Physical Chemistry Third Edition

204 5 Phase Equilibrium

b.There are five components. Although six species are present, there is a requirement of

electrical neutrality. It would be possible to make the system with five substances: water,

NaCl, KBr, KCl, and LiCl. No NaBr or LiBr is needed.

c.There is one component, since the amount of N 2 O 4 is determined by the amount of NO 2

and the conditions of the equilibrium.

d.There are two components, since electrical neutrality imposes a relation on the amounts

of Ca^2 +and Cl−ions.

Exercise 5.2

Determine the number of components in:

a.A solution made from water, NaCl, and KBr.

b.An aqueous solution containing Na+,Cl−,K+, and Br−. Explain any difference from part a.

c.A gaseous system containing PCl 5 , PCl 3 , and Cl 2 at chemical equilibrium.

d.A solid mixture containing powdered graphite and powdered diamond without a catalyst or

other means of converting one phase to the other.

e.A gaseous mixture containing carbon dioxide and water vapor.

f.A gaseous mixture containing carbon dioxide and water vapor that was produced by the

combustion of a stoichiometric mixture of methane and oxygen. Assume that the residual

amounts of methane and oxygen are negligible.

g.A system containing solid Na 2 SO 4 and an aqueous phase containing Na+and SO^24 −ions,

which was produced by dissolving some of the sodium sulfate decahydrate.

The Gibbs Phase Rule

If the phases in a multiphase simple system ofpphases andccomponents are separated

from each other so that they cannot equilibrate, there arec+1 independent intensive

variables for each phase, a total ofp(c+1) variables. Now place the phases in contact

with each other, open them to each other, and allow them to equilibrate. There are three

aspects of equilibrium.Thermal equilibriumimplies that all phases have the same

temperature,mechanical equilibriumimplies that all phases have the same pressure,

andphase equilibriumimplies that the chemical potential of every substance has the

same value in every phase.

Each new equality turns one variable into a dependent variable. Specifying that one

variable has the same value in two phases means one equality, specifying that one

variable has the same value in three phases means two equalities, and so on. There

arep−1 equalities for one variable andpphases. The number of variables that have

equal values in all phases isc+2(T,Pand the chemical potentials ofccomponents),

for a total of (p−1)(c+2) equalities. This means thatf, the number of independent

intensive variables after equilibration of all phases, is equal to

fp(c+1)−(p−1)(c+2)pc+p−pc+c− 2 p+ 2

fc−p+2 (Gibbs phase rule) (5.2-2)

This equation is thephase ruleof Gibbs. The number of independent intensive variables

denoted byfis called the number ofdegrees of freedomor thevariance. Try not to be

confused by the fact that the term “variance” is also used for the square of a standard

deviation of a distribution.