Hong Life CalculatorsUnderstanding the rate constant calculator — concept and principle
This calculator finds a reaction's rate constant k from a measured rate and concentrations, from concentrations at two times using an integrated rate law, or from a half-life. It gives k with its units, the overall order, k per minute and per hour, the half-life and the initial rate. It is used in chemical kinetics courses and labs.
How it is calculated
Rate law: rate = k [A]^m [B]^n, so k = rate ÷ ([A]^m [B]^n); overall order = m + n
Integrated laws: zero order k = ([A]₀ − [A]) ÷ t; first order k = ln([A]₀/[A]) ÷ t; second order k = (1/[A] − 1/[A]₀) ÷ t
Half-lives: zero order [A]₀ ÷ 2k; first order ln 2 ÷ k; second order 1 ÷ (k [A]₀)
- Units of k: M^(1−order)·s⁻¹; per minute × 60, per hour × 3,600.
The principle
The rate law describes how a reaction's speed depends on the concentrations of reactants, raised to powers called orders that are found by experiment. The rate constant is what is left when the concentration dependence is taken out: it depends on temperature but not on concentration. Its units change with the order so that the rate always comes out in M/s. Integrating the rate law over time gives the concentration–time relations used with two measurements or a half-life.
Worked example
Default inputs: rate law, rate = 0.00024 M/s, [A] = 0.1 M (m = 1), [B] = 0.2 M (n = 1).
- Overall order = 1 + 1 = 2, so the units are M⁻¹·s⁻¹.
- k = 0.00024 ÷ (0.1 × 0.2) = 0.012 M⁻¹·s⁻¹.
- Per minute: 0.012 × 60 = 0.72; per hour: 43.2.
- Initial rate = 0.00024 M/s; the half-life row needs a single-reactant order, so it shows —.
| Order in A (m) | Rate constant k |
|---|---|
| 0.25 | 0.002134 |
| 0.5 | 0.003795 |
| 0.75 | 0.006748 |
| 1 | 0.012 |
| 1.25 | 0.02134 |
| 1.5 | 0.03795 |
| 2 | 0.12 |
How to read the result
Compare k only for the same reaction order and units. For first-order reactions the half-life is constant, so a quick check is whether successive half-lives are equal. A larger k means a faster reaction at the same concentrations; k usually rises steeply with temperature.
Common mistakes
- Using stoichiometric coefficients as orders without experimental evidence.
- Giving k without units.
- Mixing seconds and minutes.
- Using log₁₀ instead of the natural logarithm.
Frequently asked questions
What are the units of a first-order k?
s⁻¹.
Why is first-order half-life constant?
ln 2 ÷ k contains no concentration.
Are reaction orders the same as coefficients?
Not in general; they must be determined experimentally.
How does temperature affect k?
k usually increases strongly with temperature, as described by the Arrhenius equation.
Sources: OpenStax, Chemistry 2e (2019), sections 12.3 "Rate Laws" and 12.4 "Integrated Rate Laws"