A first-order reaction has a half-life of 100 s . If the initial concentration of the reactant is 0.2 M , what will be the instantaneous rate of the reaction after 200 s ?

Step-by-step solution

The rate constant k for a first-order reaction is related to its half-life by: k = 0.693 t_ 1/2 = 0.693 100 = 6.93 10⁻³ s ⁻¹ The time elapsed is 200 s , which corresponds to exactly two half-lives ( n = 200 100 = 2 ). The concentration of the reactant remaining after two half-lives is: [A]_t = [A]₀ 2^n = 0.2 2^2 = 0.2 4 = 0.05 M The instantaneous rate of the reaction at this time is given by the differential rate law: Rate = k[A]_t = (6.93 10⁻³ s ⁻¹) 0.05 M = 3.465 10⁻⁴ M s ⁻¹ Using the initial concentration instea