How this instrument works
The rate constant, k, is the proportionality factor in a reaction's rate law — the equation describing how a reaction's speed depends on reactant concentration. For a reaction involving a single reactant A, the rate law takes one of three basic forms depending on the reaction's order: rate = k for zero order (independent of concentration), rate = k[A] for first order (directly proportional to concentration), or rate = k[A]^2 for second order (proportional to the square of concentration). Each rearranges to a different formula for k.
Reaction order isn't something you choose or assume — it's determined experimentally, typically by measuring how rate changes as concentration changes across several trials. Once that's known, though, finding k from a single rate-and-concentration measurement is just algebra: divide rate by concentration for first order, or by concentration squared for second order, or read k directly off that value for zero order (since concentration doesn't enter that case at all).
One property of the rate constant is easy to get backwards: k itself does not depend on the concentrations you plug in to find it — it's a fixed property of the reaction at a given temperature, changing only with temperature (and catalysts), not with how much reactant happens to be present at the moment you measure it. Different rate/concentration pairs from the same reaction at the same temperature should all yield the same k, whatever order that reaction actually follows.
- Choose the reaction's order from the Reaction order dropdown — zero, first, or second — based on how the reaction's rate is known to depend on concentration.
- Enter the measured reaction rate into Reaction rate.
- Enter the reactant concentration at which that rate was measured into Concentration, [A].
- Read Rate constant, k below the inputs — its unit changes with reaction order, so check units against your specific reaction before reporting a result.
Worked example — a first-order reaction
Select First order from Reaction order, enter 0.5 into Reaction rate, and enter 2 into Concentration, [A]. Rate constant, k reads 0.25: k = rate / [A] = 0.5 / 2 = 0.25 (units of inverse time, such as per second, for a first-order reaction).
That k = 0.25 describes the reaction's intrinsic speed at whatever temperature the measurement was taken — if you instead measured this same reaction at a concentration of 4 M and it still gave a rate of 1 M/s (since 0.25 x 4 = 1), that would confirm k really is 0.25 regardless of which concentration you happened to measure it at, which is exactly the internal consistency check a first-order rate constant should pass.
Questions
How do I know if my reaction is zero, first, or second order?
Reaction order is determined experimentally, not by looking at the balanced chemical equation — the standard method is to measure the initial rate at several different starting concentrations of the reactant and see how it scales with concentration (unchanged means zero order, proportional means first order, proportional to the square means second order). This calculator assumes you already know that from experimental determination; it doesn't work it out itself.
Does the rate constant depend on the concentration I enter?
No — that's the entire point of a rate constant. It's a fixed property of the reaction (at a given temperature) that doesn't change with concentration; concentration is just one of the inputs used to calculate what that fixed k value equals. If two different rate/concentration measurements from the same reaction at the same temperature give noticeably different k values, that's usually a sign the assumed reaction order is wrong.
What does change the rate constant, if not concentration?
Temperature is the main factor — rate constants increase with temperature, following the Arrhenius equation, which describes k's dependence on temperature and activation energy. A catalyst can also change k by providing an alternate reaction pathway with a lower activation energy. Concentration, by contrast, affects the reaction's overall rate but not the value of k itself.
Why do the units of k change with reaction order?
Because rate always has the same units (concentration per time, such as M/s), but the denominator changes with order — dividing by concentration once (first order) or twice (second order, effectively concentration squared) changes what units are needed to make the equation balance. Zero-order k has the same units as rate itself; first-order k has units of inverse time; second-order k has units of inverse concentration times inverse time.
Can this handle reactions with two different reactants, like rate = k[A][B]?
Not directly — this calculator is built for single-reactant kinetics (zero, first, or second order in one reactant, A). A reaction whose rate law depends on two separate reactant concentrations needs both concentrations to solve for k (k = rate / ([A][B]) for that mixed-order case), which is outside this calculator's single-concentration input.