VLE Data Sulfuric Acid

7/18/2019 VLE Data Sulfuric Acid

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UCRL- 10886UC-4 Chemis t ryTID-4500 (19th Ed. )

UNIVERSITY O F CALIFORNIALawrence Radia t ion LaboratoryBerkeley , Cal i forn iaCon tract No. W - 740 5 -.eng- 48

VAPOR-LIQUID EQUILIBRIA FOR AQUEOUS SULFURIC ACIDJohn I rv ing G m i t r o and Theodore Vermeu len

June 24 , 1963


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VAPOR-LIQUID EQUILIBRIA FOR AQUEOUS SULFURIC ACIDContents

Abs t rac t I1. Int roduct ion11. Deriva t ion of Equat ions

A, P a r t i a l - P r e s s u r e E q ua ti on e3. Dissocia t ion Constant of H2 S0 (g)4111. Thermodynamic Da taA. Pure -Component Pro pe r t i e s a e

1. H;9, for H2S04(g)2. Co f o r H2So4(g)3 . Constants in Equat ionsP

B. P a r t i a l M o la l P r o p e r t i e s I)IV . C a l cu l a ti on of Pa r t i a l P r e s s u r e s .

A. T r i a l Calcula t ions - . .

* v. 1

, . 3. 5

, . 7. 7. 9. 11. 12. . 15. 16

B. Adjus tment of High- Te mp er a tu re Partial MolalHeak Capacities I a a . . e . . 21

1. Sulfur ic Acid Azeotro pe - . - 0 - 212 . Adjus tment of Alpha , 10 to 9 8 . 5 7 0 ~ . . . 243. 9 8 , l i - and 100-70w Region . 0 . 25C. Resul ts . 0 31

V. Discuss ion and Conc lusions . 35Acknowledgment ~ ~ . . 39Notation e e 40Appendix 0 42R e f e r e nc e s . 8 1

0 . .

. . . a


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VAPO R- LIQUID EQUILIBRIA FOR AQUEOUS S ULFU RIC ACIDJohn I rv ing Gmi t ro and Theodore Vermeul en

Lawre nce Radia t ion Labo ra tory and Depar tment of Chemica l Enginee r ingUnive rs i ty of Ca l i forn ia , Be rke ley , Ca l i forn iaJune 24, 1963A S STRACT

The compos i t ion of the vapor phase ove r su l fu r ic ac id has no tbeen m eas ur ed expe r im enta l ly because of the low volat i l i ty of H SO4.A m e t hod i s de s c r i be d f o r c a lc u l at i ng t he pa r t i a l p r e s s u r e s of HZO,H2S04, and SO ba s e d upon l i qui d - pha s e pa r t i a l - m o l a l t he r m odyna m i cquant i t i e s .t i a l p r e s s u r e s f r o m - 50 t o 4 0 0" C at t h i r t y - s i x c om pos i t ions be t we e n10 and 100 weight-percent ac id.

2

3Tables and graph s a r e provided which g ive the above pa r -


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I , INTRODUCT'IOiuThe vapor phase over sulfur ic ac id solut ions i s composed of

wa te r and su l fur ic ac id , toge the r with su l fur t r iox ide f r om the d i s -soc ia t ion of the ac id:

H2SO4(g) = H2O(g) -t SO3(g) - (1 )In pr inc ip le , the d i s t r ibu t ion of these th ree components a t va r ioustem per a tu re s and ac id concent rat ions can be de te rm ined by e i the r ( a )e xpe r i m e n t a l pa r t i a l - p r e s s u r e m e a s u r e m e n t spa r t i a l p r e s s u r e s f r o m l iqu id - pha se t he r m odyna m i c dat a.

o r (b) ca lcu la tion of

Method (a ) , a lthough mo re d i rec t , i s not fully applicable to thesu lfu ric aci d sy st em beca us e of the Pow volzti l i ty of H2S04"of the pro blem s involved m ay be had f ro m the fol lowing table (der ivedf r om the pre se nt s tudy) , which g ives orde r -of -m agni tude va lues fort h e v ar i o us p a r t i a l p r e s s u r e s :

A n dea

Concent ra t io n Tem pe r a t u r e Partial p r e s s u r e (m m Hg)( 7 4 ( " C ) H2 H2s04 s03

10 25 20 10-15

50

90

100300

25100300

25PO0300

7klO26x104832.104x1 o 45 ~ 1 0 - 321.8XlQ

10-102x10-310-1010-65x10-1J O - ~6x10-21 " 2X1O2

10-1610-610-1710-1110-310-810-54

Exp er ime nta l d i f fi cu lt i es no twi ths tanding , the to ta l vapor pr e s -s u r e of s u l f u r i c a c i d , w h ic h i n m os t c a s e s i s due e n t i r e l y t o t he p a r t i a lp r e s s u r e of H 0, was the subjec t of numerous inves t iga t ions be tween21845 and 1923, Gree new alt ,r ev i ew e d 19 s e p a r a t e v a p o r - p r e s s u r e d e t e r m i n a ti o n s .s u l t , b a s e d e s s e n t i a l l y on t he m e a s u r e m e n t s of B ur t' a nd of Daudt,i s t he a c c e p t ed s t a nd a r d t ha t a ppe a r s i n todayo r e f e r e n c e w o r k s .

who in 1925 a sse mb led the ava i lab le da ta ,Hi s f i nal r e -

3


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Method ( b ) , t he ca l cu l at ional a pp r oa c h t o pa r t i a l p r e s s u r e s , r e -qui r e s two types of the rmod ynamic da ta :

(1) pure -component da ta for two l iqu ids and th ree gase sand G o ) , and(H;98' '"298 P - o r'2982 ) par t i a l mo la l da ta for b ina ry so lu tions (H298 ,-F 2 9 8 9 nd ) .PThis type of app roach was f i r s t used by Abe14 in 1946, b ase d in par t

on work by Sodens te in and Ka tayama5 who had me as ur ed KEq. ( 1 ) at 300 to 50 0C with 85 to 100 TOWaxid.

f o rT h e c a l o r i m e t r i cP

da ta ava ilab le a t tha t t ime w ere incomple te , n e c es s it a ti n g c r o s s - c o r -r e la ti o ns f r o m v a ri o u s s o u r c e s i n o r d e r t o d e t e r m i n e p a r t i a l m o l a lquant it i es . Mo re imp or tan t , va lues of CH2S04(g) we re not ava ilab le , , This l ack ne cess i t a ted the u se of Kf o r Eq. (1) in the ca lcu la tion of p which in tu r n requ i red anextrapola t ion of Bodenste in and Katayama ' s h i gh - t e m pe r a t u r e e qu i -

and So fo r0p 2 H2989 298P

H2S04l i b r i um m e a s u r e m e n t s dow n t o 25 O C.

Since 1946, addi t iona l da ta have bec om e avai lable which ma kethe ca lcu la tion of pa r t i a l p r e s su res v ia me thod (b ) c ons i de r a b l y m or ere l i ab le . Ex t rem e ly comple te t ab le s of pa r t i a l mola l quant it i e s a t2 5 " C , t e s t e d fo r inte rna l cons is tency, have been publ ished by Giauque6e t a l . who g ive f r ee ene rg i e s , en tha lp ie s , en t rop ie s , and hea t ca .pac i t i e s a t 109 d i f fe ren t su l fur ic ac id concent ra t ions f ro m 8 .93 t o~ O O T O W , In addit ion , Giguere ' ha s obtained Co S o , (F o - Hg) /T , and(Ho - El ) /T for H2S04(g) f rom spec t roscop ic data. , The la te r da ta ,when coupled with Bodenste in and Katayama 's K da ta , p rovide ath i rd- law Hodependence of K

0 PP0

Pl o rP

H2SQ4(g) and an equat ion giving the te mp er a t ur e298 f r o m 25 to SOOC ,B a s e d upon t he s e ne w da t a , t h i s pa pe r p r e s e n t s a m e thod f o r

c a l cu l a ti ng t he pa r t i a l p r e s s u r e s o f H 20 , HZSO4? and SO3of t emp era tur e and ac id concent ra t ion ,

a s funct ionsP a r t i a l m o l a l h e a t- c ap a c it y

va lues have had to be e s t im a ted by smooth ing techniques , S O t ha t s om ei na c c u r a c y s t i l l r e m a i ns ,mad e for nonidea l -gas beh avior , and 10 000 m m is viewed a s the uppe rl i m i t of appl icabi l i ty of t he r e s u l t s .

Because of th i s , no cor re c t io n has been


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11.. DERIVATION O F EQUATIONSA, P a r t i a l - P r e s s u r e E u ua ti on

F o r any component in a mul t i componen t mix tu re a t equ i l ib r ium,the pa r t i a l mo la l f r e e ene rgy of the vapor i s equa l t o the pa r t i a l mo la lf r e e e n e r g y of the l iquid:

qgg) = F(P) (2)If t h e p r e s s u r e i s low enough so t h a t t h e v a p o r a c t s as a per f ec t gas ,

Equat ion (3b) olds at any t empera tu re and compos i t ion . T h ep a r t i a l p r e s s u r e u n d e r c o ns i d e ra t i on is given by the sum of two t e r m s :a p u r e - c o m p o n e n t t e r m , -AF"JR 'L a function of. t e m p e r a t u r e o n ly ; a n da n a c ti v it y t e r m y In a , a function oi both t e m p e r a t u r e a n d c o m p o s it i o n.In o r d e r t o e v a lu a te t h e p r e s s u r e y e a c h t e r m m u s t b e r e l a t e d t o i tss t a n d a r d - s t a t e v a lu e .

