Simple rate equations, orders of reaction and rate constants

Chemistry A2 · Reaction kinetics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

A rate equation shows how the rate of a reaction depends on the concentrations of the reactants: rate = k[A]^m[B]ⁿ. The powers m and n are the orders. They can be 0, 1 or 2, and they are found only from experiments, never from the balanced equation.

Zero order means changing the concentration does not change the rate. First order means the rate doubles when the concentration doubles. Second order means the rate becomes four times greater.

Most reactions happen in several steps. The slowest one is the rate-determining step. Only the species that take part in or before this step appear in the rate equation.

Rules to remember

rate = k[A]^m[B]ⁿ; overall order = m + n
Units of k: overall order 1 → s⁻¹; order 2 → dm³ mol⁻¹ s⁻¹; order 3 → dm⁶ mol⁻² s⁻¹
Concentration–time graph: zero order is a straight line going down; first order is a curve with a constant half-life.
Rate–concentration graph: zero order is a horizontal line; first order is a straight line through the origin; second order is an upward curve.
First order: half-life is constant and does not depend on concentration; k = 0.693 ÷ t_½
An intermediate is made in one step and used up in a later step; a catalyst is used in one step and re-formed later.
Raising the temperature increases k, so the rate increases.

Common mistake

Students take the orders from the balancing numbers in the overall equation. Orders come from experimental data only; the equation tells you nothing about them.

Worked example

Initial rates for A + B → products: experiment 1, [A] = 0.10, [B] = 0.10, rate = 3.0 × 10⁻³; experiment 2, [A] = 0.20, [B] = 0.10, rate = 1.2 × 10⁻²; experiment 3, [A] = 0.20, [B] = 0.20, rate = 1.2 × 10⁻² (concentrations in mol dm⁻³, rates in mol dm⁻³ s⁻¹). Find the rate equation and k.

Experiments 1 and 2: [A] doubles, rate × 4, so second order in A.
Experiments 2 and 3: [B] doubles, rate unchanged, so zero order in B. Rate = k[A]².
k = rate ÷ [A]² = 3.0 × 10⁻³ ÷ (0.10)² = 3.0 × 10⁻³ ÷ 0.010 = 0.30.
Units: (mol dm⁻³ s⁻¹) ÷ (mol dm⁻³)² = dm³ mol⁻¹ s⁻¹.

Answer: rate = k[A]²; k = 0.30 dm³ mol⁻¹ s⁻¹

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Watch: Lecture 2 | Reaction Kinetics | Order of Reaction and Rate Equation

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