The equilibrium constant is given for two of the reactions below. Determine the value of the missing equilibrium constant.

A(g) + B(g) ? AB(g) Kc = 0.24

AB(g) + A(g) ? A2B(g) Kc = 3.8

2 A(g) + B(g) ? A2B(g) Kc = ?

A. 4.0

B. 0.91

C. 3.6

D. 16

E. 0.63

B. 091

Explanation:

When we add these two equilbria, the equilibrium constant for the resultant equilibrium is the product of the first two.

Notice that when we add the first two reactions in this question, we obtain the equilibrium for which we are seeking its equilibrium constant. Therefore,

A(g) + B(g) ? AB(g)           Kc₁ = [AB] / [A][B]          

                             +

AB(g) + A(g) ? A2B(g)       Kc₂ = [A₂B] /[ AB][A]

   2 A(g) + B(g)  ⇄ A₂B(g)    Kc₃ = [A₂B] / [A]²[B]

Kc₁Kc₂ =  [AB] / [A][B]  x  [A₂B] / [AB][A] =  [A₂B] / [A]²[B]

Thus,

Kc₃ = 0.24 x 3.8 = 0.91

This procedure is not limited to two reaction, it could done for more than two, as long as the desired equilibrium is the desired one.