The pure -componen t t e r m is eva lua ted as foPPows :d - AH"~ - -ZT -7-

T h i s i n t e g r a t e s t o give

-- -- 111-1--> Any coeff icient 0 1 abr ;cr ip t shown a s 298 i s a c t u a l l y c o m p u te d a s298-15' K (25' C) .


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The ac tiv i ty t e r m i s eva lua ted in a. s i m i l a r m a n n e r :

w he r e

- FoRT 'n a =

[T I T-R298 (&8-$) -4J s{[98298298

Combining Eqs. (3b) , (5), and , ( 7 ) , we obtain

G2 = '298 - aH:98R Y

The evalua t ion of G ( T ) m a y be m a d e by us ing he a t - c a pa c i ty3func tions in a for m g iven in the l i t e r a tu re . Fo r the gas , we have

(9 )0 2Cp(g) - a -t b T 3- c Tand f o r the liquid

(10)= (e -t a ( T - 298)P p 298

This gives , upon combining G 9 G2' and G3( T):+ C + D T + E T ' , (11)+ T298In p = A h -T

1w he r e A = - ( - a - t c , 298 - 29 8 a)


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B =- (-AH;98 -f 2 9 8 aR1 2C = - (AS:98 - a - 298 b - 298- $- 'p, 298 + L ( F - F 0 ) 2 9 8 - r 2 g 8 1 A)1E = T R c

F o r t h e s u l f u ri c a c i d s y s t e m , p a r t i a l m o la l q u a n ti t ie s a r e a v a i l -ab le fo r H 20 and fo r H2S04" Equation ( I l l ) w as t h e r e f o r e u s e d t o

and p , and the pa r t i a l p r es su re of SO3 w asH2 H2S04ca lcu la t e pca lcu la t ed f rom

p s o j K p 'H2S04 / p H 2 0 "3. Dis soc iat ion Constan t of H,S04(g)

The equi l ibr ium consta nt for the d issocia t ion of H2S04(g) , Kp.m a y be d e t e r m i n e d a s a funct ion of te mp er atu re , a s fol lows.

The equi l ibr ium or Eq. (1 ) i s given by

The t empera tu re dependence of Ka s a funct ion of temperature :

i s obta ined by exp res s in g AF71)P

dd T-14a)

T h e s t a n d a r d f r e e - e n e r g y c h a r g e for t h e r e a c t i o n i s t h e r e f o r e g iv e nby


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and the equi l ib r ium cons tan t by

Hea t -capac i ty d a ta ava i lab le in the l i t e r a tu re g ive the fo l lowingfunct ion for ACOP(1)

ACo = a ' t b ' T t . IT2 t d ' T - ' aP(1)Use of th i s to eva lua te the hea t -capac i ty in t egr a l in Eqo ( 1 6) r e s u l t s i nthe fol lowing equat ion for K :P 2 2t L/T t M t N T t QTn K = J ln (298/T) -t K/TP.whe e

J = - a ' / R ,K = d q / 2 R ,

N = b ' / Z R ,Q = cg/6R


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111, THERMODYNAMIC DATAA, Pure -Componen t P ro pe r t i e s

The pure -componen t da ta r equ i r ed in Eqs. (11) and (18) a r el i s t e d i n T a b l e I,

Hz98 fo r H2S04(g )The value of Ho l i s t ed in Tab le I fo r H2S04(g) was ca l cu -29$la te d a s fo l lows: Kel ley has tabula ted values of (Ho-Hz98) and

( S o - S ; 9 8 ) a t 100C in t e r va l s fo r HZO(g) and S03(g ) .used to ca l cu la t e the f r ee - ener gy func t ion :

T h e s e w e r e

Gigusre s t ab le s7 of (FO -H i ) /T and (Ho-Hi ) /T fo r H2S04(g)w e r e a l s o c o n v e rt e d t o th e s a m e f o r m :

HO - H0 298.15 ( ) ( 2 0 )F O - H " ~ ~ F -HoI 298I TThi s p rocedure gave the fo l lowing r esu l t s :

500 44 ,03 74-32 62 ,73600 46,72 7 6 1 ~ 2 . 2 63 ,93700 47,4L 78.17 65,19800 48 , P O 80-11 66,46

0 0These va lues a l low the calcula t ion of A ( F - H z 9 & ) / T f o r th ed i ssoc ia t ion o f HzS04 (g ) , Eq. ( I ) .and Ka tayama ' sment of AF O (1 ) J T , s i n c e

In addi t ion , ea ch of Sode nste inK d e t er m i n at i on s 5 r e p r e s e n t s a n i n di vi du al m e a s u r e -P


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Table I. Values of the rmody namic prop e r t i e s a t 298.15 OK.

Component Refe rencero pe r ty S ta te Va lue Unit s~ ~

s03 H0 g .-94.45 kca l /mole (8 )SO g 61,24 ca l /m ole-d eg (8 )

(9 )a l / m o l e -de gd=-3.22X105 ca l-deg/mole

co(a' g aZ13.90P b=6. 10X10-3 cal /m ole -de g"

H2 Elo Qgso 1

V apo r izat ion AHOASoH2S04 H0

S Ogoca:

P g

Vaporiza t ion AHOAS0Dissoc ia t ion AHo( l )AS0( 1)

1)

-68 .32 kca l /mole (8)- 57.80 kc a l / m o l e (8)16.72 ca l /mole-deg (8)45.11 ca l /mole -deg (8)a = 7.30 cal/mole-deg ( 9 )b = 2 46 x l 0 - cal/mole - de g10.52 kca l /mole28.39 ca l /mole -de g

-193 .91 kca l /mole (8)-175 .01 kca l / mole See text37.50 ca l /m ole-d eg (6)71 .93 ca l /mole -de g (7)

a = 7,86 ca l /mole -deg See textb = 4 6 ~ 5 x 1 0 ' ~ a l / m o l e - de gZc = - 2 . 6 1 2 X 1 0 - ~ c a l / m o l e - d e g ~18.90 kca l /mole F ro m Ho(R, g)34. 43 c a l / m o l e - de g F r o m S o ( Q ,g)22 ,76 kca l /m s le See t ex t34.42 ca l /m ole -d eg See texta = 13.34 ca l /m ole -d eg See t ex tb=-37.59X10- ca l/m ol e- deg 2c = 2,612k10-5 ca l /m ole-d eg3d= - 3.22X105 ca l -de g/m ole

2= a t b T -t c T I- dT-'P

----


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B y u s e o f E q , (22BU herefore, a value 0 f [AHo ]( I ' 298 f o rEq, ( 1 ) can be ca l cu la t ed f ro m each K da ta po in t :PI F-H298[ 298 T -*( ) I *Then Ho

Hi98 v a l u e s a r e k no wn EOP both H O(g ) and SO,(g).

p a r t i a l p r e s s u r e s , a nd p r e se n t e d t h e i r r e s u l ts a s lo g K v s t e m p e r -a t u r e . T a b l e II l i s t s va lues of AF" / T c a l cu l a te d f r o m t h e i r d a t a ,by use of t he conver s ion r e l a t ion

fo r H2S04(g) can be ca l cu la t ed f ro m [ AHo ]298 ( l ' 298

2Bodens te in and Ka tayama me as ure d concen t r a t ions r a t he r than

, s i n c e

C( 1 )

AF O / T = - R In K61) P= - 2,303 R log(K R T )CApplication of Eq. (22) a t eac h of t hes e da ta po int s gave an

a v e r a g e v a l ue of 2 2 7 6 0 ca l /me le f o r [AH'deviat ion was 285 call /mole,

] ; t h e s a m p l e s t a n d a r d298As shown in T able I , t h i s p r o c e d u r e= - 57.80 - 94,45 - 2 2 , 7 6= - 1 1 5 . O E kcal /mole .

H;98

The Go equation S0r H,SO,(g) l i s ted i n Tab le I w a s s e l e c t e d0 7data g iven in tabu lar f0rm by Gigukre.P

Pa s a n e m p i r i c a l f it t o theT h e m a t c h t O the data o v e r t he r eg ion of i n t e r e s t i s shown below:

C

C" P e f , 7 C'? Table IP__1__PY("Kb2 9 8 " I 5308400500600700

a9,2919.3522,19t4,4026 ,082 ? , 3 6

19.2919,3922-1424,4026"1427.36


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Table 11. Bodens te in and Ka tayama equi l ib r iu m da ta fo r~ ~ S 0 ~ ( g )HZOtg) -t S03( g ) .a

1 7417 256 8 2653621

2 646660664693708731756

3 613627639652693729660643

-3.75-3.27-1.01

0-362,09

1.170.300 , o o

-1.12- 2,22-3.35-4.24

2.601.520.990-31- 1.85

-3.68-0.32

0.68

4 5986 2263566870 1717682596

5 610635653655680707710747

3.341.980.99

-0.68- 2.47-3.32-1.85

3.13

2.871.060.200.09

-1.09-2.37- 2.48-4.47

6 6336536887117507116576 29

7 611629647660689714689658637

0.850.75

-0.66- 1 - 7 8-3.12-1.78

0.701.98

3.242.081.120.54

- 1.03- 1.88-1.03

0.501.55

a R e f e r e nc e 5.


