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OUTLINE
PART 1: Rate Laws
Relative Rates of Reaction
Reaction Order & Rate Law
Reaction Rate Constant, k
PART 2: Stoichiometry
Batch System Stoichiometric Table
Flow System Stoichiometric Table
Calculation for Concentration in terms of
Conversion
1. RELATIVE RATES OF REACTION
d
r
c
r
b
r
a
r DCBA
dDcCbBaA
212
22 NOONOrrr
EXAMPLE
Reaction
Stoichiometry
If NO2 formed at 4 mol/m3/s
(r NO2= 4 mol/m3/s), what is
the rate of formation of NO?
22 22 NOONO
1. RELATIVE RATES OF REACTION
2
//4
2
3 smmolrNO
212
22 NOONOrrr
smmolsmmol
rNO //42
//42 3
3
22
2NONOrr
If NO2 formed at 4 mol/m3/s (r NO2= 4 mol/m3/s),
what is the rate of formation of NO?
22 22 NOONO
1. RELATIVE RATES OF REACTION
The Reaction:
is carried out in a reactor. If at a particular point,
the rate of disappearance of A is 10 mol/dm3/s,
what are the rates of B and C?
CBA 532
EXERCISE
1. RELATIVE RATES OF REACTION
The relative rates are
Given, the rate of disappearance of A, -rA, is 10mol/dm3/s
Thus, solving the rates of B & C;
532
CBA rrr
CBA 532
r A= -10 mol/dm3/s
sdmmolrB //102
3 3
32
BA rr
52
CA rr
sdmmolrC //102
5 3
sdmmol //15 3 sdmmol //25 3
2. REACTION ORDER & RATE LAW
The reaction rate (rate of disappearance) depends
on temperature and composition.
It can be written as the product of reaction rate
constant, kA and a function of concentrations
(activities) of the reactants involved in the
reaction:
..., BAAA CCfnTkr
Rate law is a kinetic
expression that gives the
relationship between
reaction rate, -rA, and
concentration.
2. REACTION ORDER & RATE LAW
For reaction in which the stoichiometric coefficient is 1
for ALL species:
we shall delete the subscript on the specific reaction
rate, (e.g.; A in kA) to let
OHNaClHClNaOH kkkkk2
Rate law is a kinetic
expression that gives the
relationship between
reaction rate, -rA, and
concentration.
OHNaClHClNaOH 21111
2.1 POWER LAW MODELS & ELEMENTARY RATE LAWS
Power Law Model:
The rxn is 𝛂 order wrt reactant A
AND
The rxn is 𝛃 order wrt reactant B
The overall order of the reaction, n;
BAA CkCr
n
2.1 POWER LAW MODELS & ELEMENTARY RATE LAWS
The unit of the specific reaction, k, will vary with the
order of reaction.
Products
A
Time
ionConcentratk
n
1
AA kr sdmmolk 3/Zero order (n=0)
First order (n=1) AAA Ckr 1 sk
Second order (n=2) 2
AAA Ckr smoldmk /3
Third order (n=3) 3
AAA Ckr 123 / smoldmk
2.1 POWER LAW MODELS & ELEMENTARY RATE LAWS
Elementary reaction: a chemical reaction in which one or more of the chemical species react directly to form products in a single reaction step and with a single transition state.
Elementary rate law:
The rxn is said to follow the elementary rate law if the stoichiometic coefficients are IDENTICAL to the reaction order of each species.
A Products
BA Products
Unimolecular reaction
Bimolecular reaction
22 22 NOONO
2
2
ONONONO CCkr
Non-elementary rate laws: reactions that do not follow simple rate laws (power rate laws).
Example 1: Homogeneous Rxn
The kinetic rate law is:
Rxn order: first order wrt to CO, three-halves order wrt Cl2, five-halves order overall.
