n.
T
he
vap
or
com
po
siti
on
of
the
inte
rreb
oil
er s
tage
is 0
.34
5,
wh
ich
fro
m t
he
giv
en T
-y-x
ph
ase
equ
ilib
riu
m d
ata
corr
esp
on
ds
to a
tem
per
atu
re o
f ap
pro
xim
atel
y 1
73
oC
. T
he
inte
rreb
oil
er
cou
ld a
lso
be
loca
ted
at
the
thir
d s
tage
fro
m t
he
bo
tto
m.
Th
e w
ou
ld i
ncr
ease
th
e n
um
ber
of
stag
es b
y a
bo
ut
hal
f o
f a
stag
e an
d l
ow
er t
he
tem
per
atu
re o
f th
e in
terr
ebo
iler
sta
ge
to 1
62
oC
.
Ex
erci
se 7
.37
(co
nti
nu
ed)
An
aly
sis:
(
con
tin
ued
)
Alt
ern
ati
ve
un
it w
ith
In
terr
ebo
iler
:
Ex
erci
se 7
.38
S
ub
ject
: E
ffec
t o
f th
e ad
dit
ion
of
an i
nte
rco
nd
ense
r an
d i
nte
rreb
oil
er t
o a
dis
till
atio
n
colu
mn
sep
arat
ing n
-bu
tan
e an
d n
-pen
tan
e.
Giv
en:
D
isti
llat
e an
d b
ott
om
s co
mp
osi
tio
ns
of
actu
al o
per
atio
n (
bef
ore
ad
dit
ion
of
inte
rco
nd
ense
r an
d i
nte
rreb
oil
er)
com
par
ed t
o d
esig
n s
pec
ific
atio
n.
Ass
um
pti
on
s:
C
on
stan
t m
ola
r o
ver
flo
w.
Co
nst
ant
rela
tiv
e v
ola
tili
ty.
Co
lum
n i
s la
rge
eno
ugh
in d
iam
eter
to
han
dle
in
crea
sed
ref
lux
an
d b
oil
up
. R
aou
lt's
law
(id
eal
solu
tio
ns
and
id
eal
gas
law
).
Fin
d:
W
het
her
th
e ad
dit
ion
can
im
pro
ve
the
op
erat
ion
bec
ause
of
the
incr
ease
d r
eflu
x a
nd
bo
ilu
p p
rod
uce
d b
y t
he
inte
rco
nd
ense
r an
d i
nte
rreb
oil
er.
An
aly
sis:
F
irst
, es
tim
ate
the
aver
age
rela
tiv
e v
ola
tili
ty f
or
nC
4/n
C5.
Ass
um
e a
dis
till
ate
tem
per
atu
re o
f 1
20
oF
so
th
at c
oo
lin
g w
ater
can
be
use
d i
n t
he
con
den
ser.
T
his
co
rres
po
nd
s to
a
satu
rati
on
pre
ssu
re o
f ab
ou
t 7
0 p
sia.
U
sin
g F
ig.
2.8
wit
h E
qs.
(2
-21
) an
d (
2-4
4),
th
e re
lati
ve
vo
lati
lity
of
bu
tan
e w
ith
res
pec
t to
pen
tan
e is
α =
1.1
/0.3
8 =
2.9
. A
ssu
min
g a
5 p
si p
ress
ure
dro
p,
giv
es a
bo
tto
ms
pre
ssu
re o
f 7
5 p
sia
and
a c
orr
esp
on
din
g t
emp
erat
ure
of
20
0oF
. U
sin
g F
ig.
2.8
wit
h E
qs.
(2
-21
) an
d (
2-4
4),
α =
2.1
/0.9
= 2
.3.
Tak
e th
e av
erag
e re
lati
ve
vo
lati
lity
as
2.6
an
d
dra
w a
y-x
eq
uil
ibri
um
cu
rve
usi
ng E
q.
(7-3
),
yx
x
x
x=
+−
=+
α
α1
1
26
11
6(
)
.
.
(1)
Th
e eq
uil
ibri
um
cu
rve,
bas
ed o
n E
q.
(1)
is s
ho
wn
bel
ow
in
a M
cCab
e-T
hie
le d
iagra
m.
In
clu
ded
on
th
e d
iagra
m a
re a
rbit
rary
op
erat
ing l
ines
an
d a
q-l
ine
for
an e
qu
imo
lar
feed
th
at i
s 5
0 m
ol%
vap
ori
zed
. U
sin
g t
hes
e li
nes
, 1
5 e
qu
ilib
riu
m s
tages
are
ste
pp
ed o
ff
bet
wee
n t
he
com
po
siti
on
s o
f
the
actu
al o
per
atio
n,
x D =
1 -
0.1
34
9 =
0.8
65
1 a
nd
xB =
0.0
42
8.
Th
e sl
op
e, L
/V,
of
the
rect
ifyin
g
sect
ion
op
erat
ing l
ine
is 0
.52
.
Ex
erci
se 7
.38
(c
on
tin
ued
) A
na
lysi
s:
Act
ua
l o
per
ati
on
bef
ore
ad
dit
ion
(co
nti
nu
ed)
Ex
erci
se 7
.38
(c
on
tin
ued
) A
na
lysi
s:
Ad
dit
ion
(co
nti
nu
ed)
W
hen
an
in
terr
ebo
iler
is
add
ed b
etw
een
th
e re
bo
iler
an
d t
he
feed
sta
ge
and
an
inte
rco
nd
ense
r is
ad
ded
bet
wee
n t
he
feed
sta
ge
and
th
e o
ver
hea
d c
on
den
ser,
th
e co
lum
n i
s m
ade
up
of
4 s
ecti
on
s in
stea
d o
f 2
. E
ach
sec
tio
n h
as i
ts o
wn
op
erat
ing l
ine
as s
ho
wn
in
th
e M
cCab
e-
Th
iele
dia
gra
m b
elo
w.
