Thermodynamics and Chemistry

CHAPTER 12 EQUILIBRIUM CONDITIONS IN MULTICOMPONENT SYSTEMS

12.8 LIQUID–GASEQUILIBRIA 399

The pressure differencepìpíat equilibrium can be estimated with Eq.12.7.11, and
for the present example is found to be positive. Without this pressure difference, the solution
in phaseíwould move spontaneously through the membrane into phaseìuntil phaseí
completely disappears. With phaseíopen to the atmosphere, as in Fig.12.9, the volume
of phaseìmust be constrained in order to allow its pressure to differ from atmospheric
pressure. If the volume of phaseìremains practically constant, the transfer of a minute
quantity of solvent across the membrane is sufficient to cause the pressure difference.
It should be clear that the existence of a Donnan membrane equilibrium introduces
complications that would make it difficult to use a measured pressure difference to estimate
the molar mass of the polyelectrolyte by the method of Sec.12.4, or to study the binding of
a charged ligand by equilibrium dialysis.

12.8 Liquid–Gas Equilibria

This section describes multicomponent systems in which a liquid phase is equilibrated with
a gas phase.

12.8.1 Effect of liquid pressure on gas fugacity

If we vary the pressure of a liquid mixture at constant temperature and composition, there is
a small effect on the fugacity of each volatile component in an equilibrated gas phase. One
way to vary the pressure at essentially constant liquid composition is to change the partial
pressure of a component of the gas phase that has negligible solubility in the liquid.
At transfer equilibrium, componentihas the same chemical potential in both phases:
i(l)Di(g). Combining the relationså@i(l)=@pçT;fnigDVi(l) andi(g)Di(g)C
RTln.fi=p/(Eqs.9.2.49and9.3.12), we obtain

d ln.fi=p/

dp

D

Vi(l)

RT

(12.8.1)

(equilibrated liquid and

gas mixtures, constantT

and liquid composition)

Equation12.8.1shows that an increase in pressure, at constant temperature and liquid com-
position, causes an increase in the fugacity of each component in the gas phase.
Integration of Eq.12.8.1between pressuresp 1 andp 2 yields

fi.p 2 /Dfi.p 1 /exp

"Z

p 2

p 1

Vi(l)

RT

dp

(12.8.2)

(equilibrated liquid and

gas mixtures, constantT

and liquid composition)

The exponential on the right side is called thePoynting factor.