Concise Physical Chemistry

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

94 EQUILIBRIUM

and

GB=G◦B+RTln

pB

1. 0

where the 1.0 in the denominators signify that the partial pressures are relative to

the standard state of 1.0 bar. The difference between the chemical potentials of the

reactant state and product state is

rG=

∑

G(prod)−

∑

G(react)

which in this simple case is

rG=GB−GA=G◦B−G◦A+RTln

pB

1. 0

−RTln

pA

1. 0

or

rG=
G◦+RTln

pB

pA

As the reaction progresses,
rGis not zero andGof the reacting system is not constant

with timet,(∂G/∂t)T,p=0. When the chemical reaction has come to completion,

the pressure quotientQ=pB/pAhas arrived at a value such that(∂G/∂t)T,p=0,

hence

rG=
G◦+RTln

pB

pA

= 0

The free energy change of the system has arrived at a Gibbs potential energy mini-

mum. Under these andonly under these conditions,wehave
rG=0, so that

G◦=−RTln

pB

pA

=−RTlnKeq

The expression is frequently written in the equivalent form:

Keq=e−
G

◦/RT

7.2 GENERAL FORMULATION

A more general formulation of the equilibrium expressions above is given by the

reaction

aA+bB+... = cC+dD+...