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The va lues of Cower e ca lcu la ted Prom spec t roscopic da ta,

S o , and fr ee -e ne rg y functions given by Gigu'ereP * Because of an unce r ta in tyin account ing f s r the to r s iona l osci l l a t ions of the su l fur ic ac id OHgr oups , p r ope r t i e s w e r e t abu la te d i n r e f e r e nc e 7 both with and with-out the to r s ion a l mode inc luded,c lude the contribut ion of the tor s io nal osc i l la t io ns ; this gives a prob-ab le unceIrta.iinty i n th e H2S04(g) functions of 0 , 2 5 ca l /mole -deg .

We have used th e va lu es which in-

3 , Constants in Equat ionsIt i s de s i r a b l e for ca lcu la t iona l purposes to sepa ra te ou t the

pu r e -c om ponen t t e r m s i n Eq, ( I l ) , s in c e t he y a r e cons tan t for allac id composi t ions .Table I, th e following equation i s obta ined for ca lcula t ing p

U pon e va lua ti ng t he s e t e r m s f r o m t he da t a i nandH2pHzS04'

w he r e

E = cons tan t ,H SO4 va lue2T e r m U ni ts H 2 0 v a lu e-

A Q D i m e ns i on l e s s -3.67340 - 3,95519S fCU Damensisnle s s 10,24353 7.03845l l B 8 ("K) - 0,618943xlo- 3 1 ~ 6 14 6 X l ~ 1 - ~E ("K) - 0 - 2. 19062X10-6

K -4143,s -7 74 1 3 , 3

The cans tan t s i n the K equat ion, Eq. (481,m a y be e va lua t edPi m m e d i a t e l y , s i nc e t he y a r e a ll pure -component t e rm s , Upon sub-sti tution of the data i n Table I , we obtain the following K equa t ionF


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- 12-fo r the calculation of ps03 2In KP = J ln(298/T) t K/T t L/T t M t NT t QT2, (25)w he r e J - - 6.71464,

K = - 8.10161X104,L = ~ 9643.04,M 2 14.74965,N = - 9 . 4 5 7 7 Y ~ o - ~ ,Q = 2.19062XO- 6

The fi t of th i s equa t ion to Bodenste in and Ka tayam a ' s da t a i s shownin Fig. 1 , The constants shown fo r Eqs , (24) and (25 ) g iv e p r e s s u r e sin un i t s of a tmo sph e re s ; for r e su l t s in mm Hg, In 760 i s added to C'and to M.w a s us e d w he r e ve r 298 i s indica ted in Eqs . (11) and (18) ,

A value of 1 .98726 ca l /mole-deg was used fo r R , and 298.15

B. Part ia l Mola l Prope r t i e sT he pa r t i a l m o l a l p r ope r t i e s r e qu i r e d i n Eq. (24) for the ca l -

a r e l i s t ed i n T a b l e 111. T he s e va l uesH 2 0 and H2S04culat ion of p L0a r e f r o m t h e d a ta of Giauque et a l . , who have c a r r i ed out an ex ten-s i ve r e s e a r c h on t he t he r m odyna m i c p r ope r t i e s of aqueous su l fur icac id .da ta and g ives t ab le s of pa r t i a l m o l a l p r op e r t i e s ; t he va l ue s in Table 111

Refe rence 6 rep rese nts the f ina l cor re la . t ion of the ava i lab le

w e r e i n t er po la t ed d i r e c t l y f r o m t he s e r e s u l t s .R e f e r r i ng to Table 111, w e s e e t ha t da t a a r e l a c ki ng f o r a be-

low 250/0w and for the partial mo1a.l heat capacity of w a t e r i n a nhydrousac id . Es t im a ted va lues of these va r iab le s a r e g iven in Sec . I V , fo l -lowing evaluation cuf the bulk of the data,


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- 1 3 -

3.1

ICTIEE 3.Cv

QY

I. 7.3 I.4 1.51 0 ~ 1 ~O K )

1.6

M U - 3 1 4 4 1

Fig. 1. T h e f i t o f Eq. (25) t o Bodenstein and Katayama's data.


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T a b l e 111. P a r t i a l m o l a l q u a n ti t i e s f o r s u l f u r i c a c i d at 298.15 " K ( f r om G iauque" ) .

H2S04( % w ) % m

10 2.0020 4.3925 5.7730 7.3035 9.0040 10.9145 13.0650 15.5255 18.3360 21.6065 24.4470 30.0072 32.0874 34.3376 36.7878 39.4480 42.3582 45 . 5684 49.0986 53.0188 57.3990 62.3191 65.009 2 67.879 3 70.9394 74.219 5 77.7396 81.5197 85.5998 90.00

98.48 92.2599 94.7999.5 97.3499.8 98.9299.9 99.46100 100

W a t e r S u l fu r ic ac i d

- 26.44- 75.10- 114.9- 168.8- 241.4- 338.2- 462.2- 620.6- 821.5-1075.3-1406.3- 1836-2038- 22 6 1-2508-2783-3090-3427-3789-4167-4557-4960-5165-5375-5595-5830-6090-6390-6741- 7204-7521-7963-8692-9624-10342-12014

- 6.28- 34.0- 71.8- 136.0- 228.6- 349.0- 494.2- 662.9- 867.3- 1125.0-1903-2127-2382-2683-3039-3475-4015-4656

- 1459

-5319-5938-6419-6627-6816-6983-7139-7286-7433-7574-7712-7777-7845-7919-8337-9355-16125

17.87117.77517.78018.114 0.018618.555 0.017818.662 0 .016518.518 0.024917.731 0.023216.963 0.015316.335 0.011615.173 0.000613.398 -0.020712.570 -0.029611.762 -0.035810.33 -0.01829.77 0.011410.36 0.056813.78 0.123318.96 0.066622.76 -0.0346

11.01 -0.0330

22.13 -0.012022.30 -0.039821.48 -0.042720.44 -0.043619.32 -0.042818.06 -0.040516.64 -0.036815.05 -0.031413.25 -0.02412.25 -0.01911.03 -0.0147.0 -0.008- 4.1 -0.003-15.3 -0.0010

- 15624-14115-13373- 12600-11782- 10906- 9 9 9 5-9045-8054-7G36-5962-4838-4387-3940-3492-3046-2600-2170- 1766- 1086-816-592.8-495.2-323.5-248.4

- 1404-699

-408.5

- 178.3-114.3- 85.3- 54.6- 26.00- 9.32- 3.500

- 17078-16279- 15580-14659-13618- 12527-1 1457- 10445-9437-8405-7320-6158-5664-5144-4601-4025-3394-2705-1994- 1354-851-524-405-309-235.4-176.3- 129.6- 92.1- 64.5- 44.6- 38.9- 33.8- 30.6- 24.2- 16.70

22.1825.6525.7020.9715.9314.9015.9220.6224.4426.9530.6935.3437.1738.8040.1741.2742.0841.3737.5732.6529.9929.5429.8130.2230.6731.1031.5031.8632.1732.4332.5232.6132.7632.9533.0433.20

-0.0 26 8-0.0 156-0.0041-0.0633-0.0557-0 . O 159-0.001 10.03400.08950.10950.12200.11710.09350.0509-0.0069-0.0830-0.02700.03610.05110.05410.05570.05620.05580.05510.05430.05310.05200.05160.05140.05090.05090.05090.0509

~ ~a R e f e r e n c e 6 .


18/85

IVY CALCULATION O F PARTIAL PRESSURESIn the ca lcula t ion of par t ia l pr es su re s f ro m the equat ions pr e-

sented in Sec . 11, one depends upon room-t em pera ture heat -capaci tymea sure men t s on the so lu t ions to p r ed ic t t he i r h igh - t empera tu rep r o p e r t i e s ,la t ion of the data wi ll not genera te s igni ficant e r r o r s .cas e , i t has been r ea l i zed tha t t he the rmodynamic p ro per t i e s co l l ect edin Sec . I11 might not give a per fect a pr i or i ca lcula t ion of par t ia lp r es su re s . I n it ia l ca l cu la t ions t ended to be a r th i s ou t. Resu l t s t ot e m p e r a t u r e s n ea r 200 "C w e r e s a t i s f a c t o r y , b ut at h i g h e r t e m p e r a t u r e st h e ca l cu l at e d p a rt i a l p r e s s u r e s b e c am e p r o g r e s s i v e l y m o r e e r r a t i c .

Inherent in the method i s the assumpt ion that the ext ra po-In the p resen t

--

To co r r ec t the obse rved incons i s t enc ies , it was dec ided to ad -j u s t a , t he t emp era t u re coe ff i ci ent of t he pa r t i a l mo la l hea t capac i ty ,The choice of a a s a c o r r e c t i o n t e r m was somewhat a rb i t r a ry . Inp r inc ip le , e i the r a could be changed, o r addi tional nonl inear te r m scould be added to Eq. (10 ) to d esc r ibe ass ume d hea t - capac ity - tem-pera tu re behav ior , E i the r cho ice howeverg r equ i r es the assumpt ionsimpl i c i t i n smoo th ing the ca l cu la ted r esu l t s ; a f t e r som e cons ide ra t ion ,i t was dec ided to ad jus t a , In a f ew ca se s , minor ad jus tmen t of o the rfunc t ions was a l so neces sa ry .