In
ord
er t
o m
ain
tain
th
e sa
me
refl
ux
rat
io a
nd
bo
ilu
p r
atio
, th
e
inte
rco
nd
ense
r is
des
ign
ed t
o c
on
den
se a
mo
lar
flo
w r
ate
equ
al t
o t
hat
pro
du
ced
by t
he
inte
rreb
oil
er.
Th
us,
in
Sec
tio
n 2
bet
wee
n t
he
inte
rco
nd
ense
r an
d t
he
feed
sta
ge,
th
e L
/V r
atio
is
hig
her
th
an t
he
val
ue
in S
ecti
on
1 b
etw
een
th
e o
ver
hea
d c
on
den
ser
and
th
e in
terc
on
den
ser.
Th
us,
the
two
op
erat
ing l
ines
ab
ov
e th
e fe
ed s
tage
hav
e d
iffe
ren
t sl
op
es,
bu
t b
y m
ater
ial
bal
ance
bo
th
lin
es p
ass
thro
ugh
th
e d
isti
llat
e co
mp
osi
tio
n o
n t
he
45
o l
ine.
C
orr
esp
on
din
gly
, in
S
ecti
on
3 b
etw
een
th
e in
terr
ebo
iler
an
d t
he
feed
sta
ge,
th
e L
/V r
atio
is l
ow
er t
han
th
e v
alu
e in
Sec
tio
n 4
bet
wee
n t
he
reb
oil
er a
nd
th
e in
terr
ebo
iler
. T
hu
s, t
he
two
op
erat
ing l
ines
bel
ow
th
e fe
ed s
tage
hav
e d
iffe
ren
t sl
op
es,
bu
t b
y m
ater
ial
bal
ance
bo
th l
ines
pas
s
thro
ugh
th
e b
ott
om
s co
mp
osi
tio
n o
n t
he
45
o l
ine.
A
lso
no
te t
hat
by m
ater
ial
bal
ance
, th
e
op
erat
ing l
ines
fo
r S
ecti
on
s 1
an
d 4
in
ters
ect
on
th
e 4
5o l
ine,
an
d t
he
op
erat
ing l
ines
fo
r S
ecti
on
s
2 a
nd
3 i
nte
rsec
t o
n t
he
45
o li
ne.
S
tart
ing f
rom
x D
= 0
.99
74
, st
ages
are
ste
pp
ed o
ff f
rom
th
e to
p
bet
wee
n t
he
op
erat
ing l
ine
for
Sec
tio
n 1
an
d t
he
equ
ilib
riu
m c
urv
e fo
r a
few
sta
ges
bef
ore
sw
itch
to t
he
op
erat
ing l
ine
for
Sec
tio
n 2
. T
hen
5 s
tages
are
ste
pp
ed o
ff u
nti
l th
e fe
ed s
tage
is r
each
ed.
Th
en,
4 s
tages
are
ste
pp
ed o
ff b
etw
een
th
e o
per
atin
g l
ine
for
Sec
tio
n 3
an
d t
he
equ
ilib
riu
m c
urv
e
bef
ore
sw
itch
ing t
o t
he
op
erat
ing l
ine
for
Sec
tio
n 4
.
T
he
swit
ches
are
mad
e to
mai
nta
in t
he
sam
e n
um
ber
of
tota
l st
ages
, 1
5,
and
th
e sa
me
loca
tio
n f
or
the
feed
sta
ge.
O
ther
co
mb
inat
ion
s o
f ar
bit
rary
op
erat
ing l
ines
an
d a
q-l
ine
can
be
use
d t
o i
llu
stra
te t
he
po
ten
tial
of
an i
nte
rco
nd
ense
r an
d i
nte
rreb
oil
er.
Th
e im
po
rtan
t th
ing t
o n
ote
is t
hat
th
e ad
dit
ion
of
an i
nte
rco
nd
ense
r an
d i
nte
rreb
oil
er i
ncr
ease
s th
e d
ista
nce
bet
wee
n t
he
equ
ilib
riu
m c
urv
e an
d t
he
op
erat
ing l
ines
fo
r S
ecti
on
s 2
an
d 3
so
th
at t
he
step
s in
Sec
tio
ns
2 a
nd
3 a
cco
mp
lish
lar
ger
co
mp
osi
tio
n c
han
ges
.
Ex
erci
se 7
.38
(c
on
tin
ued
) A
na
lysi
s:
Ad
dit
ion
(co
nti
nu
ed)
Ex
erci
se 7
.39
S
ub
ject
: D
isti
llat
ion
of
a m
ixtu
re o
f p
ara-
dic
hlo
rob
enze
ne
(P)
and
ort
ho
-dic
hlo
rob
enze
ne
(O),
tw
o c
lose
-bo
ilin
g i
som
ers,
usi
ng t
he
McC
abe-
Th
iele
dia
gra
m,
wit
h t
he
Kre
mse
r eq
uat
ion
to
accu
rate
ly c
alcu
late
th
e se
par
atio
ns
at t
he
two
en
ds
of
the
colu
mn
.
Giv
en:
F
eed
of
62
mo
l% P
an
d 3
8 m
ol%
O t
hat
is
slig
htl
y v
apo
rize
d w
ith
q =
0.9
. D
isti
llat
e is
liq
uid
of
98
mo
l% P
. B
ott
om
s is
96
mo
l% O
. P
ress
ure
s at
to
p a
nd
bo
tto
m a
re 2
0 p
sia
and
15
psi
a, r
esp
ecti
vel
y.
