Half life of a first order reaction is 3 minute. What is the time required to reduce the concentration of reactant by 90 % of its initial concentration?

Step-by-step solution

First-order kinetics govern this reaction, using the half-life relation t_ 1/2 = 0.693 k . With t_ 1/2 = 3 min , the rate constant becomes k = 0.693 3 = 0.231 min ⁻¹ . Reducing the concentration by 90% leaves 10% remaining, so [A]_t = 0.10[A]₀ . The integrated rate law ( [A]₀ [A]_t ) = kt yields (10) = kt . Substituting gives 2.303 = 0.231t , solving to t 9.97 min , which corresponds to option C.