The effect of a upon pa r t i a l p r es su re can be g iven by a s i m p l i -f ied rea r ra ng em en t of Eq. ( I 1 ) :

log P log(P)a=o - Pa P ( 2 6 )where the f ac to r p i s shown in F ig . 2 a s a function of t e m p e r a t u r e ,Most of the-2 0 and + 2 5 " C ; a s m a l l number wer e based upon da ta up to 8 0 C .Above 2 0 0 " C , where F i g " 2 i nd ica t es tha t a becomes a s igni f icantv a r i a b l e i n th e p a r t i a l - p r e s s u r e e q ua ti on ( E q (24) ), t h e r e p o r t e dvalues of a wil l be see n to be inadequate , By de te rmin ing a su i t ab lea v e r a g e a fo r t he r ange o f 2 5 t o 400C, one can signif icantly a l te rh igh- t em pera tu re pa r t i a l p r es su re s withou t af f ec t ing the a l r eady sa t -i s f ac to ry low- t empe r a t u r e v a l u e s

a values of Tab le 111 were o r ig ina l ly de te rmined be tween


19/85

As explained below, a was adjus ted so t ha t p a r t ia l p r e s s u r e si n the 200 to 4 0 0 C range were cons i s ten t w i th the low- tempera tureres ul ts and with the sulf ur ic ac id azeot rope and boi l ing-point da ta .Cross -p lo t s of log p v s Tow, T o r n , and 1/T w e r e us e d a s gu i de s du r ingt h e calculation.coefficient plots and examined f0 r consis tency by us ing the Gibbs-Duhem equation.

Smoothed pa r t i a l p re s su res were checked on ac t iv i ty-

A, Tr ia l Ca lcu la t ionsand p , c a l -H O H2S04F i g u r e s 3 and 4 show t r ia l values of pcula ted from Eq, (24) and pa r t i a l molal data. l i s te d i n T a b l e 111. The

double se ts of c u r ve s at 200C and above indica te res ul ts obta ined byus ing (a ) a as given in Table 111 (dashed cur ves ) , and (b) a *- 0( so l id curve s ) . Be low 2 O O 0 C , re s u l t s ob ta ined by us ing a e i t h e r asin (a ) o r (b) wer e prac t ica l ly equiva len t , It i s not ne c e s s a r y t ha t t hepa r t i a l - p r e s s u r e c u r ve s be s m oo t hs but it is e s s e n t ia l t h a t t h e i r r i s ebe monotonic ; however , i t appears s ignif icant tha t the curves at l ow e rt e m p e r a t u r e s a r e i nde ed r e l a t ive l y s m oo t h,of a l i s t ed in Table 111, It c a n be s e e n t hat t he e r r a t i c a re a s i n t he

Figure 5 shows the va lues

ca lcu la ted pa r t i a l p re s s ur es cor re spon d to th.e "peaks I t and "va l leysin the a curv es , Fo r example , fo llowing the dashed 400C cur ve inFig. 4 , the high va lue of p a t 47 O /OW , d e c re a si n g p r e s s u r e st h r o u g h 7 4 7 ' 0 ~ ~nd ex t rem e ly h igh va lue of prespec t ive re su l t s o f a low a at 46.50/ow, in cr ea si ng va lue s of a t o

a t 847700~ r e t he2S04 H2S04a ma xi mu m at 74,50/0w, and an abrupt m ini mu m in a at 84,5 YOW.

T he va r i a t ions i n r oom - t e m pe r a t u r e Q va lues wi th concent ra -t ion, shown in Fig. 5 , re f lec t the d i f ferences in hea t -capac i ty behaviorof the var ious hydra ted forms of HZSOpos i tions a re no t so d i s t inc t at t e m p e r a t u r e s o v e r 100 to 200C.

Pos s i b l y t he hyd r a t e c o m -4"


20/85

- 1 7 -

P

0 100 200 300 400Temperature ("C

M U - 3 1 4 4 2

Fig . 2. V a l u e s of P = ( l / a ){l o g [ p/p(,=,) ] } f r o m 25 t o 400"'C.


21/85

- 18-

0IO

(u

Y-

hCTIEEv

Q)3u)u)Q,a

L-

L

-0.-cL0a

IO5

2

IO5

2IO2

5

2IO

5

2

I5

2lo- ' 0

'om Giauge

I

1\

50

2 O

75ta

20 40 60 80 100We i g h t - p e r c e n t H,SO,

M U - 3 1 4 4 3

Fig. 3 . Part ial p r e s s u r e of w a t e r , t r i a l c a lc u l at i ons .


22/85

-19-

lo4!

L

IO5

2IO?5

2IO25

2I5

2lo-'

400C3 0I

=Ofrom Giaugue et al,

0 20 40 60 80 I O 0Weight- percent H,SO,

MU - 3 1 4 4 4

Fig. 4. Par t i a l p re s sur e of su l fur ic ac id , t r i a l ca lcu lat ions .


23/85

-20 -

0.1f

N 0.1ccY0Q,-0W0\0u

v 0.05E-

0L

r) -0.05-0 . IC

Moles H, 0 /mole H, SO,6.5 4 3 2 II I I

0 2 0 40 60 80 100Weight- percent H SO,

M U - 3 1 4 4 5

6Fig. 5. Tem pera t ure coef f ic ien t o f pa r t i a l mola l hea tc a p a c it i e s , m e a s u r e d at 25" C , f r om Giauque e t a l.


24/85

-21 -

B, Adjustment of High- Te mp era tur e Pa r t i a l Molal Heat Capaci t iesshown in F ig. 5 w e r e a d -H2S0he values of a and aH2j u s t e d s o tha t par t ia l pr es su re s above Z&C we re consis tent with low-t e m p e r a t u r e r e s u l t s . C a lc u la ti o ns w e r e c a r r i e d o ut s o a s t o i n s u r e

agr eem ent wi th su l fur ic ac id azeot rope and boi ling-poin t data .1. Sulfuric Acid AzeotroDe

F igure 6 shows the pa r t i a l - .p r es su re behavio r at 2 5 C calcula tedf r o m Eqs , (24) and (25) with the smoothed constants eventual ly deduced]in the v ic in i ty of t he su l fu r i c ac id azeo t rope , A n a b s c i s s a s c a l e of - logL 100-(ybw)]The pap t i a l -p re ssu re behav io r shown-P H ~ Oecrea s ing r ap id ly , and p inc re as ing r ap id ly -con tinues ath i g h e r t e m p e r a t u r e s a nd p r e s s u r e s . T h e c o n c en t ra t io n at which thea z e o tr o p e o c c u r s , h o w ev e r, d e c r e a s e s a s th e p r e s s u r e i n c r e a s e s . T h isw a s shown by K unzler , l o who obtained the fol lowing data on the concen-t ra t io n of constant -boil ing su l fu r ic ac id at v a ri o u s p r e s s u r e s :

i s used in Fig . 6 in ordeT to expand the a zeot rope region .n e a r l y c o n s t a n t ,pH2S04

s03

P (mm Hg) HZSOq (Tow) p Bmm Hg) HZS04 (TOW)100 98,790 700 98 4 9520 0 98,704 750 98,482300 98,645 800 98,469400 98,597 850 98,457500 98.557 900 98,446600 98524 950 98.4366 50 98 ,509 IO00 98 ,426-

In terpola t ion of Kunzler s da ta g ives an a zeo t rope concen t r a t ion of98,479 OW a t 7 6 0 rnrn Hg, which was adopted f o r t he p resen t s tudy .

Abel4 su rveyed t h e ava i lab le data on t h e t e m p e r a t u r e a n dc o n c e n t r a ti o n f o r t h e a t m o s p h e r i c - p r e s s u r e a z e o t r o p e ; t h e r e s u l t s ofv a r i o u s e x p e r i m e n te r s a r e a s fol lows :


25/85

e0IEE

IO -:C

L

10-:

2

IO-C

2

10-5

I d 4 ~ i

-22 -

L- 70 80 90 95 98 99 99.5 99.8 !Weight- percent H,S04 9M U - 3 1 4 4 6

Fig. 6. T he su l fu r ic ac id azeot rope at 2 5 C .


26/85

-23-

326 98.39 338 98.5330 98.33 338 98.5338 98.3 3 17 98- 54

331.7 - _ _ -In the pre se nt ca lcu la t ions , it w a s de c ide d t o ba s e h i gh - t e m pe r a t u r ep a r t i a l p r e s s u r e s o n a t e m p e r a t u r e of 326 C fo r the 1 ,O-a tm azeot rope ,a s wa.s done by Abel. 4' l 1 Although th i s t empera ture i s r a t e d a s t h em os t p r oba b l e va l ue , it i s subjec t to an unce r ta in ty of at l ea s t *5"C,

At an azeot rope the compo s i t ion of the l iqu id is e qua l t o t h ecompos i t ion of the vap or ( e , g. , i n m o l e - % un i t s ) . R e f e r r i ng t o w a sthe we ight - f rac tion of su l fu r ic ac id at t he a z e o t r ope , a nd us i ng t hes u b s c r i p t s 1 , 2, and 3 to indica tewe obtain

H 2 0 , H2S04, and SO3, r e sp ec t iv e ly ,

I p2 + p3-8 . 0 1 6 ~98.082 - 8 0 . 0 6 6 ~ ( P , - P ~ ) I- ~ 2 + ~ 3Fo r t he 1 . 0 - a t m a z e o t r ope , we t he r e f o r e ob t ai n

p2sp30.92246 =-p1 P2At th i s azeot rope we a l so have760 = p1+p2+p3 ,K = P1 P3/P, 0P

Since the va lue of K at 3 2 6 C c a n b e d e t e r m i n e d f r o mPEq. ( 2 5 ) , t h e p a rt i a l p r e s s u r e s at t h e a z e o t r o p e c a n b e d e t e r m i n e d b ycombining E q s . (28) , (29) , and (30) , E l imina t ing p2 and p3 , andus ing S = 0.92246, we obta in

( p , ) 2 + p l [ K p ( l + S ) - 7 6 0 ( 1 - S ) ] - 760K = 0 ,P


27/85

-24 -

Following evaluat ion of p f ro m Eq. (31) , p can be dete rmin ed bycombining Eqs , (29) and (30) with the el imin atio n of p3:1 2760-p ,-

p 2 - ,1+Kp/P1)The a va lues r equ i r ed to g ive the co r r ec t azeo t rope p andcan then be ca lcula ted f ro m Eq. (24) , 1p2

lowing r esu l t s fo r the su l fu r i c ac id azeo t rope :Th i s p ro cedu re gave the fo l-

In w t cond i tions Resu l t s.1 m m , a = 0.0160,1-= 326"C, KP = 130.2 mm p1 - 233P= 760 mm

TOW=98.48p2 = 338.1 m m , a 2 = 0.1249,p3 = 188.8 mm.

