The Foundations of Chemistry

EXAMPLE 15-19 Temperature Range of Spontaneity

Mercury(II) sulfide is a dark red mineral called cinnabar. Metallic mercury is obtained by

roasting the sulfide in a limited amount of air. Estimate the temperature range in which the

standardreaction is product-favored.

HgS(s)O 2 (g)88nHg(
)SO 2 (g)

Plan

We evaluate 
H^0 rxnand 
S^0 rxnand assume that their values are independent of temperature.

We find that both factors are favorable to spontaneity.

Solution

From Appendix K:

HgS(s) O 2 Hg(
)SO 2 (g)


H^0 f, kJ/mol: 58.2 200 5. 70 6. 296.8

S^0 , J/molK: 82.4 205.0 76.0 248.1

H^0 rxn
H^0 f Hg(
)
H^0 fSO 2 (g)[
H^0 f HgS(s)
H^0 fO 2 (g)]

 0 296.858.2 0 238.6 kJ/mol

S^0 rxnS^0 Hg(
)S^0 SO 2 (g)[S^0 HgS(s)S^0 O 2 (g)]

76.02248.1[82.4205.0]36.7 J/molK

H^0 rxnis negative and 
S^0 rxnis positive, so the reaction is product-favored at all tempera-

tures. The reverse reaction is, therefore, nonspontaneous at all temperatures.

The fact that a reaction is product-favored at all temperatures does not mean that the reac-

tion occurs rapidly enough to be useful at all temperatures. As a matter of fact, Hg(
) can be

obtained from HgS(s) by this reaction at a reasonable rate only at high temperatures.

EXAMPLE 15-20 Temperature Range of Spontaneity

Estimate the temperature range for which the following standard reaction is product-favored.

SiO 2 (s)2C(graphite)2Cl 2 (g)88nSiCl 4 (g)2CO(g)

Plan

When we proceed as in Example 15-19, we find that 
S^0 rxnis favorable to spontaneity, whereas


H^0 rxnis unfavorable. Thus, we know that the reaction becomes product-favored abovesome

temperature. We can set 
G^0 equal to zero in the equation 
G^0 
H^0 T
S^0 and solve for

the temperature at which the system is at equilibrium.This will represent the temperature above

which the reaction would be product-favored.

Solution

From Appendix K:

SiO 2 (s) C(graphite) Cl 2 (g) SiCl 4 (g) CO(g)


H^0 f, kJ/mol: 910.9 0 990 657.0 110.5

S^0 , J/molK:  9 41.84 5.740 223.0 330.6 197.6

Heating red HgS in air produces
liquid Hg. The gaseous SO 2 escapes.
Cinnabar, an important ore of
mercury, contains HgS.

634 CHAPTER 15: Chemical Thermodynamics