23
2ClCOCO CkCr
2.2 NON-ELEMENTARY RATE LAWS
22 COClClCO
Gas phase
synthesis of
phosgene
Example 2: Heterogeneous Rxn
The rate of disappearance of toluene per mass of
catalyst is :
where KB & KT is the adsorption constants.
TTBB
TH
TPKPK
PkPr
1
2'
2.2 NON-ELEMENTARY RATE LAWS
4662356 CHHCHCHHCcat
Gas-solid catalyzed
rxn:
Hydrodemethylation
of toluene (T)
In terms of partial
pressure rather than
concentrations
MBHTcat
2
follows Langmuir-
Hinshelwood kinetics
2.3 REVERSIBLE REACTIONS
For reversible rxn, all rate laws must reduce to the
thermodynamic relationship relating the reacting
species concentrations at equilibrium.
dDcCbBaA ⇌
b
eB
a
eA
d
eD
c
CeC
CC
CCK
Thermodynamic
Equilibrium
Relationship
2.3 REVERSIBLE REACTIONS
21012662 HHCHC ⇌
2
, BBforwardB Ckr
EXAMPLE: combination rxn of 2 mol of benzene to form 1 mol
H2 and 1 mol diphenyl.
kB
k-B
22 HDB ⇌ kB
k-B
symbolically;
The rate of disappearance of benzene; 2
, BBforwardB Ckr
The reverse rxn btween diphenyl & hydrogen;
6621012 2 HCHHC ⇌ k-B
OR
2, HDBreverseB CCkr
The rate of formation of benzene (in reverse direction);
2.3 REVERSIBLE REACTIONS
The net rate of formation of benzene is;
Multiplying both sides by -1, we obtain the rate law of
disappearance of benzene, -rB
reverseBforwardBnetBB rrrr ,,,
2
2
HDBBB CCkCk
2
2
HDBBBB CCkCkr
2
2
HD
B
BBB CC
k
kCk
2.3 REVERSIBLE REACTIONS
Replacing the ratio of the reverse & forward rate law
constant by equilibrium constants;
where
C
B
B Kk
k
2
2
HD
B
BBBB CC
k
kCkr
C
HD
BBBK
CCCkr 22
Concentration
equilibrium constant
3. THE REACTION RATE CONSTANT
RTE
A AeTk /A= preexponential factor or frequency factor
E= activation energy, J/mol or cal/mol
R=gas constant = 8.314 J/mol-K = 1.987 cal/mol-K
T= absolute temperature, K
Arrhenius
equation
-no of collision
RTEe /
A
-probability that
the collision will
result in a reaction
3. THE REACTION RATE CONSTANT
RTE
A AeTk / Activation energy is a measure of the minimum
energy that the reacting molecules must have
in order for the reaction to occur (energy required to
reach transition state).
Reactants Products
Transition state
Energy barier -total no of collision
RTEe /
A
probability that
- the collision will
result in a rxn
k - no of collision that
result in a rxn
3. THE REACTION RATE CONSTANT
RTE
A AeTk /
Taking a natural logarithm;
E ⬆, k ⬆, -r = ⬆
The larger the
activation energy,
the more
temperature
sensitive k and thus
the reaction rate.
TR
EAkA
1lnln
4. BATCH SYSTEMS STOICHIOMETRIC TABLE
Purpose of developing stoichiometric table:
To determine the no of moles of each species
remaining at a conversion of X.
