# Equilibrium Constant

Learning Goals

In this section you will learn of an important relationship between the equilibrium constant for a reaction and the change in Gibbs free energy for the reaction.

Synopsis

The reaction free energy is the change in G due to the displacement (or advancement) of the reaction and is given by the symbol G. If the reaction is at equilibrium G will be zero for at equilibrium there is no further net advancement of the reaction. For the reaction

aA + bB cC + dD

the reaction quotient (Chapter 16) is Q = [C]c[D]d/([A]a[B]b) and the relationship between the reaction free energy, the reaction quotient and the Gosystem is

G = [delta]Go + RTlnQ

At equilibrium, 0 = Go + RTlnKc where Kc is the value of the reaction quotient at equilibrium and is the thermodynamic equilibrium constant:

K = [C]c[D]d/([A]a[B]b)equil

We then have that Go = -RTlnKc which is a very useful equation. From this equation we can use values of thermodynamic data to calculate equilibrium constants. If the reactants and products are gases the Q will be expressed in terms of the partial pressures of the gases rather than the concentrations and the corresponding equilibrium constant would be written as Kp.

In section 16.3 we determined that

• When Q > K the reaction will proceed toward the reactants until equilibrium is established.
• When Q < K the reaction will proceed toward the products until equilibrium is established.
We also see from Go = -RTlnKc that if K > 1, Go will be negative so that the products will be favored at equilibrium. If K is less than 1, Go will be positive and the reactants will be favored at equilibrium. These observations are neatly seen in Figure 20.11 in your text.

Review Question

1. Work problems 38 and 40 in your text.
2. For the reaction NO(g) + O3(g) --> NO2(g) + O2(g), calculate Go and K at 298 (assumed to be at equilibrium). See problem at end of last section for data.
3. The partial pressure data for the above reaction are determined to be: PNO = 0.440 atm, PO3 = 0.211 atm, PNO2 = 0.321 atm, and PO2 = 0.167 atm. Will the reaction proceed toward the products or toward the reactants on its way to equilibrium?

Web Author: Dr. Leon L. Combs