The Foundations of Chemistry

EXAMPLE 15-17 Spontaneity of Standard Reaction

Make the same determination as in Example 15-16, using heats of formation and absolute
entropies rather than free energies of formation.

Plan
First we calculate
H^0 rxnand
S^0 rxn. We use the relationship
G^0 
H^0 T
S^0 to evaluate
the free energy change under standard state conditions at 298 K.

Solution

The values we obtain from Appendix K are:

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


H^0 f, kJ/mol: 0 0 90.25

S^0 , J/molK: 191.5 205.0 210.7

H^0 rxnn
H^0 f products n
H^0 f reactants


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


H^0 rxn[2(90.25) (00)]180.5 kJ/mol

S^0 rxnnS^0 products nS^0 reactants


S^0 rxn 2 S^0 NO(g) [S^0 N 2 (g)S^0 O 2 (g)]


S^0 rxn[2 (210.7) (191.5205.0)]24.9 J/molK0.0249 kJ/molK

Now we use the relationship
G^0 
H^0 T
S^0 , with T298 K, to evaluate the free energy
change under standard state conditions at 298 K.

G^0 rxn
H^0 rxn T
S^0 rxn

180.5 kJ/mol(298 K)(0.0249 kJ/molK)

180.5 kJ/mol7.42 kJ/mol

G^0 rxn173.1 kJ/mol rxn, the same value obtained in Example 15-16.

You should now work Exercise 100.

THE TEMPERATURE DEPENDENCE OF SPONTANEITY

The methods developed in Section 15-15 can also be used to estimate the temperature at
which a process is in equilibrium. When a system is at equilibrium,
G0. Thus,

Grxn
HrxnT
Srxn or 0 
HrxnT
Srxn

so

HrxnT
Srxn or T

H

Sr

r

x

x

n

n (at equilibrium)

EXAMPLE 15-18 Estimation of Boiling Point

Use the thermodynamic data in Appendix K to estimate the normal boiling point of bromine,
Br 2. Assume that
Hand
Sdo not change with temperature.

15-16

15-16 The Temperature Dependence of Spontaneity 631

See the Saunders Interactive

General Chemistry CD-ROM,

Screen 20.8, Free Energy and

Temperature.