General Chemistry Principles, Patterns, and Applications, 2011

5. 919 K
6.
7. MgCO 3 : ΔG° = 63 kJ/mol, spontaneous above 663 K; BaCO 3 : ΔG° = 220 kJ/mol, spontaneous above 1562 K
18.6 Spontaneity and Equilibrium
L E A R N I N G O B JE C T I V E
1. To know the relationship between free energy and the equilibrium constant.
We have identified three criteria for whether a given reaction will occur spontaneously: ΔSuniv > 0, ΔGsys <
0, and the relative magnitude of the reaction quotient Q versus the equilibrium constant K. (For more
information on the reaction quotient and the equilibrium constant, see Chapter 15 "Chemical
Equilibrium".) Recall that if Q < K, then the reaction proceeds spontaneously to the right as written,
resulting in the net conversion of reactants to products. Conversely, if Q > K, then the reaction proceeds
spontaneously to the left as written, resulting in the net conversion of products to reactants. If Q = K, then
the system is at equilibrium, and no net reaction occurs. Table 18.3 "Criteria for the Spontaneity of a
Process as Written" summarizes these criteria and their relative values for spontaneous, nonspontaneous,
and equilibrium processes. Because all three criteria are assessing the same thing—the spontaneity of the
process—it would be most surprising indeed if they were not related. The relationship between ΔSuniv and
ΔGsys was described in Section 18.5 "Free Energy". In this section, we explore the relationship between the
standard free energy of reaction (ΔG°) and the equilibrium constant (K).
Table 18.3 Criteria for the Spontaneity of a Process as Written
Spontaneous Equilibrium Nonspontaneous*
ΔSuniv > 0 ΔSuniv = 0 ΔSuniv < 0
ΔGsys < 0 ΔGsys = 0 ΔGsys > 0
Q < K Q = K Q > K
*Spontaneous in the reverse direction.
Free Energy and the Equilibrium Constant
Because ΔH° and ΔS° determine the magnitude of ΔG° (Equation 18.26), and because Kis a measure of
the ratio of the concentrations of products to the concentrations of reactants, we should be able to
express K in terms of ΔG° and vice versa. As you learned in Section 18.5 "Free Energy", ΔG is equal to the
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