1.1 What is Chemistry?

http://www.ck12.org Chapter 19. Chemical Equilibrium

The Equilibrium Constant (K

The Law of Mass Action

Consider again a generic reversible reaction in which reactants A and B react to form products C and D. This
equilibrium is shown below, where the lower case letters represent the coefficients of each substance.

aA+bBcC+dD

Let’s assume that this reaction occurs by a single elementary step. If that were the case, the rate law for the forward
reaction would have the following form:

Ratef orward=kf[A]a[B]b

where the concentrations of each reactant, indicated by the square brackets around the formula, are measured in
molarity units (mol/L).

Similarly, the rate law for the reverse reaction can be written using the concentrations of C and D (the reactants for
the reverse process):

Ratereverse=kr[C]c[D]d

In a reaction at equilibrium, the rate of the forward reaction equals the rate of the reverse reaction. Mathematically,
this means the following:

Ratef orward=Ratereverse

kf[A]a[B]b=kr[C]c[D]d

kf

kr

=

[C]c[D]d

[A]a[B]b

The ratio of the two rate constants would just be another constant. This new constant, written as Keq, Kc, or simply
K, is known as theequilibrium constantfor this reaction. Theequilibrium constant expressionhas the following
form:

Keq=[C]

c[D]d

[A]a[B]b

We derived this expression based on reactions that occur by a single elementary step. However, it turns out that the
equilibrium constant expression is valid for any reaction, even those that occur by a multi-step mechanism. For any
reaction at equilibrium, the ratio of product concentrations to reactant concentrations (along with the appropriate
exponents) is equal to a constant. This is known as thelaw of mass action.

Example 19.1

Write the equilibrium constant expression for the following reaction:

2SO 3 (g)2SO 2 (g)+O 2 (g)

Answer:

The products go in the numerator, and the reactant goes in the denominator. Any component that has a coefficient in
the balanced equation is raised to that power in the equilibrium constant expression.

Keq=[SO^2 ]

(^2) [O 2 ]
[SO 3 ]^2