20.3. Free Energy and Equilibrium http://www.ck12.org
Equilibrium Constant and∆G
The∆G value of a reaction tells us whether reactants or products are favored at equilibrium. We also know that
the equilibrium constant, Keq, relates the concentrations of all substances in the reaction at equilibrium. It stands to
reason that there is a relationship between the values of∆G° and Keq. A more advanced treatment of thermodynamics
yields the following equation:
∆G°=-RT ln(Keq)The variable R is the ideal gas constant (8.314 J/K•mol), T is the Kelvin temperature, and ln(Keq) is the natural
logarithm of the equilibrium constant.
When Keqis large, the products of the reaction are favored, so∆G° should be negative. When Keqis small, the
reactants are favored. The natural logarithm of a number less than one is negative, so the sign of∆G° is positive
when Keq<1. The table below (Table20.3) summarizes the relationship between∆G° and Keq.
TABLE20.3: Relationship between∆G°and K
Keq ln(Keq) ∆G° Description
>1 positive negative Products are favored at
equilibrium.
1 0 0 Reactants and products
are equally favored.
<1 negative positive Reactants are favored at
equilibrium.Knowledge of either the standard free energy change or the equilibrium constant for a reaction allows for the
calculation of the other. The following two sample problems illustrate each case.
Sample Problem 20.2: Gibbs Free Energy and the Equilibrium Constant
The formation of nitrogen monoxide from nitrogen and oxygen gases is a reaction that strongly favors the reactants
at 25°C.
N 2 (g) + O 2 (g)2NO(g)The actual concentrations of each gas would be difficult to measure, and so the Keqfor the reaction can more easily
be calculated from the∆G°, which is equal to 173.4 kJ/mol.
Step 1: List the known values and plan the problem.
Known
- ∆G° = +173.4 kJ/mol
- R = 8.314 J/K•mol
- T = 25°C = 298 K
Unknown
- Keq=?