Ref
lux
rat
io,
R =
1.1
5 t
imes
min
imu
m.
Ass
um
pti
on
s:
C
on
stan
t m
ola
r o
ver
flo
w.
To
tal
con
den
ser
and
par
tial
reb
oil
er.
Av
erag
e
rela
tiv
e v
ola
tili
ty b
ased
on
Rao
ult
's l
aw.
Fin
d:
N
um
ber
of
theo
reti
cal
stag
es f
rom
McC
abe-
Th
iele
dia
gra
m,
usi
ng K
rem
ser
sup
ple
men
t
for
the
two
en
ds
of
the
colu
mn
.
An
aly
sis:
Fro
m a
sim
ula
tio
n p
rogra
m o
r h
and
bo
ok
, th
e te
mp
erat
ure
s at
th
e to
p a
nd
bo
tto
m o
f
the
colu
mn
, b
ased
on
th
e giv
en p
ress
ure
s an
d p
rod
uct
co
mp
osi
tio
ns,
are
det
erm
ined
to
be
app
rox
imat
ely 3
50
an
d 3
80
oF
. F
rom
vap
or
pre
ssu
re d
ata,
e.g
. fr
om
CH
EM
CA
D,
usi
ng E
q.
(7-1
),
αα
P,O
oP O
P,O
oP O
at
35
0F
=
and
at
380
F
=
P P
P P
s s
s s=
==
=1
56
5
13
41
11
67
23
16
19
98
11
59
. ..
. ..
Tak
e th
e av
erag
e re
lati
ve
vo
lati
lity
as
(1.1
67
+ 1
.15
9)/
2 =
1.1
63
.
Fro
m E
q.
(7-2
6),
th
e sl
op
e o
f th
e q
-lin
e =
q/(
q -
1)
= 0
.9/(
0.9
- 1
) =
-9
. F
eed
is
10
mo
l%
vap
ori
zed
.
Ap
ply
th
e F
ensk
e-U
nd
erw
oo
d-G
illi
lan
d m
eth
od
to
ob
tain
an
in
itia
l es
tim
ate
of
refl
ux
an
d s
tage
req
uir
emen
ts.
Can
use
th
e S
HO
R m
od
el i
n C
HE
MC
AD
. T
he
resu
lts
are:
Nm
in =
48
, R
min
= 9
.37
R
= 1
.15
Rm
in =
10
.77
N
= 1
03
(1
02
+ r
ebo
iler
)
N
of
feed
= s
tage
50
fro
m t
he
top
To
co
nst
ruct
th
e eq
uil
ibri
um
cu
rve
for
the
McC
abe-
Th
iele
met
ho
d,
use
Eq
. (7
-3),
yx
x
x
xP
P-O
P
PP
-O
P
P1
+1
+=
−=
α
α1
11
63
01
63
��
.
.
(1
)
Fro
m E
q.
(7-9
), t
he
slo
pe
of
the
rect
ifyin
g s
ecti
on
op
erat
ing l
ine
is,
L/V
= R
/(R
+1
) =
10
.77
/(1
0.7
7 +
1)
= 0
.91
50
Ex
erci
se 7
.39
(c
on
tin
ued
) A
na
lysi
s:
(co
nti
nu
ed)
Th
is l
ine
pas
ses
thro
ugh
x =
0.9
8 o
n t
he
45
o l
ine.
T
he
equ
atio
n f
or
this
lin
e is
giv
en b
y E
q.
(7-9
),
yL V
xR
xx
xD
=� ��� ��
++
� ��� ��
=+
+
� ��� ��
=+
1
10
91
51
11
77
10
98
09
15
00
83
26
..
(.
).
.
(2)
Bel
ow
th
e fe
ed s
tage,
wit
h 1
0 m
ol%
vap
ori
zati
on
of
the
feed
, L
V/.
=1
05
35
. F
rom
a
rear
ran
gem
ent
of
Eq
. (7
-12
), t
he
bo
ilu
p r
atio
, V
B,
is 1
8.6
91
6.
T
he
equ
atio
n o
f th
e st
rip
pin
g
sect
ion
op
erat
ing l
ine
is g
iven
by E
q.
7-1
4),
yL V
xV
xx
xB
D=� ��� ��
−� ��� ��
=−� ��
� ��=
−1
10
53
51
18
69
16
00
41
05
35
00
02
14
..
(.
).
.
(3)
T
he
equ
atio
n f
or
the
q-l
ine
is g
iven
by E
q.
(7-2
6),
yq
qx
qz
xx
F=
−
� ��� ��
−−
� ��� ��
=−
� ��� ��
−−
� ��� ��
=−
+1
1
1
09
09
1
1
09
10
62
96
2.
..
(.
).
(4)
Bas
ed o
n E
qs.
(1
) to
(4
), t
he
McC
abe-
Th
iele
dia
gra
m i
n t
erm
s o
f P
, th
e m
ore
vo
lati
le c
om
po
nen
t,
is d
raw
n b
elo
w f
or
thre
e re
gio
ns:
(2
) x
= 0
.2 t
o 0
.4,
(3)
x =
0.4
to
0.6
, an
d (
4)
x =
0.6
to
0.8
, in
ord
er t
o g
ain
acc
ura
cy.