2, Adjus tment of Alpha, 10 to 98.5 OWF i g u r e 7 shows the values of a ca lcu la t ed in th i s paper . The

method of ca lcula t io n used was suggeste d by the prop er t y of a m e n -t ioned in Sec. IV : a change in a s t rong ly a f f ec t s h igh - t empera tu repar t i a l p r e ss u r es without a l t e r ing low- tem pera tu re va lues .c e d u r e u s e d w a s a s f o l lo w s :

The p ro -

(a) P a r t i a l p r e s s u r e s f r o m 25 t o 4 0 0 C w e r e c a lc u -l a t ed a t t em pera tu re in t e rv a l s of 25"C, with a = 0 a t all weigh t -pe r -cen t s .

(b) Sta r t ing a t 25"C, p r es su re s w ere p lot ted on log p -At each 25" C i n t e r -s - concen t r a t ion and log p -v s - l / T coord ina tes .

v a l , p r e s s u r e s at a = 0 w e r e c he ck e d a g ai n s t p r e s s u r e s c a lc u la t edf r o m Eq. (26) , by using a equa l t o the azeo t rope va lue. Up to150C the re was no apprec iab le d i f f e r ence .

(c ) At 150C the d i f fe r ence between the p r es su re s ca l -culated with a = 0 and a equal to the azeo t rope value was not iceable .The ef fec t was a para l l e l ( downward) sh i ft of t he p r es su re cu rve ; noi r r e g u l a r i t i e s w e r e v i s ib l e , At s u bs e q ue n t 2 5 C i n t e r v a l s , p r e s s u r e sw e r e c a l cu l a te d f r o m Eq. (26 ) by us ing the app ropr i a t e p and with aequa l t o the azeo t rope va lue,

(d) By 2 0 0" C , i r r e g u l a r i t i e s o c c u r r e d i n t he p r e s s u r ecurv es a t ac id concen t ra t ions wherem u m ,

a r e a c h e s a m a x i m um o r a mini -Refe r r ing to F ig . 7 , t h e s e v a l u es w e r e 90, 8 2 , and 4ODJow f o r


28/85

both H 2 0 and H2S04r,a req ui r ed to g ive the sm oothed px-essure was ca lcula ted f r om Eq. (26).T h e s e n e w a va lues w ere then used fo r the next t emp era tu re in t e rva l .

( e ) The p rocedure of r a i s ing the t em per a tu re by 25Cand easing the a f rom the previous s t ep to p r e d i c t p r e s s u r e s at tha tt empera tu re was con t inued ,c o o r d i n at e s y s t e m s w e r e v ie w ed a s a whole, and any d i sc r e panc iesco r r ec t ed . At t emp era tu re s over 200C the ne t e f fec t on a w a s t ofi l l i n the po r tions be tween the m ax i ma and min im a in theF ig . '7,

I r r egu l a r i t i e s were smoothed v i sua l ly and the

At 400C the pre ssu ye cur ves on the two

a c u r v e s ,

H, 0The above proce dure was fol lowed for ca lcula t ing both aa n d a Fo r eas e of in terpola t ion , p was smoothed onLH2S04 H2weight -perc ent coordin ates , and pHzSo4 on mole -perce nt coo rdina tes .

F i g u r e 8 shows the heat capa.ci ty sf su l fu r i c ac id a t 25"C, a st abu la t ed in r e f e r ence 6 ; t he p a r t i a l m o l a l h e a t c a p a c i t ie s a r e d e r i v e df r o m t h e s lo pe of t h i s cu rve , The a va lues shown in Fig. 7 indicatetha t at 400 C the wave between 15 and 45 Tow becomes m or e p ronounced ,whi le th e '%u mpY ' e tween 75 and 90 TOW s s l ight ly broadened.

In the reg ion between the aze ot rop e and 10070a c i d a check ofthe ac t iv i ty coef f ic ients showed t h a t a adjustments a lone would notg ive cons i s t en t r e su l t s over the comple te t em per a tu re r ange . Th i sw a s e s p e c i a ll y t r u e i n th e c a s e of pin the h igh-weigh t -pe rcen t r eg ion , Fu r th e rm or e , t he su l fu r ic ac i dh e a t - c ap a c i t y d a t a l i s t e d in r e f e r e n c e 6 show a c u s p at 10070HZSO4'mak ing the pa r t i a l mo la l hea t capac i ty of wate r inde te rmina te at thatpoint,be tween 96 and 102 Tow.Giauque which Ciauque s smoothed va lues (dashed cu r ve ) dv notfolllow ve ry c losely , The so l id cuyve coincides wi th the data l i s tedi n r e f e r e n c e 6 below 98-5Tow a nd n e a r 101 TOW.

which changes ve ry l i t t leH2S04

Figure 9 s h o w s the poption of the hea t - capac i ty cu rve (F ig . , 8)l 2 6

The da ta poin ts a r e those of Kunzler and

Resu l t s be tween theseweigh t -pe rcen t s were ca l cu la ted as fo' l ows .

0F o r s u l f u r i c a ci d , values oi ( F - F were ad jus t ed a t 99 , 99.5,99.8, and 9 9 . 9 7 0 ~ o that p gave Raoult -Law behavior a t 25 CH 2 0 4


29/85

- 2 6 -

i

0.2 50 .2 c

0.15NcY

CTQ, 0.IC'301-E" 0.05..0u-

0U- 0.05- 0. C I I I I

M U - 3 1 4 4 7

Fig. 7. Average tempera ture coe f f ic ien t of pa r t i a l m o l a lhea t capac i t i e s , be tween 25 and 400 C.


30/85

- 2 7 -

I.o

ED 0.6-VY

Q0

0.4

Moles H,O/mole H, SO,6.5 4 3 2 I 0

0 2 0 40 60 80 IO0Weight - percent H,SO,

MU - 3 1 4 4 8

Fig . 8. The hea t capac i ty of aqueous su l fur ic ac id at 2 5 C .


31/85

-28 -

96 97 98 99 100 IO IWeight pe rcen t H SO4

MU - 3 1 4 4 9

Fig. 9. The heat capac i ty o f aqueous sulfur ic ac id n e a r 1005;H2S04.


32/85

(bas ed on two ions f orm ed per molecule of H 2 S 0by Young and Walraf en. 13 ) Then e,cons i s ten t p

added , a s ind ica tedand a were ad jus ted to g ive

a t t he s a m e t i m e ,and a a t ?OO # we re var ie d to give smoo th ac t ivi ty-coeff ic ient be-

4P'behavior a t h igh tem per a tu re s ;H SO

Pha v i o r be tw e en 98.5 a nd 1 0 0 7 0 ~ .gave a h eat capa city at 10070, along with the 10070 in ter ce pt s of the

Refe r r ing to F ig. 9, t h i s p r oc e dur e

s lop es of the hea t-capaci ty curve taken at 9 9 , 99.5, 99.8, and 9 9 . 9 7 0 ~ -between 98,5 and 1000/0w we re then calcu lated

by a ssu min g va r ious %eat -capac ity curves th rough th i s r eg ion . Pa r t i a lmol a l heat capac i t i e s w ere ca lcu la ted f ro m the 10070 n t e r c e p t s de -te r rnined above , and the ass um ed hea t capac i ty; then p wasca lcu la ted by a s sum ing va lues of a . New heat-capaci ty cur ves and

were obta inedlphas we re a s sum ed unt il cons i s ten t va lues of pat 99, 99.5, 99.8, and 9 9 . 9 7 0 ~ . The hea t -capaci ty curv e was chosens o tha t these pr e s su re s2 when ex t rapola ted , gave an acceptab le bo il ingpoint at 10070 aci d, Then and a for HzO we re f i t ted to the r e -s u l ti ng 100% p r e s s u r e s .

H Oalu es of p

H2

H2

PThis pr oced ure re su l ted in the hea t-capac i ty curve shown in

Fig. 9 for the 98.5- to 99.9-70w region and fo r the int e rcep t and s lop eat 10070, The calcula ted valu e of (c for 10070 was la rg e andpos i t ive , ind ica t ing tha t the peak in the hea t -capac i ty curv e occu rsbelow 100%.100 to 101 TOW w e r e d r a w n by a s s um i ng a Gauss ian- type va r ia t ionaro un d t he 10070 value.

