What is the rate of reaction and how is it measured?

The rate of reaction describes how quickly reactant concentrations fall (or product concentrations rise) over time. It is measured as the change in concentration per unit time: rate = −(1/s) · Δ[A]/Δt, where s is the stoichiometric coefficient of reactant A. Units are mol L⁻¹ s⁻¹ for most solution-phase reactions.

What is the Arrhenius equation?

The Arrhenius equation k = A · exp(−Ea / RT) links the rate constant k to temperature T (in Kelvin). A is the pre-exponential (frequency) factor, Ea is the activation energy in J/mol, and R = 8.314 J mol⁻¹ K⁻¹. A higher Ea means k drops steeply as temperature falls; a lower Ea means the reaction is less sensitive to temperature changes.

How do I find activation energy from two rate constants?

Use the two-point Arrhenius form: ln(k₂/k₁) = −Ea/R · (1/T₂ − 1/T₁). Rearranging gives Ea = −R · ln(k₂/k₁) / (1/T₂ − 1/T₁). You need rate constants measured at two different temperatures. The "Activation energy" mode in this calculator does this automatically and shows every step.

What is the half-life of a first-order reaction?

For a first-order reaction t½ = ln(2) / k ≈ 0.6931 / k. Crucially, the half-life is constant — it does not depend on the initial concentration. For a second-order reaction t½ = 1 / (k · [A]₀), so each successive half-life doubles as the concentration falls.

How does reaction order affect the rate law?

If r = k[A]^m, then order m controls how sensitively rate responds to [A]. For m = 0 (zeroth order) rate is constant. For m = 1 (first order) rate is proportional to [A]. For m = 2 (second order) doubling [A] quadruples the rate. The overall order equals the sum of all individual orders (m + n + ...).

What is the difference between average rate and initial rate?

Average rate = total change in concentration divided by total elapsed time — it smears out any curvature in the concentration–time profile. Initial rate is the instantaneous rate at t = 0, approximated by the slope of the tangent to the concentration–time curve at the start. Initial rates are preferred for determining rate laws because no products have yet built up to cause reverse reactions.

Yes. Every calculation runs entirely in your browser using JavaScript. No concentrations, temperatures, or rate constants are ever sent to a server.

Rate of Reaction Calculator

Chemical kinetics underpins everything from industrial reactor design to drug metabolism to food spoilage. This calculator consolidates six essential rate-of-reaction calculations in one place — no pen, paper, or spreadsheet required.

What it covers

Mode	Formula	Typical use
Average rate	`rate = −(1/s) · Δ[A]/Δt`	Lab titration data
Initial rate (tangent)	`r₀ ≈ ([A]₀ − [A]ₜ)/t`	Determining rate laws from experiments
Arrhenius k	`k = A · exp(−Ea/RT)`	Predicting k at any temperature
Rate law	`r = k[A]^m[B]^n`	Computing rate from concentrations
Half-life	`t½ = ln2/k` or `1/(k[A]₀)`	Decay and clearance problems
Activation energy	`Ea = −R·ln(k₂/k₁)/(1/T₂−1/T₁)`	Experimental Ea from two k/T pairs

How it works

Average rate uses the standard definition: the negative of the concentration change of a reactant divided by the time interval and its stoichiometric coefficient. The sign convention ensures a positive rate whether you track a reactant falling or a product rising.

Initial rate approximates the tangent to the concentration–time curve at t = 0. Use the smallest measurable time interval for highest accuracy; the approximation improves as t approaches zero.

Arrhenius equation — k = A · exp(−Ea / RT) — takes the pre-exponential factor A (units match k), the activation energy Ea in J/mol, and the absolute temperature T in Kelvin. The universal gas constant R = 8.314 J mol⁻¹ K⁻¹ is built in.

Rate law evaluates r = k[A]^m[B]^n. Enter fractional or decimal orders; the calculator handles non-integer exponents (common in enzyme kinetics and heterogeneous catalysis).

Half-life covers both first-order (t½ = ln 2 / k, concentration-independent) and second-order (t½ = 1 / (k · [A]₀), which lengthens as the reaction proceeds).

Activation energy from two points rearranges the Arrhenius equation into its linear two-point form. Measure k at two temperatures T₁ and T₂ and the calculator returns Ea in both J/mol and kJ/mol.

Worked example — Arrhenius at 298 K and 350 K

A reaction has A = 1 × 10¹³ s⁻¹ and Ea = 75,000 J/mol.

At T = 298 K: k = 10¹³ × exp(−75000 / (8.314 × 298)) = 10¹³ × exp(−30.27) ≈ 0.713 s⁻¹

At T = 350 K: k = 10¹³ × exp(−75000 / (8.314 × 350)) = 10¹³ × exp(−25.77) ≈ 64.0 s⁻¹

Feeding those two k/T pairs into the activation energy mode returns Ea ≈ 75,000 J/mol — confirming the round-trip. Notice that a 52 K rise multiplied k by roughly 90×, illustrating why even modest temperature increases dramatically accelerate reactions with large Ea.

Formula reference

All six formulas use standard IUPAC notation. Concentrations are in mol L⁻¹ (molarity), temperatures in Kelvin, energies in J/mol, and time in seconds unless the rate constant units imply otherwise. The rate constant k carries composite units that depend on overall reaction order: s⁻¹ for first order, L mol⁻¹ s⁻¹ for second order, L² mol⁻² s⁻¹ for third order.

Every result includes a step-by-step working box so you can verify each arithmetic operation — useful for checking exam answers or debugging a lab calculation.