In
th
ese
thre
e re
gio
ns,
28
sta
ges
are
ste
pp
ed o
ff i
n t
he
rect
ifyin
g s
ecti
on
up
to
x =
0.8
, an
d 3
4.3
sta
ges
are
ste
pp
ed o
ff i
n t
he
stri
pp
ing s
ecti
on
do
wn
to
x =
0.2
.
L
et r
egio
n (
1)
exte
nd
fro
m x
= 0
.8 t
o 0
.98
(i.
e. x
D).
A
pp
ly t
he
Kre
mse
r eq
uat
ion
, E
q.
(7-3
9)
to t
his
reg
ion
. A
pp
ly t
his
eq
uat
ion
to
th
e h
eav
y c
om
po
nen
t, O
. O
bta
in t
he
K-v
alu
e fo
r O
fro
m t
he
top
α o
f 1
.16
7,
tak
ing t
he
K-v
alu
e fo
r P
= 1
.00
. T
her
efo
re,
KO =
1/1
.16
7 =
0.8
57
.
Th
eref
ore
, th
e ab
sorp
tio
n f
acto
r, A
= L
/KV
=
0.9
15
/0.8
57
= 1
.06
7.
Oth
er q
uan
titi
es n
eed
ed i
n
Eq
. (7
-39
) ar
e: x
o =
1 -
(x D
) P =
1 -
0.9
8 =
0.0
2
y 1 =
xo =
0.0
2
Fro
m E
q.
(2),
fo
r x N
= 0
.8,
yN
+1 f
or
P =
0.8
15
3.
Th
eref
ore
, fo
r O
, y N
+1 =
1 -
0.8
15
3 =
0.1
84
7.
NA
A
yx
K
yx
K
AR
o
o=
+−� ��� ��
− −
� ��� ��
��� �� =
+−� ��
� ��− −
� ��� ��
��� �� =
log
log
..
..
(.
)
..
(.
).
11
11
10
67
11
10
67
01
84
70
02
08
57
00
20
02
08
57
12
36
N+
1
1
log
log
.06
7
L
et r
egio
n (
5)
exte
nd
fro
m x
= 0
.04
(i.
e. x
B)
to 0
.20
. A
pp
ly t
he
Kre
mse
r eq
uat
ion
, E
q.
(7-4
0)
to t
his
reg
ion
. A
pp
ly t
his
eq
uat
ion
to
th
e li
gh
t co
mp
on
ent,
P.
Ob
tain
th
e K
-val
ue
for
P
fro
m t
he
bo
tto
m α
of
1.1
59
, ta
kin
g t
he
K-v
alu
e fo
r O
= 1
.00
. T
her
efo
re,
KP =
1.1
59
. T
her
efo
re,
the
abso
rpti
on
fac
tor
in t
he
stri
pp
ing s
ecti
on
is
AL
KV
==
=/
./
..
10
53
51
15
90
90
85
. O
ther
val
ues
nee
ded
in
Eq
. (7
-40
) ar
e x 1
= x
B =
0.0
4
and
xN
+1 =
0.2
0.
Th
eref
ore
,
N
AA
xx
K
xx
K
A
S=
+−
− −
� ��� ��
��� ��
� ��� ��
=
+−
− −
� ��� ��
��� ��
� ��� ��
=
log
/ /lo
g.
..
./
.
..
/.
.
10
90
85
10
90
85
02
00
04
11
59
00
40
04
11
59
13
5
1
11
��
��
N+
1
log
1lo
g1
0.0
98
5
Ex
erci
se 7
.39
(c
on
tin
ued
) A
na
lysi
s:
(co
nti
nu
ed)
Su
mm
ing t
he
abo
ve
resu
lts,
N
um
ber
of
equ
ilib
riu
m s
tages
in
th
e re
ctif
yin
g s
ecti
on
= 2
8 +
23
.6 =
51
.6 s
tages
N
um
ber
of
equ
ilib
riu
m s
tages
in
th
e st
rip
pin
g s
ecti
on
= 3
4.3
+ 1
3.5
= 4
7.8
sta
ges
C
all
it 9
9 s
tages
in
th
e co
lum
n p
lus
a p
arti
al r
ebo
iler
wit
h t
he
feed
to
sta
ge
52
fro
m t
he
top
.
Th
is c
om
par
es t
o 1
02
sta
ges
in
th
e co
lum
n p
lus
a p
arti
al r
ebo
iler
wit
h t
he
feed
to
sta
ges
50
fro
m t
op
as
det
erm
ined
by t
he
Fen
ske-
Un
der
wo
od
-Gil
lila
nd
met
ho
d.
Ex
erci
se 7
.39
(c
on
tin
ued
) A
na
lysi
s:
(co
nti
nu
ed)
E
xer
cise
7.3
9 (c
on
tin
ued
)
A
na
lysi
s:
(co
nti
nu
ed)
Ex
erci
se 7
.40
S
ub
ject
: U
se o
f a
McC
abe-
Th
iele
dia
gra
m t
o d
eter
min
e st
age
req
uir
emen
ts f
or
the
dis
till
atio
n o
f ai
r in
to n
itro
gen
an
d o
xygen
usi
ng a
Lin
de
do
ub
le c
olu
mn
.
Giv
en:
A
s sh
ow
n i
n F
ig.
7.4
5,
the
dis
till
atio
n c
on
sist
s o
f an
up
per
co
lum
n (
UC
) o
per
atin
g a
t 1
atm
, o
n t
op
of
a lo
wer
co
lum
n (
LC
) o
per
atin
g a
t 4
to
5 a
tm.
Co
mp
ress
ed a
ir,
con
tain
ing 7
9
mo
l% N
2 i
s co
nd
ense
d t
o s
up
ply
hea
t in
th
e re
bo
iler
of
LC
, an
d t
hen
is
fed
as
liq
uid
air
to
an
inte
rmed
iate
tra
y o
f L
C.
