Question

A decomposition reaction has a rate constant of 0.0037 yr ⁻¹.

(a) What is the half-life of the reaction?
yr

(b) How long does it take for [reactant] to reach 12.5% of its original value?
yr

Answer 1

a)Rate constant is given as 0.0037Yr^-1. From th unit of rate constant, we get the order of reaction as first order.

For a first order reaction, t_1/2 = 0.693/ k

   Thus   half -life t 1/2 = 0.693/ 0.0037 = 187.297 Yr.

b)In first order reaction the half- life time does not depend on initial concentration . thus in first half life the reactant concentration decreases to 50% , in the second half-time to 25% and in the third half life to 12.5%.

Hence to reach 12.5% of original value, 3 half lifes are required. = 187.297 x 3 = 561.891 Yr.