Physical Chemistry , 1st ed.

Example 5.4

For molar amounts, the standard Gibbs energy of reaction for the following

reaction at 25°C is 457.14 kJ:

2H 2 (g) O 2 (g) →2H 2 O (g)

In a system where pH 2 0.775 bar,pO 2 2.88 bar, and pH 2 O0.556 bar, de-

termine (^) rxnG. Use 1.00 bar as the standard pressure.
Solution
First, we construct the proper expression for Q. Using equation 5.9, the bal-
anced chemical reaction, and the conditions given:

2


0

1

.5

.0

5

0

6

b

b

a

a

r

r



2

Q

2



0

1

.7

.0

7

0

5

b

b

a

a

r

r



2



2

1

.

.

8

0

8

0

b

b

a

a

r

r



Q0.179

Using equation 5.7 and solving:

(^) rxnG457.14 kJ 8.314 
K

J

(298 K) (ln 0.179) 

1

1

00

k

0

J

J



(^) rxnG461 kJ
Note the conversion from joules to kilojoules in the solution. Note that the
unit on (^) rxnGis simply kJ, since we are considering molar stoichiometric
amounts of reactants and products. If we want to report (^) rxnGin terms
of unit molar amounts of reactants or products, it would be given as
231 kJ/mol H 2 ,461 kJ/mol O 2 ,or 231 kJ/mol H 2 O.
For chemical equilibrium, (^) rxnG0. Equation 5.7 becomes
0 rxnG°RTln Q
(^) rxnG°RTln Q
Because (^) rxnG° has a characteristic value for a chemical process, the value of
the reaction quotient Qat equilibrium will have a characteristic value as well.
It is called the equilibrium constantfor the reaction and is given the new sym-
bol K. We therefore write the above equation as
(^) rxnG°RTln K (5.10)
Since Kis defined in terms of pressures of products and reactants at equilib-
rium, the standard Gibbs free energy of a reaction gives us an idea of what the
relative amounts of products and reactions will be when the reaction reaches
chemical equilibrium. Large values ofKsuggest more products than reactants
at equilibrium, whereas small values ofKsuggest more reactants than prod-
ucts. Equilibrium constants are never negative. Using the (^) rxnG° value from
Example 5.4, we can calculate a value ofKof 1.3  1080 , implying a large
amount of product and a minuscule amount of reactants when the reaction
reaches equilibrium.
Remember that a chemical equilibrium is a dynamic process. Chemical
processes do not stop when the Gvalue of the system has been minimized.
pO 2

1.00 bar
pH 2

1.00 bar
pH 2 O

1.00 bar
5.3 Chemical Equilibrium 125