Bo
tto
ms
liq
uid
fro
m L
C,
con
tain
ing a
bo
ut
55
mo
l% N
2,
is t
he
feed
to
an
inte
rmed
iate
tra
y i
n U
C.
Th
e re
bo
iler
of
UC
is
the
con
den
ser
for
LC
.
Co
nd
ensa
te f
rom
th
e to
p
of
LC
is
nea
rly p
ure
N2
, w
hic
h i
s se
nt
as r
eflu
x t
o t
he
top
of
UC
. T
he
reb
oil
er a
t th
e b
ott
om
of
UC
pro
vid
es a
lmo
st p
ure
O2
bo
ilu
p f
or
UC
. N
earl
y p
ure
liq
uid
O2 i
s w
ith
dra
wn
fro
m t
he
UC
reb
oil
er s
um
p a
t th
e b
ott
om
of
UC
. T
he
UC
has
no
co
nd
ense
r.
Nea
rly p
ure
gas
eou
s N
2 l
eav
es
the
top
of
UC
.
Th
is i
s co
nsi
sten
t w
ith
th
e fa
ct t
hat
N2 w
ith
a n
orm
al b
oil
ing p
oin
t o
f -
19
5.8
oC
(77
.4 K
) is
mo
re v
ola
tile
th
an O
2 w
ith
a n
orm
al b
oil
ing p
oin
t o
f -1
83
oC
(9
0.2
K).
Ass
um
pti
on
s:
C
on
stan
t m
ola
r o
ver
flo
w.
Co
nst
ant
rela
tiv
e v
ola
tili
ty a
t ea
ch p
ress
ure
.
Fin
d:
C
on
stru
ctio
n l
ines
on
a M
cCab
e-T
hie
le d
iagra
m t
hat
en
able
th
e d
eter
min
atio
n o
f st
age
req
uir
emen
ts.
An
aly
sis:
I
n L
C,
the
N2 c
om
po
siti
on
ran
ges
fro
m 5
5 m
ol%
at
the
bo
tto
m t
o a
bo
ut
99
mo
l% a
t
the
top
, w
ith
a f
eed
of
79
mo
l%.
Bas
ed o
n c
alcu
lati
on
s u
sin
g K
-val
ues
fro
m t
he
SR
K e
qu
atio
n o
f
stat
e at
4.5
atm
, th
e av
erag
e re
lati
ve
vo
lati
lity
in
LC
is
2.5
. I
n U
C,
the
N2 c
om
po
siti
on
ran
ges
fro
m a
bo
ut
1 m
ol%
at
the
bo
tto
m t
o 9
9 m
ol%
at
the
top
, w
ith
a f
eed
of
55
mo
l%.
B
ased
on
calc
ula
tio
ns
usi
ng K
-val
ues
fro
m t
he
SR
K e
qu
atio
n o
f st
ate
at 1
atm
, th
e av
erag
e re
lati
ve
vo
lati
lity
in
UC
is
4.0
. U
sin
g E
q.
(7-3
), e
qu
ilib
riu
m c
urv
es f
or
thes
e co
nst
ant
α c
ases
are
sh
ow
n
in t
he
McC
abe-
Th
iele
dia
gra
m o
n t
he
nex
t p
age.
H
ow
ever
, so
as
no
t to
clu
tter
th
e d
iagra
m,
the
curv
e fo
r U
C a
t 1
atm
is
bas
ed o
n N
2,
usi
ng,
yx
x
x
xN
NO
N
NN
O
N
N2
22
2
22
2
2
21
+1
+3
=−
=−
−
α
α1
4
(1
)
wh
ile
the
curv
e fo
r L
C a
t 4
.5 a
tm i
s b
ased
on
O2,
usi
ng,
yx
x
x
x
x
xO
ON
O
OO
N
O
O
O
O2
22
2
22
2
2
2
2
21
+1
+1
-0
.6=
−=
−=
−
−
α
α1
12
5 12
51
04
��
(/
.) /
.
.
(2
)
No
te t
hat
th
e eq
uil
ibri
um
cu
rve
for
1 a
tm i
s ab
ov
e th
e 4
5o li
ne,
wh
ile
that
fo
r 4
.5 a
tm i
s b
elo
w
the
45
o l
ine.
T
yp
ical
op
erat
ing l
ines
an
d q
-lin
es a
re s
ho
wn
fo
r d
eter
min
ing t
he
stag
e
req
uir
emen
ts.
Ex
erci
se 7
.40
(c
on
tin
ued
) A
na
lysi
s:
(co
nti
nu
ed)
Ex
erci
se 7
.41
S
ub
ject
: C
om
par
iso
n o
f m
easu
red
wit
h p
red
icte
d p
late
eff
icie
ncy
fo
r d
isti
llat
ion
of
a
met
han
ol-
wat
er m
ixtu
re.
Giv
en:
P
erfo
rman
ce d
ata
for
a d
isti
llat
ion
co
lum
n.
Vap
or-
liq
uid
eq
uil
ibri
um
dat
a.
Ass
um
pti
on
s:
P
arti
al r
ebo
iler
is
an e
qu
ilib
riu
m s
tage.
C
on
stan
t m
ola
r o
ver
flo
w.
Fin
d:
(a)
O
ver
all
pla
te e
ffic
ien
cy f
rom
per
form
ance
dat
a.
(b
) P
red
icte
d p
late
eff
icie
ncy
fro
m D
rick
amer
-Bra
dfo
rd c
orr
elat
ion
.
