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].
- [A] = 1.00 e^(−0.001×600) = e^(−0.6) ≈ 0.549 M.
- 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.
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