Isothermal liquid—vapour equilibrium in the systems n-heptane—toluene and toluene—dimethylformamide at 40 °C

J . D O J Č A N S K Ý , Ľ. SAKÁLOŠOVÁ, a n d J . S U R O V Ý

Department of Chemical Engineering, Slovak Technical University, 880 37 Bratislava

Received 10 J u l y 1973

T h e values of t o t a l v a p o u r pressure were d e t e r m i n e d over liquid solutions of k n o w n composit ion of t h e b i n a r y sys tems n-heptane — t o l u e n e a n d toluene — dimethy l formamide a t 40°C are presented . B y using t h e coexis­tence e q u a t i o n t h e equi l ibr ium composit ion in v a p o u r phase as well as t h e act iv i ty coefficients of t h e c o m p o n e n t s in l iquid solutions have been calcu­lated.

W i t h t h e view of s tudy ing t h e t h e r m o d y n a m i c propert ies of t e r n a r y sys tems of t h e type h y d r o c a r b o n — p o l a r solvent, t h e P — x re lat ionship was m e a s u r e d for t h e b i n a r y solutions n-heptane — t o l u e n e a n d to luene — dimethy l formamide over t h e whole con­cent ra t ion range a t c o n s t a n t t e m p e r a t u r e . T h e e x p e r i m e n t a l d a t a were used for t h e calculat ion of i sothermal l iquid — v a p o u r equi l ibr ium a n d for t h e d e t e r m i n a t i o n of t h e act iv i ty coefficients of t h e c o m p o n e n t s in t h e liquid phase .

E x p e r i m e n t a l

Preparation of substances

Analytical grade to luene a n d chemical grade n-heptane were purified b y twofold rectification on a co lumn wi th t h e efficiency of 70 theoret ica l p la tes . F o r t h e p r e p a r a t i o n of d imethy l formamide (DMFA) a p u r e chemical was used, purified b y twofold recti­fication in vacuo on a co lumn w i t h t h e efficiency of ca. 10 theoret ica l p la tes .

The physical propert ies of t h e substances t h u s p r e p a r e d are c o m p a r e d wi th t h e lite­r a t u r e d a t a in Table 1.

Table 1

Physical propert ies of t h e used substances

Substance

n- Heptane

Toluene

DMFA

ЯП

Refractive index n^

Exper.

1.3876

1.4967

1.4305

Ref.

1.38765 [1]

1.49693 [1]

-

Dei

Exper.

0.6834

0.8665

0.9556

Chem

isity at 20°C [g cm- 3 ]

Ref.

0.68368 [1]

0.S6693 [1]

-

>,. zvesti 28 (2) 100 -105 (1074)

1ЛЦ!'П)-\*АН01Ж EQUILIBKR'M

Measurements of vapour pressure

T h e s ta t ic m e t h o d was used for t h e m e a s u r e m e n t of t o t a l v a p o u r pressure over t h e

liquid solution of k n o w n composit ion. A detai led descr ipt ion of t h e a p p a r a t u s used a n d

t h e scheme of its wiring are available in t h e original p a p e r [2]. T h e t o t a l pressure was

de termined wi th t h e accuracy of ± 0 . 1 —0.2 t o r r a t t h e c o n s t a n t t e m p e r a t u r e of 40 —

4- 0.05°C.

The results of m e a s u r e m e n t s of t o t a l pressure are compiled in Tables 2 a n d 3.

Table 2

E x p e r i m e n t a l values of v a p o u r pressure in t h e

sys tem n-heptane (1) —toluene (2) a t 40°C

Xi

0 0.103 0.195 0.291 0.388 0.483 0.595 0.697 0.793 0.832 0.908 1.0

P [torr]

59.2 66.8 72.0 76.0 80.5 '82.8 86.3 88.1 89.9 90.9 91.9 92.1

Tahle 3

E x p e r i m e n t a l values of v a p o u r pressure in t h e

sys tem to luene ( l ) - D M F A (2) a t 40°C

Xi

0 0.042 0.102 0.199 0.285 0.356 0.463 0.498 0.575 0.663 0.758 0.821 0.894 0.948 1.0

P [torr]

9.75 14.3 18.9 27.0 32.7 36.4 40.7 43.4 46.1 49.2 51.1 54.1 56.1 57.2 59.2

Chem. zvesti 28 (2) 16.) - 165 (1974) 1 6 1

J. DOJČANSKÝ, L. SAKÁLOŠOVÁ, J. SUKOVÍ

Interpretation of the experimental data

To express the P — x dependence the following relationship was applied

P = P\xx + P?2x2 + PE, (7)

The excess pressure PE was correlated by means of a polynomial

к

= У Aj(x1-x2y. (2) X\ X2 ' {

j = 0

The coefficients A j occuring in eqn (2) were calculated by the method of least squares

and the most proper degree of polynomial was determined by the F test.

