Question

If you know a reaction’s half-life, can you determine its rate constant? What other information do you need?

Short answer

Yes, half-life of a reaction can be determined through its rate constant without any other information.

Step-by-step solution

Definition of half-life

A reaction's half-life is the time it takes for a reactant's concentration to drop to half of its starting value.

Half-life of a reaction

The half-life of a reaction can be calculated as,

$t_{1/2}=\frac{\ln \left(2\right)}{K}=\frac{0.693}{K}$

Thus, concentration of the reactant will be half of initial equation as,

$t_{1/2}=\frac{0.693}{K}$

Half-life of a first order reaction

The half-life of a first-order reaction is constant across time and is independent of concentration. The reactant's half-life is $\frac{\ln \left(2\right)}{k}$in a first-order reaction, where is the reaction's rate constant.