H. Frank Gibbard and Mlchael R. Emptage Southern lllinois University Carbondale. 62901 ~~
~
(
Variation of Areotropie Composition and Temperature with Pressure
~
An undergraduate physical chemistry experiment The study of the properties of azeotropic mixtures has ohvious practical applications in the separation and purification o i substanc& by fractional distillation. An experiment in which azeotropic composition and temperature are measured is well suited to the undergraduate curriculum for several reasons. The apparatus and technique are simple, and accurate results can be obtained with average laboratory technique. Furthermore, the results can be predicted within the experimental precision by the use of thermodynamic equations. Thus, this experiment is a clear example of the Dower and utilitv of thermodvnamics in the solution of prae'tical problems. Daniels. e t al. (1) have described an experiment in which azeotropic composition and temperature are measured as functiuns of pressure. Their prediction of the results from theory requires the measurement of calorimetric enthalpies of solution. In this paper a different theoretical approach will he taken, which does not require any calorimetric measurements but yields an excellent prediction of the azeotropic locus. One needs only the vapor pressures of the components as functions of temperature and the azeotropic composition and temperature a t one pressure, conveniently chosen as atmospheric pressure.
-
Theory GeneralRelations for c Components h c Phases
A thermodynamic system is said to be an azeotrope when an azeotropic phase transformation can take place in it. During an azeotropic phase transformation the mass of some Dhase or uhases increases. while the mass of another phase or phases decreases, and the intensive properties of each uhase remain unchanged. In ~articular,the comuosition of each phase remainsuconst&t, and the temperature and pressure remain constant and uniform throuchout the . systim. To investigate the properties of azeotropic systems we begin by considering a closed system of c components in c phases. According to the Gibhs phase rule, two variables must he specified to describe the state of the system; these are conveniently chosen as pressure and temperature. The composition of the a t h phase is given by the set of mole fractions XI("), ~ 2 ( ~ ). ,. . , xe(=)of the components. We envision a change in state a t constant temperature and pressure, in which the number of moles of each component in each phase can vary, but the composition of each phase does not change. The initial number of moles of component i in phase a is nio(ml. Now if heat flows to the system from its surround-
ings, and the temperature and pressure of the system remain constant, the amount of substance in some phases will increase, and the amount of substance in some other phases will decrease. Let the total change in the number of moles in phase a he Ada). Then, if the composition of the nth phase does not change (the condition for an azeotropic phase transformation), we must have An,'"' = x,l"l An'"' i = 1, . . , e (1) That is, if the mole fraction of each component is to remain unchanged, then the flux of each substance into the ath phase must he proportional to the fraction of material already present in that phase. Because the system is closed, the net flux of each component must vanish xAn,'"=O i = 1 . , c
(2)
,.-, Combination of eqns. (1)and (2) gives the set of equations
This set of equations shows that the sets of mole fractions . . . , x,(") which describe the composition are linearly dependent. This means that one group of phases can be formed by combining all of the material in the other phases of the system. Note that the eqns. (3) have a nontrivial solution for the An(=) if and only if the determinant of the coefficients (the xi(%) vanishes
xl("J, xl("J,
Since the transpose of a determinant equals the original determinant (Z), we also have
For each phase the Gibbs-Duhem equation applies
Volume 52. Number 10, Ocfober 1975 / 673
where Y(")and are the molar volume and molar entropy of the olth phase
F"'= v'"', C,,,""'
.
...
x,'"
-
x ; ~ ). . . XC_,i2'
dP =
.
-
x,iC'
xc-i"l VV,
x y
dT
...
S'"
2 ,.. ~ 'x : ~ ' ...
xp' ...
dll,
...
x,,
0,
vc,,
xll'l ...
-
x j Z 1 . . xc-,12, V12)
.
...
x,'"
...
-
x " , , " 1.''"
dP
=
Azeotropic states of thousands of binary systems with liquid and vapor phases have been reported (3, 4). For most of these systems the azeotropic temperature and composition are known only a t atmospheric pressure. Because laboratory and commercial scale distillation processes are not limited to atmospheric pressure, the variation of azeotropic composition and temperature with pressure is of practical interest. For the case of binary liquid-vapor equilibrium, eqn. (4) is written
(9)
x?'
From eqn. ( 5 ) , the determinant which multiplies dr, vanishes for an azeotropic system. Thus the basic equation for an azeotropic transformation in a system of c components in c phases is x
(17)
x p ., ,
x,@~~
x?'
+
-
"'
Xr-l
( d P l d T, ),,,,
Azeotropic States of Binary Systems with Liquid and Vapor Phases
+
Vi2'
,,,. = A H I T A V
(7)
The set of eqns. (6) contains c equations in c 2 unknowns, dP, dT, and c differential chemical potentials. By Cramer's rule, the set of equations may he reduced to one equation which relates dP, dT, and one of the dr's, chosen here as d r c x,"' . . . x-:'~ SiI1 x;" . . . x-, "' p, x,i2' . . . x"_;z'
versible change a t constant temperature and pressure, AS may be replaced by A H I T to yield
XC,
"1
x,i2' . .. xC-)*' . ... x/
