Chemical Kinetics Calculator
Calculate reaction rate, half-life and concentration over time for zero, first and second order reactions using the rate constant k.
What this calculator does
Choose zero, first or second order, enter the rate constant and concentrations, and get the rate, the half-life or the concentration remaining after a given time.
When you need it
Kinetics tells you how fast a reaction runs. Half-lives and rate constants are used for drug dosing, shelf life, environmental chemistry and finding reaction mechanisms.
Formulas
- rate = k[A]ⁿ
- First order: [A] = [A]₀ e^(−kt), t½ = ln 2 ÷ k
- Zero order: [A] = [A]₀ − kt, t½ = [A]₀ ÷ 2k
- Second order: 1/[A] = 1/[A]₀ + kt, t½ = 1 ÷ k[A]₀
How to use it
- Choose whether you want the rate, the half-life or the integrated rate law.
- Select the reaction order.
- Enter k and the concentrations (and the time for the integrated law).
- Read the result and the substitution.
Worked example
A first-order reaction has k = 0.0150 s⁻¹. Find the half-life and the concentration after 100 s starting from 1.00 M.
- t½ = ln 2 ÷ k = 0.693 ÷ 0.0150 = 46.2 s
- [A] = 1.00 × e^(−0.0150 × 100) = 1.00 × e^(−1.5) = 0.223 M
Answer
The half-life is 46.2 s, and 0.223 M remains after 100 s.
Common mistakes
- Using the half-life formula of the wrong order.
- Mixing time units, such as k in s⁻¹ and t in minutes.
- Assuming the order from the coefficients of the balanced equation instead of from experiment.
Related tools
Frequently asked questions
How do you find the half-life of a first-order reaction?
t½ = ln 2 ÷ k, which does not depend on the starting concentration.
What is the rate constant k?
The proportionality constant in the rate law. Its units depend on the reaction order.
How do I know the reaction order?
It is found from experiments, for example by seeing how the rate changes when the concentration changes.