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The equilibrium constant of the following are: N2 + 3H2 ⇌ 2NH3 K1 N2 + O2 ⇌ 2NO K2 H2 + 1/2 O2 ⇌ H2O K3 The equilibrium constant (K) of the reaction: 2NH3 + 5/2 O2 ⇌ 2NO + 3H2O, will be:

1. K2K3^3 / K1
2. K2K3 / K1
3. K2^2K3^3 / K1
4. K1K3^3 / K2

Correct answer: K2K3^3 / K1

Solution

To derive the equilibrium constant for the given reaction, we manipulate the given reactions and their equilibrium constants. The reverse of the first reaction gives 2NH3 ⇌ N2 + 3H2 with equilibrium constant 1/K1. Adding this to the second and third reactions (appropriately scaled) gives the desired reaction, and the equilibrium constant becomes K2K3^3 / K1.

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