4. BATCH SYSTEMS STOICHIOMETRIC TABLE
Species Initially
(mol)
Change
(mol)
Remaining
(mol)
A
B
C
D
I
Totals
Components of stoichiometric table:
refers to moles of
species reacted or
formed
Recall from Chapter 2:
Factorizing;
4. BATCH SYSTEMS STOICHIOMETRIC TABLE
0
0
A
AA
N
NNX
XNNN AAA 00
XNN AA 10
moles of A reacted
aA + bB cC + dD
moles of A remaining
in the reactor at a
conversion
of X
4. BATCH SYSTEMS STOICHIOMETRIC TABLE
Moles B
reacted, NB
XNa
dA0
XNa
cA0
Moles C
formed, NC
Moles D
formed, ND
XNa
bA0
Moles B reacted
Moles A reacted
Moles A reacted
4. BATCH SYSTEMS STOICHIOMETRIC TABLE
moles B remaining
in the system, NB
XNa
bN AB 00
NC
moles of B
initially in the
system
moles of C
formed
XNa
cN AC 00
ND XN
a
dN AD 00
moles of B
reacted
moles of D
formed
4. BATCH SYSTEMS STOICHIOMETRIC TABLE
Species Initially
(mol)
Change
(mol)
Remaining (mol)
A
B
C
D
I -
Totals
0AN
0BN
0CN
0DN
0IN
XNa
bA0
XNa
cA0
XNa
dA0
XNA0
XNa
cNN ACC 00
XNa
dNN ADD 00
XNa
bNN ABB 00
XNNN AAA 00
0II NN
XNa
b
a
c
a
dNN ATT 00 1
0TN
4. BATCH SYSTEMS STOICHIOMETRIC TABLE
XNa
b
a
c
a
dNN ATT 00 1
Total no of moles per mole of A reacted can be
calculated as:
where
XNN AT 00
1a
b
a
c
a
d
Change in the total number of moles per
mole of A reacted
4. BATCH SYSTEMS STOICHIOMETRIC TABLE
Species Initially Change Remaining Concentration
A
B
C
D
I
Totals
Can we express concentration of each species??
AA kCr 2
AA kCr 3
AAA Ckr
Concentration of each species in terms of
conversion can be expressed as:
4. BATCH SYSTEMS STOICHIOMETRIC TABLE
V
XN
V
NC AA
A
10
V
XNabN
V
NC ABB
B00 /
Remaining (mol)
A
B
C
D
XNa
cNN ACC 00
XNa
dNN ADD 00
XNa
bNN ABB 00
XNNN AAA 00
V
XNacN
V
NC ACC
C00 /
V
XNadN
V
NC ADD
D00 /
Recall from
stoichiometric
table
V
XabNNN ABA // 000
4. BATCH SYSTEMS STOICHIOMETRIC TABLE
V
XNabNC AB
B00 /
V
XNacNC AC
C00 /
V
XacNNN ACA // 000
V
XabN BA /0
V
XacN CA /0
V
XadNNN ADA // 000
4. BATCH SYSTEMS STOICHIOMETRIC TABLE
V
XNadNC AD
D00 /
V
XadN DA /0
0
0
0
0
0
0
A
i
A
i
A
ii
y
y
C
C
N
N
4. BATCH SYSTEMS STOICHIOMETRIC TABLE
Species Initially Change Remaining Concentration
A
B
C
D
I -
0AN
0BN
0CN
0DN
0IN
XNa
bA0
XNa
cA0
XNa
dA0
XNA0
XNa
cNN ACC 00
XNa
dNN ADD 00
XNa
bNN ABB 00
XNNN AAA 00
0II NN
V
XNC A
A
10
V
XabNC BA
B
/0
V
XacNC CA
C
/0
V
XadNC DA
D
/0
IOC
X
a
b
N
NNXN
a
bNN
A
BAABB
0
0000
X
a
bN BA0
0
0
0
0
0
0
A
i
A
i
A
ii
y
y
C
C
N
N
4. BATCH SYSTEMS STOICHIOMETRIC TABLE
Species Initially Change Remaining Concentration
A
B
C
D
I -
0AN
0BN
0CN
0DN
0IN
XNa
bA0
XNa
cA0
XNa
dA0
XNA0
X
a
bNN BAB 0
XNNN AAA 00
0II NN
V
XNC A
A
10
V
XabNC BA
B
/0
V
XacNC CA
C
/0
V
XadNC DA
D
/0
IOC
X
a
cNN CAC 0
X
a
dNN DAD 0
Given the saponification for the formation of soap
from aqueous caustic soda & glyceryl stearate is:
Letting X the conversion of sodium hydroxide, set up a
stoichiometric table expressing the concentration of
each species in terms of its initial concentration and the
conversion.
