Thermodynamics and Chemistry

CHAPTER 12 EQUILIBRIUM CONDITIONS IN MULTICOMPONENT SYSTEMS

12.8 LIQUID–GASEQUILIBRIA 405

 Thuscompared to the liquid, the gas phase is richer in the component whose addi-
tion to the liquid at constant temperature causes the total pressure to increase. This
statement is a version ofKonowaloff’s rule.
In some binary liquid–gas systems, the total pressure at constant temperature exhibits
a maximum or minimum at a particular liquid composition. At this composition, dp=dxA
is zero but dpA=dxAis positive. From Eq.12.8.21, we see that at this compositionxA=xB
must equalyA=yB, meaning that the liquid and gas phases have identical mole fraction
compositions. The liquid with this composition is called anazeotrope. The behavior of
systems with azeotropes will be discussed in Sec.13.2.5.

12.8.4 Gas solubility

For the solution process B(g)!B(sln), the general expression for the thermodynamic equi-
librium constant isKDaB(sln)=aB(g).
The activity of B in the gas phase is given byaB(g)DfB=p. If the solute is a nonelec-
trolyte and we choose a standard state based on mole fraction, the activity in the solution is

aB(sln)Dx;B (^) x;BxB. The equilibrium constant is then given by

KD

x;B (^) x;BxB
fB=p

(12.8.22)

and the solubility, expressed as the equilibrium mole fraction of solute in the solution, is
given by

xBD

KfB=p

x;B (^) x;B

(12.8.23)

(nonelectrolyte solute in

equilibrium with gas)

At a fixedTandp, the values ofKandx;Bare constant. Therefore any change in the

solution composition that increases the value of the activity coefficient (^) x;Bwill decrease
the solubility for the same gas fugacity. This solubility decrease is often what happens
when a salt is dissolved in an aqueous solution, and is known as thesalting-out effect(Prob.

12. 11 ).
    Unless the pressure is much greater thanp, we can with negligible error set the pres-
    sure factorx;Bequal to 1. When the gas solubility is low and the solution contains no

other solutes, the activity coefficient (^) x;Bis close to 1. If furthermore we assume ideal gas
behavior, then Eq.12.8.23becomes
xBDK
pB
p

(12.8.24)

(nonelectrolyte solute in equilibrium

with ideal gas,x;BD 1 , (^) x;BD 1 )
The solubility is predicted to be proportional to the partial pressure. The solubility of a gas
that dissociates into ions in solution has a quite different dependence on partial pressure.
An example is the solubility of gaseous HCl in water to form an electrolyte solution, shown
in Fig.10.1on page 285.