(c
) P
red
icte
d p
late
eff
icie
ncy
fro
m O
'Co
nn
ell
corr
elat
ion
.
(d
) P
red
icte
d e
ffic
ien
cy f
rom
Ch
an-F
air
corr
elat
ion
.
An
aly
sis:
(a
) C
on
ver
t th
e p
erfo
rman
ce d
ata
for
feed
an
d p
rod
uct
flo
w r
ates
an
d
com
po
siti
on
s fr
om
mas
s u
nit
s in
to m
ole
un
its,
mo
lecu
lar
wei
gh
ts o
f 3
2.0
4 f
or
met
han
ol
and
18
.02
fo
r w
ater
. T
he
resu
lts
are
as f
oll
ow
s:
F
low
ra
te,
lbm
ol/
h:
M
ole
fra
ctio
n:
Co
mp
on
ent
Fee
d
Dis
till
ate
B
ott
om
s F
eed
D
isti
lla
te
Bo
tto
ms
Met
han
ol
7
09
.1
70
2.7
6.4
0
.36
0
0.9
15
0
.00
53
Wat
er
12
60
.8
6
5.3
1
19
5.5
0
.64
0
0.0
85
0
.99
47
To
tal:
1
96
9.9
7
68
.0
12
01
.9
1.0
00
1
.00
0
1.0
00
0
Use
th
e M
cCab
e-T
hie
le m
eth
od
, b
ased
on
met
han
ol
mo
le f
ract
ion
s, t
o f
ind
th
e n
um
ber
of
equ
ilib
riu
m s
tages
nee
ded
. T
he
slo
pe
of
the
rect
ifyin
g s
ecti
on
op
erat
ing l
ine
is g
iven
by E
q.
(7-
7).
L
/V =
R/(
R +
1)=
0.9
47
/(1
.94
7)=
0.4
86
. T
his
lin
e in
ters
ects
th
e 4
5o l
ine
at x
= 0
.91
5.
Th
e sl
op
e o
f th
e st
rip
pin
g s
ecti
on
op
erat
ing l
ine
is g
iven
by E
q.
(7-1
2).
LV
VV
BB
//
=+
1��
= (
1.1
38
+ 1
)/1
.13
8 =
1.8
8.
Th
is l
ine
inte
rsec
ts t
he
45
oi l
ine
at x
= 0
.00
56
.
Th
e M
cCab
e-T
hie
le d
iagra
m i
s giv
en b
elo
w i
n t
wo
par
ts t
o a
chie
ve
accu
racy
. F
rom
th
e tw
o p
arts
of
the
dia
gra
m,
it i
s o
bse
rved
th
at t
he
two
op
erat
ing l
ines
do
no
t in
ters
ect
on
th
e q
-lin
e.
Th
is i
s
pro
bab
ly b
ecau
se t
he
assu
mp
tio
n o
f co
nst
ant
mo
lar
ov
erfl
ow
is
no
t v
alid
an
d t
he
op
erat
ing l
ines
hav
e so
me
curv
atu
re.
Ass
um
ing t
he
feed
sta
ge
in t
he
actu
al c
olu
mn
is
nea
r th
e o
pti
mal
lo
cati
on
,
the
qu
esti
on
able
McC
abe-
Th
iele
dia
gra
m g
ives
5 e
qu
ilib
riu
m s
tages
in
th
e st
rip
pin
g s
ecti
on
, o
ne
of
wh
ich
is
the
par
tial
reb
oil
er,
and
4.2
eq
uil
ibri
um
sta
ges
in
th
e re
ctif
yin
g s
ecti
on
. T
hu
s, t
he
tota
l eq
uil
ibri
um
sta
ges
in
th
e co
lum
n =
Nt =
8.2
+ t
he
par
tial
reb
oil
er.
Th
e co
lum
n c
on
tain
s 1
2
pla
tes
+ t
he
par
tial
reb
oil
er.
Fro
m E
q.
(6-2
1),
th
e o
ver
all
pla
te e
ffic
ien
cy i
s,
Eo =
Nt /
Na =
8.2
/12
= 0
.68
or
68
%.
Th
e co
lum
n c
on
tain
s 5
pla
tes
in t
he
rect
ifyin
g s
ecti
on
. T
his
is
equ
ival
ent
to a
pla
te e
ffic
ien
cy i
n
that
sec
tio
n o
f 4
.2/5
= 0
.84
or
84
%.
Th
e st
rip
pin
g s
ecti
on
co
nta
ins
6 p
late
s p
lus
the
feed
pla
te.
Ex
erci
se 7
.41
(co
nti
nu
ed)
An
aly
sis:
(a
) (
con
tin
ued
)
Th
eref
ore
, th
e ef
fici
ency
in
th
is s
ecti
on
is
4/7
= 0
.57
or
57
%.
No
te t
hes
e re
sult
s ar
e su
bje
ct t
o d
egre
e o
f cu
rvat
ure
of
the
op
erat
ing l
ines
an
d t
he
pla
cem
ent
of
the
feed
in
th
e M
cCab
e-T
hie
le m
eth
od
. I
n t
he
McC
abe-
Th
iele
met
ho
d,
if o
ne
mo
re e
qu
ilib
riu
m
stag
e is
ad
ded
to
th
e st
rip
pin
g s
ecti
on
, so
as
to g
ive
5 s
tages
plu
s th
e p
arti
al r
ebo
iler
, th
en t
he
rect
ifyin
g s
ecti
on
on
ly n
eed
s 3
.8 e
qu
ilib
riu
m s
tages
. T
hen
th
e o
ver
all
pla
te e
ffic
ien
cy i
s 7
3%
,
wit
h
71
% i
n t
he
stri
pp
ing s
ecti
on
an
d 7
6%
in
th
e re
ctif
yin
g s
ecti
on
. T
his
sti
ll d
oes
no
t ac
cou
nt
for
the
effe
ct o
f cu
rvat
ure
of
the
op
erat
ing l
ines
.