The following characteristic of the P—x relationship was obtained for the system

n-heptane (1) —toluene (2)

P = 92.10.Ti + 59.20 X2 + Я1Я2[31.35 - 10.45(si - x2) +

+ 0.188(#i - x2)2 - 0.246(a;i - * 2 ) 3 + 15.92(3,4 - х2Щ.

For the sjrstem toluene (1) —DMFA (2) another relationship is convenient

P = 59.20 xi + 9.75 x2 + xi я2[35.84 - 10.48(ял - x2) -

- 10.31(#i - x2)2 - 119.37(a;i - x2)* + 23.63(si - x2)* +

+ 384.69(a;i - x2)5 - 16.35(a?i - x2)* - 319.36(a;i - х2Щ.

The average deviation of the correlated values from the measured values of total

pressure in the systems n-heptane —toluene and toluene —DMFA is i 0.17 torr and

±0.10 torr, respectively. The maximum deviation in both systems is 0.4 torr.

In view of the relatively low pressures in the systems studied it is possible to use

the virial equation of state with secondary coefficients [3] for expressing the volume

properties of vapour phase. The coexistence equation allowing the direct calculation

of the equilibrium vapour composition at constant temperature assumes thus the follow­

ing form

dyi V - (1 - 2yi) (2Л - xi) (Ô/RT)

where

a n d

d P [(2/1 - *i)/2/i(l - 2/i)] - (2/1 - *i) (2(5 P/RT)

_ 2/1 2/2 d - Vb + a?i £ii + a?2 #22 J_

RT P

ô = 2J5i2 - An - B22. (5)

In this study it was assumed (5 = 0. The secondary virial coefficients of hydrocarbons

and DMFA were calculated according to the correlation put forward by O'Connell and

Prausnitz [4]. The molar volumes of pure components were used for the calculation of

the molar volume of liquid solution

VL = xľ V\ + x2 Vh (<5)

i n 9 Chem. zvesti 28 (2) 1G0 -105 (1974)

LIQUID-VAPOUR EQUILIBRIUM

The values of secondary virial coefficients a n d t h e molar volumes of p u r e c o m p o n e n t s

are listed in Table 4.

Table 4

Values of secondary virial coefficients a n d molar

volumes of p u r e c o m p o n e n t s a t 40°C

Substance г о " i n г •? * i n [cm J mol - 1 ] L c m mol J

?i-Heptane

Toluene

DMFA

- 2 4 4 5

- 2 1 0 0

- 3 8 5 0

150.4

108.6

63.7

B y dividing relat ionship (3) b y d#i a n d rearranging we obta in

da* (i/i — xi) da* (?)

The simplified form of coexistence eqn (7) was appl ied t o t h e calculat ion of t h e equi­

l ibr ium v a p o u r composit ion b y using t h e procedure described in l i t e ra ture [5].

F o r t h e first s tep in t h e numerica l integrat ion of t h e differential e q u a t i o n t h e subse­

q u e n t a p p r o x i m a t i o n was used

di/i Ayľ

da* Ax\

where

Ayi = (yi)Xl = e ~ (yi)xl = o = (yi)ii-e-

F o r calculation of t h e first value y± we obta in e q n (8) from relat ionship (7) as a result of t h e integrat ion s teps £

\ d a * / í -г xi

The following values i/i were calculated b y solving eqn (7) b y t h e m e t h o d of R u n g e —

— K u t t a . T h e numerical integrat ion of coexistence equat ion, as s t a t e d b y van Ness [6]

m u s t always proceed in t h e direction of increasing t o t a l pressure. O u r case concerns

t h e systems w i t h a positive deviat ion from t h e R a o u l t ' s law which do n o t show a n y

azeotropic p o i n t ; t h a t is w h y t h e calculat ion s t a r t s in t h e p o i n t xi = 0 a n d goes on t o

t h e point xi = 1.

T h e accuracy in t h e calculation of t h e values yi is also affected b y t h e m a g n i t u d e

of integrat ion s tep e. B y r e p e a t e d calculat ion involving t h r e e a r b i t r a r y e values (0.01,

0.005, a n d 0.001), t h e same values were obta ined for t h e y—x re lat ionship in t h e sj^stem

n-heptane —toluene, b u t in t h e sys tem to luene — D M F A t h e deviat ions of y\ were as

far as t h e t h i r d decimal place.

