The Foundations of Chemistry

EXAMPLE 15-16 Spontaneity of Standard Reaction

Diatomic nitrogen and oxygen molecules make up about 99% of all the molecules in reason-

ably “unpolluted” dry air. Evaluate 
G^0 for the following reaction at 298 K, using 
Gf^0 values

from Appendix K. Is the standard reaction spontaneous?

N 2 (g)O 2 (g)88n2NO(g) (nitrogen oxide)

Plan

The reaction conditions are 1 atm and 298 K, so we can use the tabulated values of 
G^0 ffor

each substance in Appendix K to evaluate 
G^0 rxnin the preceding equation. The treatment of

units for calculation of 
G^0 is the same as that for 
H^0 in Example 15-9.

Solution

We obtain the following values of 
G^0 ffrom Appendix K:

N 2 (g) O 2 (g) NO(g)


G^0 f, kJ/mol: 0 0 86.57

For the reverse reaction at 298 K,

G^0 rxn173.1 kJ/mol. It is product-
favored but very slow at room
temperature. The NO formed in
automobile engines is oxidized to even
more harmful NO 2 much more rapidly
than it decomposes to N 2 and O 2.
Thermodynamic spontaneity does not
guarantee that a process occurs at an
observable rate. The oxides of nitrogen
in the atmosphere represent a major
environmental problem.

630 CHAPTER 15: Chemical Thermodynamics

Problem-Solving Tip:Some Common Pitfalls in Calculating G^0 rxn

Be careful of these points when you carry out calculations that involve 
G^0 :

1.The calculation of 
G^0 rxnfrom tabulated values of 
G^0 fis valid onlyif the reaction is

at 25°C (298 K) and one atmosphere.

2.Calculations with the equation 
G^0 
H^0 T
S^0 must be carried out with the

temperature in kelvins.

3.The energy term in 
S^0 is usually in joules, whereas that in 
H^0 is usually in kilo-

joules; remember to convert one of these so that units are consistent before you

combine them.

G^0 rxnn
G^0 f productsn
G^0 f reactants

 2 
G^0 f NO(g)[
G^0 fN 2 (g)
G^0 fO 2 (g)]

2(86.57)[00]

G^0 rxn173.1 kJ/mol rxn for the reaction as written

Because 
G^0 is positive, the reaction is nonspontaneous at 298 K under standard state condi-

tions.

You should now work Exercise 99.

The value of 
G^0 can also be calculated by the equation

G^0 
H^0 T
S^0 (constant Tand P)

Strictly, this last equation applies to standard conditions; however, 
H^0 and 
S^0 often do

not vary much with temperature, so the equation can often be used to estimatefree energy

changes at other temperatures.