Ex
erci
se 7
.41
(co
nti
nu
ed)
An
aly
sis:
(a
) (
con
tin
ued
)
(b
) F
rom
Eq
. (7
-42
),
Eo =
13
.3 -
66
.7 l
og µ
T
ake
the
vis
cosi
ty a
s th
at o
f th
e fe
ed =
0.3
4 c
P
E
o =
13
.3 -
66
.7 l
og (
0.3
4)
= 4
4.6
%
Th
is i
s p
oo
r ag
reem
ent
wit
h t
he
per
form
ance
dat
a.
(c
) F
rom
Eq
. (7
-43
), E
o =
50
.3(α
µ)-0
.22
6
At
the
feed
co
mp
osi
tio
n,
x =
0.3
6 a
nd
y =
0.7
1.
Th
eref
ore
, fr
om
Eq
s (2
-19
) an
d (
2-2
1 c
om
bin
ed,
the
rela
tiv
e v
ola
tili
ty i
s, α
= (
y/x
)/[(
1 -
y)/
(1 -
x)]
= (
0.7
1/0
.36
)/(0
.29
/0.6
4)
= 4
.4
Ex
erci
se 7
.41
(co
nti
nu
ed)
An
aly
sis:
E
o =
50
.3[(
4.4
)(0
.34
)]-0
.22
6 =
45
.9%
No
w c
orr
ect
for
len
gth
of
liq
uid
pat
h f
rom
Fig
. 7
.5.
Co
lum
n d
iam
eter
= 6
ft.
A
ssu
me
len
gth
of
liq
uid
pat
h =
70
% o
f co
lum
n d
iam
eter
= 0
.7(6
) =
4.2
ft.
F
rom
Fig
. 7
.5,
corr
ecti
on
to
be
add
ed =
10
%.
Th
eref
ore
co
rrec
ted
Eo =
45
.9 +
10
= 5
5.9
%
Th
is a
lso
ap
pea
rs t
o b
e lo
w.
(d
) F
rom
Eq
. (6
-56
),
NO
G =
- l
n (
1 -
EO
V).
T
her
efo
re,
EO
V =
1 -
ex
p(-
NO
G)
Use
Eq
s. (
6-6
2,
(6-6
4),
(6
-66
), a
nd
(6
-67
) as
in
Ex
amp
le 6
.7.
Car
ry o
ut
the
calc
ula
tio
ns
at t
he
bo
tto
m t
ray b
ased
on
met
han
ol
dif
fusi
on
. C
on
dit
ion
s ar
e:
G
as
Liq
uid
Mo
lar
flo
w r
ate,
km
ol/
h
63
0
1,1
92
Mo
lecu
lar
wei
gh
t 1
8.5
1
8.0
Den
sity
, k
g/m
3
0.6
57
9
40
Est
imat
e li
qu
id d
iffu
siv
ity o
f m
eth
ano
l in
wat
er a
t 2
12
oF
= 3
73
K.
Fro
m P
erry
's H
and
bo
ok
, D
L =
1.6
x 1
0-5
cm2/s
at
25
oC
. T
he
vis
cosi
ty o
f w
ater
at
21
2oF
= 0
.25
cP
. U
sin
g E
q.
(3-3
9)
to c
orr
ect
for
tem
per
atu
re a
nd
vis
cosi
ty,
DL =
1.6
x 1
0-5
(3
73
/29
8)(
1/0
.25
) =
8 x
10
-5 c
m2/s
Est
imat
e gas
dif
fusi
vit
y o
f m
eth
ano
l in
wat
er v
apo
r fr
om
Eq
. (3
-36
).
T =
37
3 K
MA
B =
2/[
(1/3
2)
+ (
1/1
8)]
= 2
3.
Usi
ng T
able
3.1
,
=+
+=
��
15
92
31
46
11
31
31
31
..
()
..
,.
= w
ater
meth
ano
lV
V
DV
=+
=0
00
14
33
73
15
11
47
23
31
31
31
03
01
75
12
13
13
2
.(
)
(.
/.
)[
..
].
.
//
/cm
2/s
Req
uir
ed t
ray d
imen
sio
ns:
D
T =
6 f
t,
A =
3.1
4(6
)2/4
= 2
8.3
ft2
= 2
.63
m2
Aa =
0.9
1 A
=
0.9
1(2
.63
) =
2.3
9 m
2 =
23
,90
0 c
m2,
Lw =
42
.5 i
n.
= 1
.08
m
Tra
y c
on
dit
ion
s:
φε
= 1
- 0
.61
7 =
0.3
83
, q
L =
47
,30
0/(
60
)(8
.33
) =
94
.6 g
pm
= 5
,97
0 c
m3/s
Fro
m E
q.
(6-5
4),
C
l = 0
.36
2 +
0.3
17
ex
p[-
3.5
(2)]
= 0
.36
2
Fro
m E
q.
(6-5
1),
h l
=+� ��
� �� �� �
� �� �==
03
83
20
03
62
94
6
42
50
38
31
21
30
8
23
..
..
(.
)(.
).
.
/
in
. c
m2
f =
0.4
0,
Fro
m E
q.
