At a given temperature, the rates of two first order reactions, `A rarrB and Crarr D " are " k_(1) and k_(2)` respectively. If `k_(1)ltk_(2)` , then which of these reactions will have a shorter half-life?

Explanation

The half-life of a first order reaction is `t_(1//2)=(0.693)/(k)` indicating that `t_(1//2)prop(1)/(k)` at a given temperature. Therefore, a reaction with a larger rate constant (k) has a shorter half-life Hence, the reaction `CrarrD` will have a shorter half-life ,as its k is larger than the value of k for the reaction `ArarrB`.