4. BATCH SYSTEMS STOICHIOMETRIC TABLE
3533517533517 33 OHHCCOONaHCHCOOHCaqNaOH
EXAMPLE
4. BATCH SYSTEMS STOICHIOMETRIC TABLE
3533517533517 33 OHHCCOONaHCHCOOHCaqNaOH
We know that this is a liquid-phase reaction.
Therefore, V=V0
XC
V
XN
V
XNC A
AAA
1
110
0
00
DCBA 33
XC
V
XabNC BA
BAB
3
1/0
0
0
1313 dcba
EXAMPLE
4. BATCH SYSTEMS STOICHIOMETRIC TABLE
Species Initially Change Remaining Concentration
A
B
C
D
I -
Total 0
0AN
0BN
0CN
0DN
0IN
XNA03
1
XNA0
XNA03
1
XNA0
XNN BAB
3
10
XNN AA 10
0II NN
XCC AA 10
XCC BAB
3
10
XCC CAC 0
XCC DAD
3
10
IOC
XNN CAC 0
XNN DAD
3
10
EXAMPLE
0TN 0TT NN
5. FLOW SYSTEMS STOICHIOMETRIC TABLE
Purpose of developing stoichiometric table:
To determine the effluent flow rate of each species at
a conversion of X.
5. FLOW SYSTEMS STOICHIOMETRIC TABLE
Species Feed rate to
reactor
(mol/time)
Change within
the reactor
(mol/time)
Effluent rate
from reactor
(mol/time)
A
B
C
D
I
Totals
Components of stoichiometric table:
5. FLOW SYSTEMS STOICHIOMETRIC TABLE
Species Feed rate
to reactor
(mol/time)
Change
within the
reactor
(mol/time)
Effluent rate from
reactor (mol/time)
Concentration
(mol/L)
A
B
C
D
I -
Totals
0AF
00 ABB FF
00 ACC FF
00 ADD FF
00 AiI FF
XFa
bA0
XFa
cA0
XFa
dA0
XFA0
X
a
bFF BAB 0
XFFF AAA 00
IAI FF 0
X
a
cFF CAC 0
X
a
dFF DAD 0
0TF XFFF ATT 00
XFC A
A
10
XabFC BA
B
/0
XacFC CA
C
/0
XadFC DA
D
/0
IA
I
FC
0
QUIZ 3
Given a liquid phase reaction:
A+ 2B C + D
The initial concentration of A and B are 1.8 kmol/m3
and 6.6 kmol/m3 respectively. Construct a
stoichiometric table for a flow system considering A as
the basis of calculation.
ANSWER FOR QUIZ 3
A+ 2B C + D
Given:
From stoichiometry, we know that,
3
3
0
/6.6
/8.1
mkmolC
mkmolC
BO
A
0
0
0
0
0
0
A
i
A
i
A
ii
y
y
C
C
F
F
67.38.1
6.6B
1121 dcba
0
0
A
ii
C
C
08.1
0C
3
3
0
/0
/0
mkmolC
mkmolC
DO
C
Since C & D are
products.
