Physical Chemistry , 1st ed.

At constant temperature and pressure, this becomes

(dG)T,p

0

i

idni

Substituting for dnifrom equation 5.2, this becomes

(dG)T,p

0

i

i (^) id
Since the extent variable is the same for all species, we can divide both sides by
d to get






G



T,p



0

i

i (^) i (5.3)
In equations 4.9, we stated that a system was at equilibrium if G0 or,
equivalently for an infinitesimal process,dG0. For chemical equilibrium,we
require that the derivative in equation 5.3, defined as the Gibbs free energy of
reaction (^) rxnG,be zero:






G



T,p

 (^) rxnG
0
i
i (^) i 0 for chemical equilibrium (5.4)
Figure 5.3 illustrates the meaning of equation 5.4. At some extent of reaction,
the overall Gof the system reaches some minimum value. At that extent, we
say that the system has reached chemical equilibrium. (We recognize that de-
rivatives also equal zero at curve maxima.However, we will not encounter such
situations in our discussion of thermodynamics.)
Example 5.3
The following reaction is set up in a sealed container:
2NO 2 (g) →N 2 O 4 (g)
Initially, there are 3.0 mol NO 2 present and no N 2 O 4. Write two expressions
for the extent of the reaction, and one expression that must be satisfied in or-
der for chemical equilibrium to exist.
Solution
An expression for can be written in terms of either NO 2 or N 2 O 4 :
 
Chemical equilibrium will exist if the following expression, written in terms
of the chemical potentials of NO 2 and N 2 O 4 , is satisfied:
N 2 O 4  2 NO 2  0
This expression comes directly from equation 5.4.
Consider a general gas-phase reaction:
aA →bB
For this process, equation 5.4 would be written as
(^) rxnGbBaA
nN^2 O^4
 1
nNO^2 3.0 mol
 2
5.3 Chemical Equilibrium 123
Extent of reaction, 
Equilibrium extent
G
G )( ^0
system
Figure 5.3 Over the course of the reaction
(labeled “extent of reaction” on the x-axis), the
overall Gibbs free energy comes to a minimum. At
this point, the reaction is at chemical equilibrium.