P 54The por t ion s of the c urv e be tween 99 .9 to 100 70w and

The va lues of the pa r t i a l mola l p r ope r t i e s for the 98-5- t o100-TOW egion a r e shown i n Table IV, below, The lOO($o values givea n anhydrous-ac id boi l ing point of 2 7 2 "C , within the 27'0 to 280Cr a nge g i ven i n t he l i t e r a t u r e . 14


33/85

Fa+5

- 30 -

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3 o o o no 0 Q (3 o i5 (3o u o o o Q CJ o o 3 o 3 a o o o o o o o o o

0mI-Or-Ir l

00.P-N9I

.r l

0a0mmr lI

. *clrm9JIr l

' 0n,9

I

.dmd

0PNmN

1

.4

0P-ln*4r lI

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-31-

C. Resu l t sTab le IV l i s t s t h e th e r m o d y n a m ic p r o p e r t i e s u s e d i n t h e c a l -

culat ion of pthose given in '$able 111, exce$ fo r the new va lues of a (F ig . 7 ) a n dt .ie othcr changes indicated above fo r th e 99-to 100-TOW egi on. Par t ia l, i-' .j:~u.rescalculated f rom E q s . (24) and ( 2 5 ) , a n d th e d a t a i n T a b l e I V ,d r c s ~ ~ ) w i ~n F i g s . 10, 11, and 12. Comple te t ab l es o f pa r t i a l p r e s -s u r e s a p p e a r i n t h e A pp en di x, t o g e t he r w it h t h e F o r t r a n p r o g r a m u s e dfo r the ca l cu la t ion .

The values shown a r e i den t i ca l w i thH 0 and PH2S0 -


35/85

- 3 2 -

10

lo5

IO

to3

- 2oooc-150C--tow&--

0 20 40 60 8 0 100Weight - percent H 2 S 0 4

MU R - I998

Fig. 10. T he pa r t i a l p r e s s u r e o f H 0 o v e r aqueous s u l f u r i c a c i d .2


36/85

- 33 -

Weight .- percent H2S0,

M11R - I 9B Y


37/85

-34 -

Weight - p e r c e n t H,SO,

MUR-2000

Fig. 1 2 . The p a r t i a l p r e s s u r e of SO over aqueous su l fu r i c ac id .3


38/85

-35-

V. DISCUSSION AND CONCLUSIONST he pa r t i a l p r e s s u r e s p r e s e n t e d a bove a g r e e i n f o r m w it h t hos e4rep or t ed by Greenewal t ' and Abel.ment o ccu rs a t low tem per a tu re s and low ac id concent ra t ions w here

t he obs er va b l e vapor p r e s s u r e i s predominant ly due to p

In bot h c a s e s t he c l o s e s t a g r e e -

H 2 0At higher tempera tures Greenewal t * s t o t a l - p r e s s u r e c o r r e -Aa t ions gave s l igh t ly h ighe r pr e s su res than those repo r ted he re .

comple te compar i so n of h i s r e su l t s was not poss ib le , s ince h i s c or -r e l a t ions w e r e t e r m i na t e d a t 1 a tm.

Abel us ed a K equation and an azeot rope compos i t ion d if -Pf e r e n t f r om t hos e u s e d i n t h is w or k , His re su l t s , while no t d i rec t lyc om pa r a b l e t o t hos e p r e s en t e d he r e , s how t he s a m e t r e nd s i n va por -p r e s s u r e b eh av io r as do Figs. 10, 1 1 , and 12, At 2 5 " C , however ,h i s c a lc u l at e d p r e s s u r e s a r e no t i n a g r e e m e n t w i th the t he r m odyna m i cdata now avai lable ,

By re fe r r in g to the me thod jus t desc r ibed for ad jus t ing a ,i s the mos t ac cur a te of the ca lcu la tedt beco mes appa rent tha t p

v a p o r p r e s s u r e s .va po r - p r e s s u r e da t a t o a id i n a d j ust i ng a in the low-%w ranges withthe azeot rope da ta for ca lcu la t ing a in th e high-yow re gi on , To t e s tthe re l iab i l i ty of pGibbs-D uhem equation w%s appl ied in the fo rm sugges ted by Redl ichand E s t e r , l 5 a s s um i ng t ha t the s u l f u r i c a ci d s y s t e m acts as aH 2 0 / H 2 S 09 9 % m ywhere i t would have a negligible effect .r e su l t of th i s t e s t a t 2 0 0 C; the pos i t ive ( l e f t -hand) a re a i s 86.5 un i t sand the nega tive ( r igh t -hand) a r ea i s 87.5 uni t s , which ind ica te s tha t

T h i spH2S04unce r ta in ty app ea rs to l i e wi th in the accuracy of the pre sent ca lcu -la t ions , and has no t been fur th e r ad jus ted .

H2Fo r th i s ca lcu la tion we have the pure -component

for which we have only azeot rop e da ta , theH 2S0 '

b i na r y , T h i s a ss um pt i on a ppe a r s s a t i s f a c t o r y e xc ep t a bove4 F i g u r e 1 3 shows the

m a y b e a t r i f le high in the low-weig ht-percent region,

R e ga r d l e s s of the ca lcu lat iona l me thod used fo r a , p r e s s u r e sc a l c u l a te d a t low t e m p e r a t u r e s ( w he r ea r e a s a c cu r a te a s the ava i iab le the rmodynam ic da ta a l low,

a i s not a s i gn if i ca n t v a r i a b l e )Changes


39/85

-36 -

0 20 40 60 80 100Mole - percent H2S04

M U . 3 1 4 5 0

Fig. 13. T he r m odyna m i c - c ons i s te nc y t e s t a t 2 0 0 " C.


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3 7 -

in a p t o c o r r e c t t he h i gh - t e m pe r a tu r e p r e s s u r e s , a f fe ct e d t he r e s u l t sup to 100C by no m or e than 27'0,

The re la t ive accuracy of t he pa r t i a l p r e s s u r e s c a l cu l a te d i n di f -fe ren t t em per a tu re and compos it ion reg ions e s t ima ted qua li t at ivelyf r om the foregoing cons ide ra t ion s , i s shown in Table V.

It i s f e 1 tha t the r ea l u t il ity of the re su l t s p re sented h e r edepends not upon the i r abso lu te accura cy but r a th e r upon the i r in te rna lconsis tenc y and upon the vers a t i l i ty of the ca lcula t ional method. Whenaddi tiona l da ta become ava i lab le , pa r t i cu la r ly in the 1.O -atm a z e o t r operegion , they ma y be incorpora ted in to the gene ra l f r amework of theca lcula t ion and the e f fec t upon ca lcula ted resul ts de termined.


41/85

-38-

Table V, E s t i m a t e d m e a n unc e rt a in t y i n pa r t i a l - p r e s s u r e va l ue s ,

Tempe ra t ur e r ange 0-150C 150-300C 300-400CCompos i tion ran ge , TOW 10-80 80-100 10-80 80-100 10-80 80-100Water f 470 8 8 16 12 24Sul fur ic ac id *loyo 4 20 8 30 12 Sulfur t r ioxide * l W O 9 22 18 32 27


42/85

-39 -

ACKNOWLEDGMENTT h i s w o r k r e p o r t e d h e r e i n w a s c a r r i e d ou t at t he Lawrence

Rad iat ion Lab ora to ry under the ausp ice s of t he U. , Atomic Energ yC o m m i s s ion


43/85

-40-

NOTATIONSuper sc r ip t B

o ( lower -case p V ~ h ' f )e fe r s to va lues a t s t a ndard s t a t e-. (ov er s co re ) Refe r s to pa r t i a l mo la l quan t ity

Subscr ip tsIL R e f e r s t o H 2 02 R e f e r s t o HZS043 R e f e r s t o SO3

2 9 8O(zem) Refe r s to p roper ty a t 0 OK( 1 ) R e f e r s t o proper ty o r Eq. ( l ) , t h e d issoc ia tion of

Refe r s t o proper ty at 298.15"K

H2SO4 (gThermodynamic Funct ions

F F r e e e n e rg yH EnthalpyS Ent ropyG Heat capacitya ActivityY Activi ty coeff icient

P

P a r t i a l Molal Functions( F - F O )E Part ial mola l en thalpy

R e la t iv e p a r t i a l m o l a l f r e e e n e r g y- P a r t i a l m o l a l h e a t c a p ac i tya. Temperature coef f ic ient ofcP

P'a = d /dTP


44/85

-41-

Other Symbolsp P a r t i a l p r e s s u r eP T ot a l p r e s s u r et T e m pe r a t u r e "CT T e m pe r a t u r e , " KK Equi l ibr ium cons tan t fo r the d i s soc ia t ion of HZSO (8 )P 4R Gas con stan t, 1.98726 cal/m ole-d eg1 Refe rs to l iquid s ta t eg R e f e r s t o ga s s t a t e70w W e ight - f rac t ion 1 0T o r n Male-f rac t ion KlOO


45/85

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APPENDIXTables A- I through A-111 presen t t he de ta i led r esu l t s ca lcu lat ed

f r o m E q s , (24) and (25) and the pa r t i a l mo la l p roper t i e s l i s t ed inTable IV,

Table A-I con ta ins the low- tempera tu re r e su l t s ; i o e . , t hoseresu l t s unaf f ec t ed by changes in a,5O C in tervals between -50 and t 1 0 0 " C a r e tabu la t ed fo r the 36 weight-per cen ts shown in Table IV.

P a r t i a l an d t o ta l p r e s s u r e s a t

Tab le A-11 p resen t s genera l i zed r esu l t s f ro m 0 t o 4 0 0 C .P a r t i a l p r e s s u r e s of H 0 , H2S04, and SO3 p lu s t he t o ta l p r e s s u r e a r eshow n in Subt ables ILA, LIB, TIC, and IID, respect ively . Tabula tedpr es su re s a r e rounded to fou r s ign if i can t f igu res and t e rm ina t ed at10 and 10 mm Hg.

