Exemplar Problems

Problem 4 : Consider the following reaction at a certain temperature:

N₂(g) + 3H₂(g) ⇌ 2NH₃(g) The equilibrium constant Kc for this reaction is 0.05. If the initial concentration of NH₃ is 0.2 M, calculate the equilibrium concentrations of N₂ and H₂.

Solution :

Let’s denote the initial concentration of NH₃ as [NH₃]₀, and the equilibrium concentrations of N₂ and H₂ as [N₂] and [H₂], respectively. We are given: [NH₃]₀ = 0.2 M Kc = 0.05

Using the balanced equation, we know that at equilibrium: [N₂] = [N₂]₀ + x [H₂] = [H₂]₀ - 3x [NH₃] = [NH₃]₀ - 2x

Now, we can write the expression for Kc: Kc = ([NH₃]²) / ([N₂] * [H₂]³)

Substitute the expressions for [N₂], [H₂], and [NH₃]: 0.05 = ([NH₃]₀ - 2x) * ([N₂]₀ + x) * ([H₂]₀ + 3x)³ / ([N₂]₀ * [H₂]₀³ * [NH₃]₀²)

Now, solve for x. Since the calculation can be quite complex, you can use numerical methods or a calculator to find the value of x.