CORRESPONDENCE
Isobaric Vapor-Liquid Equilibria
SIR: I n the article by Chao [IAD. EX. CHEW.51, 93 (1939)l the following equations are given :
From which we may deduce that:
i2
Hence, if
(a) is dT
.=-e(") =-n+(B-b) RT2 +
(Y?
From which A H may be estimated. The interesting thing about this equation is that if it is assumed that
(g)p
remains finite, AH is not zero for
pure components and hence the correlation cannot be valid for the entire range and is not thermodynamically selfconsistent. iVould it not have been better to fit the constants B, C, D to the curve of GE/RT LIS. X i and, in fitting the curve of In y1/y2 L'S. X,to represent Z by a form which becomes zero for pure components? One more point: The correlation for pentane-benzene requires, with the constants given, that In y , ; ' ~ ?t's. .Y be a straight line-but it is clearly curved in the illustration.
- C) ( 6 ~ 1 . ~-2 1 ) + ( 0 - d ) ( Q - S l i ( 1 - 8 X I X - . ) (1)
-x
+
~ ) (C
.At either ,tl = 1 .O or
X?
= 1.O,A H =
0.
I t follo\vs that: (-a
p
(X,- Xi) (C - C)(GXII'Y? - 1 ) (D - d)('Y? - .Y1)(1 - 8'Yl.Y?)
+
I
Fur the system benzene-heptane undcr I-arm. pressuIe and a t X I = O,.?, 0 7'
(
-a
- (R
c:. Fstirnated froin 1.3
22.9 2
F'or azeotrope-forming
- h ) - (C - c) - (I) - d ) = 0
Instead of determining B, C, D, etc., by fitting the excess free energy expression, this condition permits evaluation of rhese constants from n, 6, c, d, etc. Thus, limiting ourselves to t e r m u p to c and C. and solving the equations, 'R
,
=
b
C = c - a
(31
\l'hen terms up to d a n d D or above are included. the solution is not as straightforivard because of a n indeterminancy condition. More elaborate mathematical technique would be required to evaluate the best constants to satisfy the conditions of vanishing AH. However, a simple set of relations may satisfy the consistency conditions-namely,
INDUSTRIAL AND ENGINEERING CHEMISTRY
=
Y' = 88' C:. taken froin ( 3 ) t i = -0.0149 taken from ( 2 )
l h e heat of mixing estimated froin Cquation .i is 232 cal. gram-mole. 'I'his may be compared with the valur of 180 cal. pram-mole a t 70' C:. for the same mixture (i).
+ ( R - b ) - ic - c ) + ( I ) - d ) =( 20)
(4) LEONARDR l . SAPHTALI ,\D= d Polytechnic Institute of Brooklyn Brooklyn 1: N. Y . \l:hen terms u p to b and B only are included, the condition of vanishing AH cannot be strictly satisfied. SIR: The heat of mixing, Aff, in my
13 18
'The fitrinq of vapor-liquid equili 1~rit111~ data \
