Reaction: A(g) + B(g) ⇌ C(g) + D(g), occurs in a single step. The rate constant of forward reaction is 2.0 × 10⁻³ mol⁻¹ L s⁻¹. When the reaction is started with equimolar amounts of A and B, it is fou

Question

Reaction: A(g) + B(g) ⇌ C(g) + D(g), occurs in a single step. The rate constant of forward reaction is 2.0 × 10⁻³ mol⁻¹ L s⁻¹. When the reaction is started with equimolar amounts of A and B, it is found that the concentration of A is twice that of C at equilibrium. The rate constant of the backward reaction is

Prashant Kotian · Accepted Answer

Correct answer: B. Initial [A] = a, [B] = a. At equilibrium, [A] = a-x, [B] = a-x, [C] = x, [D] = x. Given [A] = 2[C], so a-x = 2x, meaning x = a/3. Eq concentrations: [A]=[B] = 2a/3, [C]=[D] = a/3. K_c = ([C][D]) / ([A][B]) = (a/3 × a/3) / (2a/3 × 2a/3) = 1/4 = 0.25. K_c = k_f / k_b => k_b = k_f / K_c = 2.0 × 10⁻³ / 0.25 = 8.0 × 10⁻³ mol⁻¹ L s⁻¹. Therefore, correct answer is B.

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