Rate Constant Calculator

Calculate rate constant k from experimental rate and concentration data. Determine k for first order, second order, and zero order reactions from initial rates.

⏱️ Kinetics📐 k = rate / ([A]^m[B]^n)🧪 Chemistry

Observed reaction rate (mol/L·s)

[A] concentration (mol/L)

Reaction order m for A

[B] concentration (mol/L)

Reaction order n for B

Please enter valid values.

Formula & Reference

Variable	Symbol	Formula	Units
Rate Constant Calculator	See formula	k = rate / ([A]^m[B]^n)	varies with order

Step-by-Step Examples

Example 1

First Order k

Rate = 0.0100 mol/Ls, [A] = 0.200 M, m = 1.

k = rate/[A]^1 = 0.0100/0.200
k = 0.0500 s^-1

✓ k = 0.0500 s^-1 (first order)

Example 2

Second Order k

Rate = 0.0400 mol/Ls, [A] = 0.100 M, order 2.

k = 0.0400/(0.100)^2
k = 0.0400/0.0100 = 4.00 L/mols

✓ k = 4.00 L/mol-s

Example 3

Method of Initial Rates

Experiment 1: [A]=0.10 M, rate=5.0x10^-3. Experiment 2: [A]=0.20 M, rate=1.0x10^-2.

ratio: 1.0x10^-2/5.0x10^-3 = 2.0 when [A] doubled
2 = 2^m => m = 1 (first order)
k = 5.0x10^-3/0.10 = 0.050 s^-1

✓ m = 1, k = 0.050 s^-1

Real-World Applications

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Temperature Dependence

k changes with temperature via Arrhenius equation: k = A*exp(-Ea/RT).

🏭

Reactor Design

k determines how large a reactor must be to achieve target conversion.

💊

Drug Development

Rate constants for drug metabolism determine dosing frequency.

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Catalyst Evaluation

Comparing k with and without catalyst quantifies catalytic improvement.

Common Mistakes to Avoid

⚠️

k is NOT a concentration

k is rate constant with specific units. Do not confuse with equilibrium constant K.

⚠️

Units depend on order

First order k: s^-1. Second order k: L/mol-s. Wrong units indicate wrong order.

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k must be determined at constant T

Arrhenius: k varies with temperature. Always report k with the temperature at which it was measured.

Frequently Asked Questions

How is k related to temperature? ▾

Via Arrhenius equation: k = A*exp(-Ea/RT). A is pre-exponential factor, Ea is activation energy, R=8.314 J/molK, T in Kelvin.

Can k be negative? ▾

No. k is always positive. The sign of the rate depends on whether you define rate as consumption (-) or production (+).

What is k for an elementary reaction? ▾

For elementary step A + B to products: rate = k[A][B] (second order). k is related to collision frequency and fraction with sufficient energy.

How do I find k from a concentration-time graph? ▾

First order: k = -slope of ln[A] vs t plot. Second order: k = slope of 1/[A] vs t plot. Zero order: k = -slope of [A] vs t plot.

What is the relationship between k_forward and k_reverse? ▾

K_equilibrium = k_forward / k_reverse. At equilibrium, forward and reverse rates are equal.

Related Chemistry Calculators

Formula Explorer connections

Interpretation: This formula connects concentration, time, temperature or transport to the speed of a chemical process. Assumption: The reaction order and mechanism must match the model. Temperature, catalyst, mixing and mass-transfer limitations can alter the observed rate.

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