08.1
0D
11 a
b
a
c
a
d
ANSWER FOR QUIZ 5
Species Feed rate to
reactor
(mol/time)
Change
within the
reactor
(mol/time)
Effluent rate from
reactor (mol/time)
A
B
C
D
Totals
0AF
BAB FF 00
CAC FF 00
DAD FF 00
XFA02
XFA0
XFA0
XFA0
XFF BAB 20
XFF AA 10
XFF AC 0
XFF AD 0
0TF XFFF ATT 00
ANSWER FOR QUIZ 5
Species Feed rate to
reactor
(mol/time)
Change
within the
reactor
(mol/time)
Effluent rate from
reactor (mol/time)
A
B
C
D
Totals
0AF
00 67.3 AB FF
00 CF
00 DF
XFA02
XFA0
XFA0
XFA0
XFF AB 267.30
XFF AA 10
XFF AC 0
XFF AD 0
0TF XFFF ATT 00
Substituting the numerical values;
1. For liquid phase:
Batch System:
6. CONCENTRATION IN TERMS OF CONVERSION
0VV
V
XN
V
NC AA
A
10
V
NC B
B
V
NC C
C
V
NC D
D
V
XabN BA /0
V
XacN CA /0
V
XadN DA /0
0
0 /
V
XabN BA
0
0 /
V
XacN CA
0
0 /
V
XadN DA
XabC BA /0
XacC CA /0
XadC DA /0
1. For liquid phase:
Flow System -
6. CONCENTRATION IN TERMS OF CONVERSION
0
XFFC AA
A
10
B
B
FC
C
C
FC
D
D
FC
XabF BA /0
XacF CA /0
XadF DA /0
0
0 /
XabF BA
0
0 /
XacF CA
XabC BA /0
XacC CA /0
XadC DA /0
0
0 /
XadF DA
2. For gas phase:
Batch System
From equation of state;
At any time t,
At initial condition (t=0)
6. CONCENTRATION IN TERMS OF CONVERSION
V
NC A
A Need to substitute V
from gas law equation
RTZNPV T
T= temperature, K
P= total pressure, atm (1 atm= 101.3 kPa)
Z= compressibility factor
R= gas constant = 0.08206 dm3-atm/mol-K
00000 RTNZVP T
(1)
(2)
2. For gas phase:
Batch System
Dividing (1) by (2);
6. CONCENTRATION IN TERMS OF CONVERSION
RTZNPV T
00000 RTNZVP T
(1)
(2)
000
00
T
T
N
N
Z
Z
T
T
P
PVV
Recall from stoichiometric table
XNNN ATT 00 (4)
Dividing (4) by NT0 ;
XN
N
N
N
T
A
T
T 0
0
0
1
XyA01
(3)
2. For gas phase:
Batch System
Applies for both
batch and flow
systems
6. CONCENTRATION IN TERMS OF CONVERSION
XyN
NA
T
T0
0
1
XN
N
T
T 10
0
01T
A
N
N
a
b
a
c
a
d
0Ay
At complete conversion (for irreversible rxn): X=1, NT=NTf
XN
NN
T
TT
0
0
Rearranging;
0
0
T
TTf
N
NN
Will be substitute
in (3)
2. For gas phase:
Batch System
Substituting the expression for NT/NT0 in (3),
6. CONCENTRATION IN TERMS OF CONVERSION
000
00
T
T
N
N
Z
Z
T
T
P
PVV
(3)
XZ
Z
T
T
P
PVV
1
00
00
If the compressibility factor are not change
significantly during rxn, Z0⩳Z
0
00 1
T
TX
P
PVV
(5)
2. For gas phase:
Flow System
From gas law, at any point in the reactor,
At the entrance of reactor;
6. CONCENTRATION IN TERMS OF CONVERSION
ZRT
PFC T
T
0
0
0
0T
T
P
P
F
F
T
T (3)
00
0
0
00
RTZ
PFC T
T
(1)
(2)
Dividing (1) by (2)
j
j
FC
Need to substitute υ
from gas law equation
0
0
0
0T
T
P
P
F
F
T
T
2. For gas phase:
Flow System
Substituting for FT;
6. CONCENTRATION IN TERMS OF CONVERSION
Recall from stoichiometric table
XFFF ATT 00
0
0
0
000
T
T
P
P
F
XFF
T
AT
0
0
0
00 1
T
T
P