(6-6
4),
t L
= (
3.0
8)(
23
,90
0)/
5,9
70
= 1
2.3
s
Ex
erci
se 7
.41
(co
nti
nu
ed)
An
aly
sis:
(d
)
(co
nti
nu
ed)
Th
e co
nti
nu
ity e
qu
atio
n i
s,
63
0(1
8.5
)(2
.20
5)/3
60
0,
so
,ft/
s6
.8 f
t/s
28
.3(0
.91)
(0.6
57
/16
.02
)
VV
aa
Va
aV
mm
UA
UA
=ρ
==
=ρ
= 2
.07
m/s
Fro
m E
q.
(6-6
5),
t G
==
(.
)(.
)
(.
)(.
)(.
)()
.0
61
73
08
03
83
68
25
41
20
02
4 s
Fro
m b
elo
w E
q.
(6-6
7),
F=
Ua
0.5
Vρ
= 2
.07
(0.6
57
)0.5
= 1
.68
(k
g/m
)0.5
/s
Fro
m E
q.
(6-6
7),
ka
L=
×+
=−
78
81
01
68
04
25
14
85
05
.(8
)(
..
).
. s
-1
Fro
m E
q.
(6-6
6),
k
aG
=−
=1
03
00
30
04
00
84
20
40
30
88
53
12
2
12
,(
.)
..
(.
)
..
/
/ s
-1
Fro
m E
q.
(6-6
3),
N
ka
tL
LL
==
=1
48
12
31
82
.(
.)
.
Fro
m E
q.
(6-6
2),
N
ka
tG
GG
==
=8
53
00
24
20
5.
(.
).
Fro
m t
he
vap
or-
liq
uid
eq
uil
ibri
um
dat
a at
th
e b
ott
om
of
the
colu
mn
,
Km
eth
anol =
0.1
56
/0.0
24
6 =
6.3
4
Ab
sorp
tio
n f
acto
r =
KV
/L =
(6
.34
)(6
30
)/1
,19
2 =
3.3
5
Fro
m E
q.
(6-6
1),
1
11
20
5
33
5
18
20
48
80
18
40
67
2N
N
KV
L
NO
GG
L
=+
=+
=+
=(
/)
.
. ..
..
N
OG =
1/0
.67
2 =
1.4
88
Th
us,
th
e gas
-ph
ase
resi
stan
ce i
s m
ore
im
po
rtan
t th
an t
he
liq
uid
-ph
ase
resi
stan
ce.
Fro
m E
q.
(6-5
6),
1
exp
()
1e
0.7
74
or
xp
(1
.48
77
.4)
%8
=−
−=
−−
=V
OG
OE
N
Th
is i
s in
ver
y g
oo
d a
gre
emen
t w
ith
th
e p
erfo
rman
ce d
ata.
E
xer
cise
7.4
2
Su
bje
ct:
Est
imat
ion
of
effi
cien
cies
, E
MV a
nd
Eo f
rom
EO
V f
or
met
han
ol-
wat
er m
ixtu
re,
as
mea
sure
d w
ith
a s
mal
l O
lder
shaw
co
lum
n.
Giv
en:
C
olu
mn
co
nd
itio
ns
fro
m E
xer
cise
7.4
1.
Fin
d:
E
MV a
nd
Eo
An
aly
sis:
Cas
e 1
: A
ssu
me
com
ple
te m
ixin
g o
n t
he
tray
s.
E
MV =
EO
V =
0.6
5 o
r 6
5%
Cas
e 2
: A
ssu
me
plu
g f
low
of
liq
uid
wit
h n
o l
on
git
ud
inal
dif
fusi
on
. T
ake
con
dit
ion
s at
th
e to
p o
f th
e co
lum
n.
Fro
m E
q.
(7-7
),
L/V
= R
/(R
+ 1
) =
0.9
47
/(1
+ 0
.94
7)
= 0
.48
6
Fro
m E
q.
(6-3
3),
λ
= m
/(L
/V)
Fro
m t
he
vap
or-
liq
uid
eq
uil
ibri
um
dat
a giv
en i
n E
xer
cise
7.4
1,
m =
dy/
dx
= (
1 -
0.9
15
)/(1
- 0
.79
3)
= 0
.41
λ =
0.4
1/0
.48
6 =
0.8
44
Fro
m E
q.
(6-3
2),
[]
[]
{}
11
exp
()
1ex
p0
.84
4(0
.65
0.7
54
or
)1
0.8
75
.4
44
%=
λ−
=−
=λ
OV
MV
EE
Th
e ac
tual
val
ue
of
EM
V
pro
bab
ly l
ies
inb
etw
een
6
5%
an
d 7
5.4
%,
or
say 7
0%
.
Fro
m E
q.
(6-3
7),
ass
um
ing t
hat
th
e eq
uil
ibri
um
an
d o
per
atin
g l
ines
are
str
aigh
t,
[]
[]
log
1(
1)lo
g1
0.7
0(0
.84
41)
log
log
(0.8
44
)0
.68
or
68
%+
λ−
+−
==
λ=
o
MV
EE
![Separation Processes - ChE 4M3 0.5cm [width=0.2]/Users ... · 2.Perry’s Chemical Engineers’ Handbook, Chapter 21.1 3.Seader, Henley and Roper, \Separation Process Principles",](https://img.pdfslide.us/doc/110x75/5e8866476557a55b4e3217db/separation-processes-che-4m3-05cm-width02users-2perryas-chemical.jpg)
(2)](https://img.pdfslide.us/doc/110x75/55cf9ba7550346d033a6e0e5/warren-d-seider-j-d-seader-daniel-r-lewinbookfiorg2.jpg)
