Question

For the equilibrium reaction: \[ N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g) \] At a certain temperature, the equilibrium constant \( K_c \) is 4.0. If the concentrations of \( N_2 \), \( H_2 \), and \( NH_3 \) are 0.2 M, 0.6 M, and 0.4 M, respectively, calculate the reaction quotient \( Q_c \) and determine whether the reaction is at equilibrium.

• A. \( Q_c = 1.2 \), the reaction will shift to the left.
• B. \( Q_c = 4.0 \), the reaction is at equilibrium.
• C. \( Q_c = 2.0 \), the reaction will shift to the right.
• D. \( Q_c = 0.5 \), the reaction will shift to the left.

Hint:

If \( Q_c < K_c \), the reaction will shift towards the products (right). If \( Q_c > K_c \), the reaction will shift towards the reactants (left).

Answer 1

The Correct Option is D

The reaction quotient \( Q_c \) is calculated using the same expression as the equilibrium constant, but with the concentrations of the reactants and products at a given moment, not necessarily at equilibrium: \[ Q_c = \frac{[NH_3]^2}{[N_2][H_2]^3} \] Substitute the given concentrations: \[ Q_c = \frac{(0.4)^2}{(0.2)(0.6)^3} = \frac{0.16}{0.2 \times 0.216} = \frac{0.16}{0.0432} \approx 3.7 \] Since \( Q_c = 3.7 \), which is less than the equilibrium constant \( K_c = 4.0 \), the reaction will shift to the left to reach equilibrium. Thus, the reaction will shift to the left.