For a reaction, A B , rate equation is ' r=K[A]^ ' If initial concentration of reactant is 'a' mol~ dm ⁻³ find half life time of reaction.

Step-by-step solution

The reaction A B follows a zero-order rate law r = K[A]^0 , where the rate is independent of reactant concentration. The integrated rate law for zero-order kinetics is [A]_t = [A]₀ - Kt . At half-life t_ 1/2 , the concentration reduces to [A]_ t_ 1/2 = [A]₀ 2 . Substituting into the rate law: [A]₀ 2 = [A]₀ - K t_ 1/2 Solving for t_ 1/2 yields: K t_ 1/2 = [A]₀ - [A]₀ 2 = [A]₀ 2 t_ 1/2 = [A]₀ 2K Given [A]₀ = a , the half-life becomes t_ 1/2 = a 2K , which corresponds to option D. Final answer: D