Concise Physical Chemistry

c07 JWBS043-Rogers September 13, 2010 11:25 Printer Name: Yet to Come

CHEMICAL POTENTIAL: NONIDEAL SYSTEMS 101

written

Keq=

fB

fA

or Keq=

aB

aA

The Gibbs free energy of apuresubstance is a function of the temperature and

pressure only,G=g(T,p), but the free energy of a many-component system is a

function ofT,p, and the amounts of each componentni,G=g(T,p,ni). The total

change in free energy for a mixture is

dG=

(

dG

dT

)

p,ni

dT+

(

dG

dp

)

T,ni

dp+

∑

i

(

dG

dni

)

p,T

dni

It is the last term that we are interested in. At constantTandp,wehave

dG=

∑

i

(

dG

dni

)

p,T

dni

where thenjare constant (j=i). In the simple illustrative reaction mixture,

A(g) →← B(g)

in the ideal case,

G=
G◦+RTlnQ=
G◦+RTln

pB

pA

where thepvalues are partial pressures. In the nonideal case the form of the pressure

quotientQstill holds, but the partial pressures are replaced by the fugacitiesf.The

change in the Gibbs free energy is also given a different symbol
μto denote the

nonideal case:

μ=
μ◦+RTlnQ=
μ◦+RTln

fB

fA

Evidently,

μ=μB−μA

and

μ◦=μ◦B−μ◦A