Rate Constant Calculator

Explore reaction order, concentration curves and half-life — with units that make sense.

Kinetic measurements

rate = k[A]^m[B]ⁿ

Reaction rateConcentration [A]Order in A · morder Include reactant B

Optional second reactant with its own concentration and partial order.

Display time

Model & assumptions

The input rate is the disappearance rate −d[A]/dt, or an already normalized rate using a consistent stoichiometric convention. Single-reactant projections use −d[A]/dt = k[A]^q. The optional product curve assumes a 1:1 irreversible conversion at constant volume, initially with no product.

A+B data alone does not specify both trajectories. Confirm constant B only when experimentally justified. Fractional differential orders from 0 to 5 per reactant are supported.

Orders are experimental inputs. A single rate measurement cannot establish reaction order.

Unit derivation

Total order · m + n1

[k] = M^{1 − (m+n)} · s⁻¹s⁻¹

Equivalent rate constant3.000 min⁻¹

Rate constant & concentration profile

RATE CONSTANT · k0.0500 s⁻¹

First-order disappearance of A · reference concentration 0.100 M

Total order1.00

Initial half-life13.86 s

90% conversion46.05 s

Concentration vs. time

Single-reactant model

Reactant [A]Product [P] · 1:1

20.0 s · [A] = 0.0368 M

Model projection at fixed conditions, not measured experimental data.

How reaction order changes the curve

Normalized comparison

Zero orderFirst orderSecond order

Equal starting concentration and equal initial half-life. Each curve uses its own dimensionally appropriate k.

Concentration & conversion table

The same first-order model at selected times.

Time	[A] remaining	Conversion
0 s	0.1000 M	0.0%
10 s	0.0607 M	39.3%
20 s	0.0368 M	63.2%
30 s	0.0223 M	77.7%
60 s	0.0050 M	95.0%

Half-life depends on the model.

For a first-order process, t½ = ln(2)/k. Zero- and second-order half-lives also depend on the starting concentration.

From reactant to product

A compact molecular view of the same illustrative A → P conversion.

Start100% A · 0 s

1 half-life50% A · 13.86 s

2 half-lives25% A · 27.73 s

The particles are a teaching model

Blue represents A; teal represents P. Fewer A particles remain as the reaction progresses.

The snapshots illustrate fractions, not actual molecule counts or a molecular mechanism.

[A]ₜ = [A]₀e^−kt
[P]ₜ = [A]₀ − [A]ₜ

Formula & worked example

k = rate / ([A]^m[B]ⁿ)

For rate = 0.005 M/s, [A] = 0.100 M and m = 1:

k = 0.005 / 0.100 = 0.0500 s⁻¹
t½ = ln(2) / 0.0500 = 13.86 s

Integrated and half-life modes use −d[A]/dt = k[A]^q with q = 0, 1 or 2. Rate definitions and stoichiometric conventions must remain consistent.

Frequently asked questions

Why do the units of k change?

Rate has concentration per time units. Dividing by the concentration factors leaves M raised to one minus the total order, per unit time.

Can reaction order be fractional?

Yes. Empirical partial orders need not be integers; they should come from experimental evidence.

Can I infer order from one measurement?

No. A rate and a concentration alone cannot identify both order and k. Multiple controlled measurements are required.

Is the product curve always valid?

No. Here it assumes a one-to-one irreversible conversion at constant volume, initially with no product.

Does a high k always mean a faster reaction?

Compare k only with compatible orders, units and conditions. The actual rate also depends on concentrations.

Live calculation requires JavaScript. The displayed values are a fixed first-order example: rate 0.005 M/s, [A] 0.100 M and k 0.0500 s⁻¹. Formulas and source text remain readable.

Sources & Reference Guides

IUPACIUPAC Gold BookRate laws, partial orders and rate coefficients.NISTNIST Chemical Kinetics DatabaseReference data for gas-phase reactions.

OpenStax Chemistry 2e, §12.4 · Integrated rate laws
Independent references, no institutional endorsement.

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