Chemistry

Kinetics Calculator

Use zero-, first-, and second-order integrated rate laws to find concentration, time, k, or half-life.

Kinetics calculator

Zero-, first-, and second-order integrated rate laws

ln[A] = ln[A]₀ − kt

k
0.001
693.147
[A]ₜ
0.548812 M
t
600

First-order half-life is independent of [A]₀.

Assumes a single-reactant integrated rate law with a constant rate constant. Use M for concentration and one consistent time unit throughout.

What is the Kinetics Calculator?

Chemical kinetics describes how fast concentrations change. For elementary decay of a single reactant, the integrated rate laws for orders 0, 1, and 2 relate [A], t, and k. Half-life t½ is the time for [A] to fall to half of its initial value; only first-order t½ is independent of [A]₀.

The Kinetics Calculator solves for remaining concentration, time, rate constant, or half-life once you choose the order and provide the known quantities.

  • Zero order: [A] = [A]₀ − kt
  • First order: ln[A] = ln[A]₀ − kt
  • Second order: 1/[A] = 1/[A]₀ + kt

Mathematical / chemical formulas

Half-lives:

0th: t½ = [A]₀ / (2k)
1st: t½ = ln 2 / k
2nd: t½ = 1 / (k[A]₀)

Step-by-step example: First-order remaining concentration

[A]₀ = 1.00 M, k = 0.001 s⁻¹, t = 600 s. Find [A].

  1. [A] = 1.00 e^(−0.001×600) = e^(−0.6) ≈ 0.549 M.
  2. t½ = ln2 / 0.001 ≈ 693 s.

Order 1, Find [A]ₜ, k = 0.001, [A]₀ = 1, t = 600.

Frequently asked questions

How do I know the order?

From experiment: linear plots of [A], ln[A], or 1/[A] versus time identify orders 0, 1, or 2. The calculator does not invent the order—you select it from the problem statement or data analysis.

What units does k have?

They depend on order: M/time (0), 1/time (1), 1/(M·time) (2). Keep time units consistent throughout.

References & further reading

Standards bodies, university open courseware, and peer-reviewed references that align with the methods used on this page.

Keep learning with more calculators and study guides on Online Science Tools.

Practice problems & worked examples

Practice alongside the kinetics above. Each problem includes a full worked solution so you can check your reasoning step by step.

Practice problem 1

First-order half-life

k = 0.001 s⁻¹ for a first-order decay. Find t½.

Show solution

Worked solution

  1. t½ = ln 2 / k ≈ 0.693 / 0.001 = 693 s.

Answer: t½ ≈ 693 s

Practice problem 2

Remaining concentration

[A]₀ = 1.0 M, first-order k = 0.001 s⁻¹, t = 600 s. Find [A].

Show solution

Worked solution

  1. [A] = e^(−0.6) ≈ 0.549 M.

Answer: [A] ≈ 0.549 M

Practice problem 3

Second-order half-life

Second order, k = 0.50 L/(mol·s), [A]₀ = 0.20 M. Find t½.

Show solution

Worked solution

  1. t½ = 1/(k[A]₀) = 1/(0.50×0.20) = 10 s.

Answer: t½ = 10 s

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