This example problem demonstrates how to find the equilibrium constant of a reaction from equilibrium concentrations of reactants and products.

### Problem:

For the reaction

H_{2}(g) + I_{2}(g) ↔ 2 HI(g)

At equilibrium, the concentrations are found to be

[H_{2}] = 0.106 M

[I_{2}] = 0.035 M

[HI] = 1.29 M

What is the equilibrium constant of this reaction?

### Solution

The equilibrium constant (K) for the chemical equation

aA + bB ↔ cC + dD

can be expressed by the concentrations of A,B,C and D at equilibrium by the equation

K = [C]^{c}[D]^{d}/[A]^{a}[B]^{b}

For this equation, there is no dD so it is left out of the equation.

K = [C]^{c}/[A]^{a}[B]^{b}

Substitute for this reaction

K = [HI]^{2}/[H_{2}][I_{2}]

K = (1.29 M)^{2}/(0.106 M)(0.035 M)

K = 4.49 x 10^{2}

### Answer:

The equilibrium constant of this reaction is 4.49 x 10^{2}.