PX
F
F
T
A
0
000 1
T
T
P
PXyA
0
00 1
T
T
P
PX (4)
2. For gas phase:
Flow System
Substituting υ & Fj;
0
00 1
T
T
P
PX
6. CONCENTRATION IN TERMS OF CONVERSION
(4)
j
j
FC
Need to substitute υ
from gas law equation
0
00
0
1T
T
P
Px
XvFC
jjA
j
XvFF jjjj 0(5)
T
T
P
P
x
XvC
jj
A0
0
01
Stoichiometric
coefficient
(d/a, c/a, -b/a, -a)
0
00 1
T
T
P
PX
2. For gas phase:
Flow System
Concentration for each species:
6. CONCENTRATION IN TERMS OF CONVERSION
aA + bB cC + dD
XFFC AA
A
10
B
B
FC
C
C
FC
D
D
FC
XabF BA /0
XacF CA /0
XadF DA /0
0
00
1
/
P
P
T
T
x
XabC B
A
0
00
1
/
P
P
T
T
x
XacC C
A
0
00
1
/
P
P
T
T
x
XadC D
A
0
00
1
1
P
P
T
T
x
XCA
I
I
FC
IIF
0
0
00
1 P
P
T
T
x
C IA
SUMMARY
Elementary rate law:
The rxn that in which its stoichiometic coefficients are IDENTICAL to the
reaction order of each species.
Non-elementary rate laws:
The reactions that do not follow simple rate laws (power rate laws) in
which its stoichiometic coefficients are NOT IDENTICAL to the reaction
order of each species.
Reversible reaction:
All rate laws must reduce to the thermodynamic relationship relating the
reacting species concentrations at equilibrium.
Power Law Model:
SUMMARY
Reaction Rate Constant, k
RTE
A AeTk /
E ⬆, k ⬆, -r ⬆
The larger the activation energy,
the more sensitive k is, (towards
the change in temperature)
SUMMARY
Stoichiometric Table for Batch Systems
Species Initially Change Remaining
A
B
C
D
I -
0AN
0BN
0CN
0DN
0IN
XNa
bA0
XNa
cA0
XNa
dA0
XNA0
XNa
cNN ACC 00
XNa
dNN ADD 00
XNa
bNN ABB 00
XNNN AAA 00
0II NN
Species Feed rate to
reactor
(mol/time)
Change within the
reactor (mol/time)
Effluent rate from
reactor (mol/time)
A
B
C
D
I -
Totals
SUMMARY
Stoichiometric Table for Flow Systems
0AF
00 ABB FF
00 ACC FF
00 ADD FF
00 AiI FF
XFa
bA0
XFa
cA0
XFa
dA0
XFA0
X
a
bFF BAB 0
XFFF AAA 00
IAI FF 0
X
a
cFF CAC 0
X
a
dFF DAD 0
0TF XFFF ATT 00
Expression of V and υ in calculating the concentration of each species:
Batch systems
Liquid phase:
Gas phase:
Flow systems
Liquid phase:
Gas phase:
SUMMARY
0VV
0
P
P
T
TXVV 0
0
0 1
P
P
T
TX 0
0
0 1
EXERCISE
Given a gas phase reaction:
A+ 2B 2C
Construct a stoichiometric table for a flow system
considering A as the basis of calculation with
equimolar feed of 50% A and 50% B. Derive the
concentration for each species (for an isothermal
gas phase reaction, with no pressure drop).
.
Spe
cies
Feed rate
to reactor
(mol/time)
Change
within the
reactor
(mol/time)
Effluent rate
from reactor
(mol/time)
A
B
C
0AF
00 AB FF
00 CF
XFA02
XFA02
XFA0
XFF AB 210
XFFF AAA 00
XFF AC 02
XFFC AA
A
10
B
B
FC
C
C
FC
XFA0
0
00
5.01
21
P
P
T
T
X
XCA
0
00
5.01
2
P
P
T
T
X
XCA
0
00
5.01
1
P
P
T
T
X
XCA
XFA 210
From stoichiometry table
0
00
0
0
0RT
Py
RT
PC AA
A