Chemical Equilibrium: Diagram-Based Questions (1)

Question

For the reaction $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$, $0.5$ mol $N_2$ and $1.5$ mol $H_2$ are taken in a $1$ L container at $400$ K. At equilibrium, $0.4$ mol of $NH_3$ is formed. Calculate $K_c$.

Solution — Step by Step

Why This Works

The equilibrium constant $K_c$ depends only on temperature for a given reaction — it’s a thermodynamic quantity. The key step is converting “moles of $NH_3$ formed” into changes in all species using stoichiometry, then computing the equilibrium concentrations.

The $1$ L volume is important: concentrations equal moles. For other volumes, divide each mole figure by $V$.

Alternative Method

Use degree of dissociation. Let $\alpha$ = fraction of $N_2$ converted. Initial $N_2 = 0.5$, so $\alpha \times 0.5 = 0.2$, giving $\alpha = 0.4$. Then express equilibrium concentrations in terms of $\alpha$ and substitute. Useful when the question asks for $\alpha$ directly.

Common Mistake