First-Order Rate Law

\[[A]=[A]_0 e^{-kt}\]

Variables

Areactant concentration at time t (mol/L)

A0initial reactant concentration (mol/L)

kfirst-order rate constant (s⁻¹)

ttime (s)

Description

What is this formula?

The first-order rate law describes the exponential decrease of a reactant concentration when the reaction rate is proportional to the concentration of one reactant.

When to use it

Use this formula for first-order reactions, radioactive decay, unimolecular decomposition, solvolysis reactions, and many degradation processes.

Example

Given:

A0 = 0.80 mol/L

k = 0.030 s^-1

t = 25 s

Formula:

A = A0 e^(-kt)

Substitution:

A = 0.80 × e^(-0.030×25)

Result:

A = 0.378 mol/L

Applications

Chemical kinetics

Decomposition reactions

Organic reaction mechanisms

Pharmaceutical degradation

Environmental chemistry

Note

This integrated rate law applies when the reaction follows first-order kinetics under the conditions studied. Real systems may deviate from first-order behavior due to competing reactions, changes in mechanism, catalyst deactivation, transport limitations, or non-ideal reaction conditions.