What this calculator does
The rate constant k links a reaction's rate to the concentrations of its reactants, through the rate law: rate = k[A]ᵐ[B]ⁿ, where m and n are the reaction orders in each reactant. Given one measured rate at known concentrations, the rate law rearranges directly to solve for k.
This differs from finding k via the integrated rate law (which uses a full concentration-versus-time data set) or via the Arrhenius equation (which finds k at a different temperature from an already-known k and activation energy). This calculator instead works from a single rate measurement, the most direct route when the reaction orders are already known from a separate kinetics study.
The formula
Raise the concentration of A to its reaction order, and, if a second reactant is involved, raise its concentration to its own order and multiply the two together. Divide the measured rate by that product to get the rate constant k.
| Term | Meaning |
|---|---|
| k | The rate constant, whose units depend on the overall reaction order. |
| m, n | The reaction orders in A and B respectively, determined experimentally, not read off the balanced equation. |
| Overall order | m + n, which sets the units of k (per second for order 1, L/(mol·s) for order 2, and so on). |
The inputs explained
| Field | What to enter |
|---|---|
| Measured reaction rate (mol/(L·s)) | The measured initial reaction rate at the concentrations given. |
| Concentration of A, [A] (mol/L) | The concentration of reactant A at the moment the rate was measured. |
| Order in A (m) | The experimentally determined reaction order in A. |
| Concentration of B, [B] (leave at 1 if only one reactant) (mol/L) | The concentration of a second reactant B, if the rate law includes one; leave at 1 with an order of 0 if there is only one reactant. |
| Order in B (n), leave at 0 if only one reactant | The experimentally determined reaction order in B; leave at 0 for a single-reactant rate law. |
When to use it
Finding k from a single kinetics measurement
Once reaction orders have been established (from an initial-rates study or elsewhere), a single rate measurement at known concentrations is enough to compute k directly.
Checking units against reaction order
The units of k change with overall reaction order, which is a common source of confusion; this calculator reports the overall order alongside k so the units can be checked.
Working with a two-reactant rate law
For reactions with a rate law depending on two reactants, both concentrations and both orders are needed to isolate k, since neither alone determines the overall rate.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the rate constant and its units change with reaction order in A
The same measured rate and concentration, at a range of reaction orders.
| Order in A (m) | Rate constant k | Overall reaction order |
|---|---|---|
| 0 | 0.002 mol/(L·s) | 0.00 |
| 1 | 0.004 /s | 1.00 |
| 2 | 0.008 L/(mol·s) | 2.00 |
| 3 | 0.016 (mol/L)^-2/s | 3.00 |
Questions
How do I know the reaction orders m and n?
They must be determined experimentally, typically from an initial-rates study across several concentrations, and cannot in general be read directly from the stoichiometric coefficients of the balanced equation except for elementary reactions.
What are the units of k for a second-order reaction?
L/(mol·s), since dividing a rate in mol/(L·s) by a concentration squared (mol/L)² leaves a factor of L/(mol·s). Units of k always adjust to make the rate law dimensionally consistent, given the overall reaction order.
What if my reaction only has one reactant?
Leave the concentration of B at 1 and its order at 0; then [B]⁰ contributes a factor of 1 and drops out of the calculation entirely, leaving k = rate ÷ [A]ᵐ.
How is this different from using the integrated rate law?
The integrated rate law extracts k from how concentration changes over an entire reaction, using a whole time-course data set, and can itself be used to determine the reaction order. This calculator instead assumes the order is already known and solves for k from one rate measurement.
To find k from a full concentration-versus-time data set instead, see the rate constant from concentration vs. time calculator. To find k at a different temperature from a known activation energy, see the Arrhenius equation calculator.