Chem. zvesti 28 (2) 1G0-1P5 (1974) i g q

о о о о о о о о о о о р о о о о о о о o^boôo^^bsbsuiui^^ôočoiowi-'b-io ^ О С Л О С Л О С Л О С П О С Л О С Л О С Л О С П О С Л

o o o o o o o o o o o o o o o o o o o

W ^ Č 0 Ó w o b 5 t o b l ^ í - , - - l w Ô 5 b 5 C C ) 0 0 C 0 C C i

o o o o o o o o o o o o o o o o o o o č o č c č o č o Č D Č o c D Ó o b o b o o o b o b o ^ j ^ i ^ i 0 5 0 i c o ^ Ф с л о о ь о н о ф о о о г с л с о н о о с л о ю м м

o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o OO»—'»—'i—>i—' •— i—< L>0 ьэ Ю tO W W CO ̂ ^ U» Oi

o o o o o o o o o o o o o o o o o o o

t D O O O O H H H W W W W ^ ^ Ü i Ü i O l O J O O

C 0 0 - 3 0 5 0 5 ^ C C I O I O N - ^ H - O 0 0 0 0 0 0 H O 0 0 « 0 O * J < 1 » - 1 H 0 1 W O V | Ü I W M M W H

o o o o o o o o p o p o o p p p o o o Ь Ь Ь о д а - 1 ^ а Ь с л с л ^ 1 й - м м ь 5 К ) н н Ь O i O C J i O Ü i O O i O O i O O i O O i O Ü i O O i O Ü i o o o o o o o o o o o o o o o o o o o

О О К ' Ю О О О О О О С Л О ^ Ф О С Л Н О ) ^ !

p o p o o p o o p o p o o p o o p o p

4 ^ C n Ü i ^ C O C O C H C D 0 0 0 5 ^ 1 0 5 W Ü i ^ 0 0 0 5 C r x O

o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o 0 0 0 0 © н - г - н - > н - > — (—tOtötOtOWCCOOrf^

о р о р р р о о р р о о р р р р о р и b c O í O C O C O O C O C O í D C O t O í D C O C O C O C O O C O O t O C D C O C D C O C O C D C O C D C D C D t O C O t O í O C D C D í D O

O O O O O O O O O i — h - ^ - i — ' Ю W Ь5 W ^ СЯ

M O ( r . 0 0 W C 0 O 0 0 « 4 O W O ^ ( » Ü < v | ^ K i 0 0

^ W I O U Í I O U Í H - H - K - H - O O O O O O © © © W O ^ Ü 4 t » t O C O O ) W O a j < l Ö i ^ W t O H O O ^ CO M O) H о w w W 00 ее о О W Ю W ^ -J H

LIQUID-VAPOUR EQUILIBRIUM

At t h e end t h e act iv i ty coefficients of c o m p o n e n t s y\ a n d yi were ca lculated by m e a n s

of the formula

P?X:

(9)

where Ф, is defined b y eqn (10)

(pO _ p) ( F L _ B x

RT

T h e calculated values of y\, y i , 72, Ф1, a n d Фо are presented in Tables 5 a n d 0.

Symbols

au mole fraction of t h e c o m p o n e n t in liquid

y i mole fraction of t h e c o m p o n e n t in v a p o u r

P{- pressure of t h e s a t u r a t e d v a p o u r of p u r e c o m p o n e n t

P t o t a l pressure

PK excess pressure

A j coefficient of polynomial

B11 secondary virial coefficient of p u r e c o m p o n e n t

7? gas c o n s t a n t

T absolute t e m p e r a t u r e

V]J molar vo lume of p u r e liquid c o m p o n e n t

ľ L molar v o l u m e of l iquid solution y i a c t i v i t y coefficient of t h e c o m p o n e n t in liquid д 2B12—B11 — B22, function of t h e secondary virial coefficients

Ф* correct ion factor expressed b y eqn (10) XF defined b y e q n (4)

F in tegrat ion s tep

j e x p o n e n t expressing t h e degree of polynomial

Subscripts 1, 2, a n d i denote more volatile component , less volatile c o m p o n e n t , a n d

c o m p o n e n t i, respectively.

References

1. Rossini, D., Selected Values of Properties of Hydrocarbons. Circular С 641. N a t i o n a l

Bureau of S t a n d a r d s . Washington, 1947.

2. Surový. J . , Habilitation Thesis. Slovak Technical Univers i ty , Bra t i s lava , 1969. 3. P rausn i tz , J . M., Ecker t , С. A., Orye, K. V., a n d O'Connell, J . P . , Computer Calcula­

tions for Multicomponent Vapor—Liquid Equilibria. Prent ice-Hal l , Englewood Cliffs,

New York, 1967.

4. O'Connell, J . P . a n d P r a u s n i t z , J . M., Ind. Eng. Chem., Process Design Develop. 6,

245 (1967).

5. Chang, S. D . a n d L u B. C. Y., Can. J. Chem. Eng. 46, 273 (1968).

О. Van Ness, H . C , AICHE J. 16, 18 (1970).

Translated by R. Donianský

Chem. zvesti 28 (2) 160 -1С5 (1974) I ß -