Half-Life of Reaction

What is this formula?

The half-life of a reaction is the time required for the concentration of a reactant to decrease to one-half of its initial value.

For first-order reactions, the half-life is constant and depends only on the rate constant.

When to use it

Use this formula when analyzing first-order reactions, radioactive decay, pharmaceutical degradation, and many natural exponential decay processes.

Example

Given:

k = 0.035 s^-1

Formula:

t½ = ln(2)/k

Substitution:

t½ = 0.693/0.035

Result:

t½ = 19.8 s

After 19.8 seconds, the reactant concentration will have decreased to one-half of its original value.

Applications

Chemical kinetics

Radioactive decay

Pharmaceutical stability

Environmental chemistry

Reaction engineering

Note

This formula applies specifically to first-order kinetics. Unlike first-order reactions, the half-life of zero-order and second-order reactions depends on the initial concentration and therefore changes as the reaction proceeds.

Because of its simplicity and broad applicability, the first-order half-life is the most commonly reported half-life in chemistry, pharmacology, and nuclear science.