2

4 - 4Table A-1.11 i s included a s a qu ick r e f e r enc e s ourc e and sum-

Abbreviated l ists of p a r t i a l p r e s s u r e sa r y of r e s u l t s .pres ente d in Subtables I IIA, I IIB, and I IIC. P re ss u re s a r e roundedto th r ee s ign i fi can t f igu res and a r e t e rmin a ted at IO4 and 10res u l t s a r e shown f rom -50 to 390"C,

a r e-2 mm Hg;

Table s A-IV and A-V a r e included to a id in in terpola t ionTable A-IV l i s t s the value s of the consta ntsmong the above t ab les ,i n Eq. (24) at the weight-percents used in Tables A-I and A-11;

Tab le A-V shows values of K f r o m -50 t o 390C,PThe For t r a n l i s t ing of t h e p r o g r a m u s e d t o c a l c u la t e th e p r e s -su re s l i s t ed in Tab le A-I1 is included as Tab le A-VI.we re wri t ten to produce Ta bles A-I and A-111.

Similar p r o g r a m s


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m u a h -0 . 0 . N C J

N0

U m C e a NO C , d r n *00000.....b) " -N U N. . . . .U 4 N C C" " l m u Q

N JN 4 J L n P. . . . .W 3 W N m . D"N

m 0 l r . mQ N I Q NN J Q 0 . 3. . I . ,"

N

" mm -00 0 ' 2 - N. . . . .000000b . . . . .c 0 . m o . oFNt7.d.O"NN"1-3- m m oC a G O -1 3 0 T 3 ". . . . 0 . 4 0 . 0 Q- m m o *

(3 3 0 4 . .. . . . .n9. QC r - m c mP N Q O L n4 d N N

. . . . .0.0" " J m ca m o m s. . . . .

d " . .

- m a0 0. .0 0 0

- m m w r - 0 . 0 .00 L70"Nb. . . . . . .O L I,' C'" m m o r - m0 C ? L I - ( " N. . . . . .0 030 00

0Q. 0 .0

s o- 0 1s .-0Lu 5 1 0a .I Qo )mU

0L u .e u3 -v)v)uL O0 .N2 .Yo1- v )N- C OZ bw wn u- 0 :Y O- I nOL c m6 - 1

30 : "w ou x .- I o3 mv)

a oz =?o n .

N ~ QO c . 00 00. . .

- ~ m ( n c - ~ N - m c o m m mO O D O u - - N ~ n r o m0000 00000 000"". . . . . . . . . . . . . .i

+N m r . o m N C ~ N ~ C30 C > ' 3 ' 3 0 3 d N l l 3 ? 1 \. . . . . . . . . . . .0 0 00000 0 0 0 0 0

30C

u- 0I OU Q

II ." N N m0000O C , 0 ". . . .

dCc02

0

N

004


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- 76 -

Table A-IV. Constants for parti al-pre ssure equations.W T PCT COMPa10.0

2 0 .o25.030 .O35.04 0 .O45.050.055.06 0 -065.070 .072.07 4 .O76.078.080.082.084.086.088.090 - 091.092.093.0'34.095.096.097.098.098.599.099.599.899.9100.0

121212121212121212121

212121212121212121212121212121212121212121212121212

A0 .982730E 01-0.128982E 020.377200E 01

-C.134*325 020 .377451E 01-0.139775E 020.105427E 02-0. 223 589 E c120.112147E 3 2-0 .308963E 620.112686E 0 2-0.323148E 020 .111961E 02-0.310513E 023.997490E 01-0 .237353E 020 .898832E 01-9.189624E 0 2-0.167992E 02O.621220E 0 1-0.126668E 0 20.366867E 01-G .627602 010.235183E 01-0.340476E 010.134506E 01-0.934196E 30

0 .170559E 0 1-0.172599E 010 .390946E 01-0.370810E C 10.611742E 510 .651030E 01I). 410187E-000.159751E 010.004282E 01

-0.537919E 0 10.122635E 0 20.127306E 0 2-0.949468E 010.118990E 02-0.920879E 010.105862E 02-0 .870240E 010.301261E 01-0.817590E 010.754884E 01-0.7h5944E 610 .631467E 01-0.733815E 010.492498E 01-0.694696E 01G.329972E 01

-0.668594E 310.1C4367E 01-0.642i308E 010 .903753E-01-0.632778E 01-0.140545E 01-3 .614434E 01-0 .489211E 01-0 .577858E 01-0.185363E 02-0.540286E 01-0.292730E G2-0.538282E 010.212753E 02-0 .548803E 01

C.799717E 01

- 0 . 3 a 3 5 6 9 ~ - ~ 0

- 0 . 3 8 6 1 3 0 ~ 0 1

- 0 . a 8 1 8 1 4 ~ 0 1

0-0.163377E 0 5-0 .749838E 04-O.l612;77E C 5-0.156870E 05

-0.749883E 04

-0 .751815E t 4-0 .769003E 04-0 .786989E 04-0.114447E 05-0.136193E 0 5

-0 794653E 04-0 1U60 69E 05-0 .799799E 04-0.103334E 05-0.784179E 04-0.773996E 04-0.117582E 05-0.112673E 05

-0.767477E 04-0.117496E 05-0.748958E 04-0.121003E 05-0 .720067E 04-0.128171E C5-0.705497E 04-0.692787E 04-0.680995E 04-0.135858E 0 5-0.670814E 04-0.137073E 05-0.661987E 04-0.137794E 05-0.691302E 04-0.134380E 05-0.812890E 04-0.120627E 05-0.998894E 04-0.103316E 05-0.111674E 05-0.936625E 04-0.115263.E 05-0.906709E 04-G. 114725E G5- 0 . 9 0 7 @ 0 9 0 4-0.113104E 0 5-0.912802E 04-0.110819E 05-0.920323E 04-0.108581E 05-0.928274E 04-0.136536E 05-0.93 37 14E 0 4-0.104 139E 05-0 .940360E 04-0.131233E f i5-0.945287E 04-0.972137E 04-0.950 1OOE 0 4-0.953695E 04-0.951834E C4-0.921465E 04-0.954960E 04-0.834654E 04-0.961414E 04-0 .564741E 04-0.968278E 04-0.408354E 04-0.968466E 04-0.186024E 05-0.966251E 04

-0.131338E 05-0.1336276 05

C0.258356E 020.272789E 020.257519E 020.302233E 0 20.303210E 020.259365E 0 20 .276911E 020.261922E 02

0.257511E 02

0.247785E 020.262859E 020.238974E 0 20.241423E 0 20.258706E 020 .262492E 02

5.264C27E 020.254900E 0 20 . 2 51806E 0 20.295357E 020.313991E 020.237319E 02

0.282963E 02

0.2460G9E 0 2

0.336749E 020.233523E 020.345232E 0 20.229998E 020 .3522 t2E 020.227125E 020 .357492E 020.225073E 020.360834E 023.224429E 0 20.361787E 020.230825E 020 .353843E 020.252743E 020.329540E 020.2836L9E 020.303G9OE 020 .333436E 020.283583E 0 20 .283356E 020 .305658E 020.281681E 020.301178E 020.283916E 020 .295050E 020.286586E 020.288080E 020.289216E 020.279833E 020.291875E 020.270105E 020.294321E 0 20.258560E 020.2965Y8E 020.244C17E 020.298651E 020.234732E 020.299497E 020.219462E 020 .300430E 020.301802E 020.114842E 020.303035E 020.883038E 010.303121E 020.414274E 020.302846E 02

0.307922E 02

0 . 1 ~ 2 5 4 3 ~2

00.816702E-,2-C. 2 1033E-2 10.816732E-42-O.258773E-u1@ . 8 1 6 7 0 2 E - i 2-0.268838E-01O - 9 17 34 3 E 8.1 2- 0 . 3 6 9 4 7 9 E - j l3 .992824E-22-0.470120E-310-992824E- ,2-3.4852 16E-J 10.972824E-32-0 .472636E-D l0.854443E-bZ0.753802E-L2-0 3418 J ~ E - 00 .643 58 1E-02-0.3267CbE- i 13 . 4 3 9 2 9 8 - ~ 2

-0.288966E-310.162535E-Lt2- 3 * 2 2 1 3 3 3 E - : 10.115738E-53-0.188325E-J1-0.139386E-u2- 0 . 1 6 3 6 4 8 E - i l-0.315510E-GZ- O . l 2 7 9 4 D E - ~ ~ l-0.516792E-C2-0 .103264E-J l-0.768395E-w2-0.700714E-32-0.843875E-wZ- 0 - 574913E-02

- 0 . 3 a 9 6 3 7 ~ - , 1

-0.416151E-S2-0.107812E-010.426718E-C2-0 .183293E-J l0 867G23E-02-0.218517E-010.892183E-uZ-0.226;65E-d10.791542E-32-0.223549E-010.640 581E-52- 3 2185 17E-u 10.464459E-32-0.213485E-010.313497E-32- 0 . 2 0 8 4 5 3 E - j l0 .2 12856E- \r2-0.206443E-320.996347E-03-0 .202918E-d l-0.387468E-03-0.201156E-31-0.265189E-02-0.198892E-L1-0.340670E-C2-0.198 I37E-5 1-0.441311E-u2-0.196124E-21-0.592273E-02-0.191847E-31-0 .188551E-b l-0.316114E-31-0.187067E-010 .129223E-51-0 .188325E-u l

- o . i ~ 7 3 i a ~ - j i


80/85

- 7 7 -

m m m d o d t Q m m0 0 0 0 0 0 0 0 0I I I Iw lLwwL iJ u J 1 1 1u rwa m * + \ t c a ~ o ~ o~ m ( r r - m m ~ ~ d 6O + ~ N S N ~ O Nm m d N . t m m w wa o o o o o o o a. . . . . . . . .

v o o o o o o o o o0 c3 0 0000 0( 3 . . . . . . . . .a d 8 t m & ( r & o . & m1 d d ~ ~ r n r nU l o O O O O CJ 0 00I

. . . . . . . . .0 0 0 0 0 0 0 0 0o - n & ~ o d ~ m m+o a o o o o o oI I I I I111uJ uJ uJ uJ uruJ uI111n l + r - a m - 4 m - 1 ~ . 0Y N N Q S d O O b Nm S a m l n d w o c aW N F m - 4 N d d \ t000000000

v 0 0 0 0 0 0 0 0 OO O O O O O O O O

. . . . . . . . .

