Question

If the mechanism of a chemical equilibrium consists of two reversible elementary steps, each with its own equilibrium constant Kc1 and Kc2, what expression relates the equilibrium constant Kc for the overall equilibrium to the two constants Kc1 and Kc2?

Answer 1

The overall equilibrium constant (Kc) = Kc1 * Kc2

Le'ts consider the following equilibria.

A B; Kc1 ...... Equilibrium 1

Kc1 = [B]/[A]

B C; Kc2 ...... Equilibrium 2

Kc2 = [C]/[B]

The overall equilibrium can be obtained by adding both the equilibria 1 and 2, as follows.

A C; Kc ...... Equilibrium 3

Here, Kc = [C]/[A]

= [B]/[A] * [C]/[B]

= Kc1 * Kc2

Therefore, Kc = Kc1 * Kc2