Question

How is the rate constant of a first order reaction related to the half-life of the reaction?

Answer 1

The rate constant (k) of a first-order reaction is directly related to its half-life (t_1/2) by the following equation:

`t_(1//2) = 0.693/k`

For a first-order reaction, the time it takes for the concentration of the reactant to be reduced by half is independent of the initial concentration. The half-life remains constant throughout the reaction. The smaller the rate constant (k), the longer the half-life (t_1/2), and vice versa. This relationship is derived from the integrated rate law for first-order reactions:

`k = 2.303/t log [R]_0/[R]`