U 0 000 0 0 0 0 00 .........w o w o o o o o o oO O O Q O O O O Oc J \ t - 4 ~ - 4 a - t ~ d aI - 4 + ~ ~ m mc. . . . . . . . .000000000

v o 0000000o a o o o o o o0 . . . . . . . . .1 1 1 0 0 0 0 0 0 0 ' 3 0a m r n o l n o l n o mI . . - I A N N ~~c


81/85

- 75 -


82/85

- 7 9 -

C110 CCYT INLF r

% K I T E C liT P U T T A P L 3 , 5 0 , A K P , ~ j k P , C K P , D K P , E K P , F K P , ( T T ( K ) , X K P ( K ) , K =l .I K T 1

C 3 1 5 P l I t J V K ) = G . 0CC T O 360

320 G = G+l.OC M = ;< Ib !TF (G)GO T O ( 3 ? 0 , 3 3 5 , 3 4 0 , 3 4 5 ) , M3 2 5 t- = 0,0001GO 10 3503 3 0 I- = O . C O 1GC T O 3 5 0

3 3 5 I- = 0.01GO T O 3507 4 0 I- = 0.1G O TC 350

3 4 5 k = 1.0

.I_-----


83/85

- 8 0 -

TASLE A-VI. (CONT.)3 55 P ( I , J , K ) = P ( I p J , K ) +H V360 C O N T I N L E V

C VC O 4 0 0 C K = l , I < TI F ( T T ( K ) 4 00 1, 4C 0 2 ,4 00 24 0 0 1 T T ( k ) = T T ( K ) - C.54 0 0 2 T T ( K ) = T l ( K ) + C.54000 I T T l K ) = T T l K I

GO TO 4000

C r o ~ O O C =1,4PM = 2J X = J 1

6000 J Y = J X + 116010 J Y = J N6 0 0 5 PM = 1

I F ( J Y - J 4 ) 5 0 0 0 ~6 0 0 5 y 6 0 1 05 0 0 0 G O TfJ ~ 5 0 0 5 ~ ~ 0 1 0 ~ 5 ~ 1 5 ~ 5 0 2 0 ~I5005 d R I T E C lJ T P lJ T T AP E 3 , 5 0 0 45006 FOLM AT ( l H 1 , 3 0 X , 5 5 H T A B L E A - I I A , CONT INUE D . C JATE R P AR T IA L PRE SSURE1, PM PC . 1

G O T U 7 0 0 05 0 1 0 W R I T E C U TP U T T AP E 3 9 5 0 1 15 0 1 1 F O R M A T ( l H l , Z h X ~6 3 H T A B L E A - 11 8, C ON TIN UE D. S U L F U R I C A C I D P A R T I A Ll P K E S S U K E , MM HG.)G O TI1 7 0 0 05 0 1 5 W R I T E C U T P b T T A P E 3 , 5 0 1 65 0 1 6 F OR MA T ( lH 1 , 25 X , 65 H T A B L E A - I I C , C O N TI NU E D- S U LF U R T R I O X I D E P A K T I A1 L P R E S S U R E , F1M HG.)G O TO 70005 0 2 0 W K I r F G U TP U T T A P E 3 1 5 0 2 1

5 9 2 1 F O R Y AT ( l H 1 , 3 4 X 9 4 7 H T A B L E A - I I D , C O N T IN U E D. T O T AL P R E S S U R E , MM HG.1 )7 0 0 0 W R IT E OU TP U T T AP E 3 9 7 0 05 , ( W ( J ) , J =J X , J Y )7 0 0 ' 5 F O K P A T ( l H 0 , S H U E G C , 4 t% , ZO H W E I G H T P E K C E N T H 2 S C 4 / 5 X , 1 2 F 9 . 1 )PMM = 2K 1 = 1K 2 = 07 0 1 0 K 2 = K 2 + 10

7 0 2 5 K2 = K J7 0 2 0 M K M = II F ( K 2 - K T ) 7 0 1 5 ~7 0 2 0 , 7 0 2 5

7 0 1 5 W K I T E CUT PUT T APE 3 , 7 0 3 O , ( I T T L K ) , ( P ( I , J , K ) 9 J = J X , J Y ) , K = K l , K 2 )7 0 3 0 F O R M A T ( l H O , I 4 , 3 X , l Z F 9 ~ 4 / ~ l X , I 4 , 3 X ~ l 2 F 9 . 4 ) )K L = K 2 + 1

7 0 3 5 J X = J Y + 18 C O O COIVT I N L E

G O T O ( 7 0 3 5 9 7 0 1 0 1 , P P MG 3 T O ( R 0 0 0 , 6 0 0 0 ) , P M

C I F ( N P R O B S - I P R O B ) 6 0 0 ~ 6 0 0 ~ 1 0 0600 CALL E X I T

END


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REFERENCES1. C. H. Gree new alt , Ind. Eng. Chem, 17, 522 (1925).2. B. C. B ur t, J. Chem . SOC. 85, 1339 (1904).3. W. Daudt, Z , physik. Chem. (Fr ank fur t ) 106, 225 (1923) .4. E. Abel, J , Phys . Chem. 50, 260 (1946).5.6 . W, F. Giauque, E. W. Hornungp J , E. Kunz le r , and T oR. Rubin,

--

--M. Bo denstein and M. Katayama , Z . Ele kt roc hem . 15, 244 (1909).-J.Arn. Chem . SOC. 82, 6 2 (1960).-

7 .8. National Bureau of Standard s Ci rcu lar 500, 1952.9. KOK. KelEey, U, . Bu rea u of Mines Bulletin 584, 1960.PO . J . E . Kun zler , Anal . Chem. 25, 93 (1953) .11 G. N. Lewis and M. Randa ll , The rmo dynam ics and the F re e

P. A, Giguk re and R. Sav oie, J . Am - Chem . SOC. 85, 287 (1963).--

E n e r g y 0 f Chemica l Subs tances , 1st ed. (McG raw-Hill BookCompany, Inc , , New York, 1923), p. 554.

12 . J . E. Kunzler and W. E", Giauque9 J . A m . Chem. SOC. 74, 3472-(1952).13. T. F. Young and G. E. Walrafen , Tra ns . Fa rad ay SOC. 57 , 34-

(1961).14. W. W. Duecke r and J , R. West, The Manufactu re of Sulfuric Acid

(Reinhold Publ ishing Corpora t ion, New York, 1959) , p. 434.15. 0, Redl ich and A. T. a s t e r , Ind. Eng. C hem . 40, 341 (1948 ).-


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T h i s r e p o r t w as p r e p a r e d a s a n a c c o u n t of G o ve rn me nts p o n s o r e d w or k. N e i t h e r t h e U n i t e d S t a t e s , n o r t h e Com-m i s s i o n , n o r a n y p e r s o n a c t i n g on b e h a l f o f t h e C o mm is si on :

A . Makes any wa r r a n t y o r r e p r e s e n t a t i o n , e x p re s s ed o ri m p l i e d , w i t h r e s p e c t t o t h e a c c u ra c y , c o m p l e t e n e s s,or u s e f u l n e s s o f t h e i n f o r m at i o n co n t a i ne d i n t h i sr e p o r t , o r t h a t t h e u s e o f a ny i n f o r m a t i o n , a p pa -r a t u s , m et ho d, or p ro c es s d i s c lo s e d i n t h i s r e p o r tmay n o t i n f r i n g e p r i v a t e l y owned r i g h t s ; or

B . Assumes a ny l i a b i l i t i e s w i t h r e s p e c t t o t h e use o f ,or f o r dam age s r e s u l t i n g f ro m t h e u s e o f a ny i n f o r -m a t i on , a p p a r a t u s , m e th o d, or p r o c e ss d i s c l o s e d i nt h i s r e p o r t .

A s u s e d i n t h e a b o v e, p e r so n a c t i n g o n b e h a l f o f t h eC o m m is s i on i n c l u d e s a n y e m p lo y e e o r c o n t r a c t o r o f the Com-m i s s i o n , or employee o f s uc h c o n t r a c t o r , t o t h e e y t e n t t h a ts u c h e m p l s y e e or c o n t r a c t o r o f t h e Commiss ion , o r employeeo f su c h c o n t r a c t o r p r e p a r e s , d i s s e m i n a t e s , or p r o v i d e s a c c e s st o , a ny i n f o r m a t i o n p u r s u a n t t o h i s employment or c o n t r a c tw i t h t h e C o mm i ss i on , o r h i s e mp lo ym en t w i t h s u ch c o n t r a c t o r .

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VLE Data Sulfuric Acid