Reaction Kinetics: Rate Equations and Catalysis

This guide covers subtopics 26.1, Simple rate equations, orders of reaction and rate constants, and 26.2, Homogeneous and heterogeneous catalysts, from Topic 26, Reaction kinetics, of Cambridge International AS & A Level Chemistry 9701, 2025–2027 series. This is A Level content.

Before studying this

This resource assumes collision theory, the Boltzmann distribution and activation energy from Reaction Kinetics: Collision Theory and Catalysis — that AS resource explains why rate changes with conditions; this one adds the quantitative rate equation and mechanism-deduction tools AS explicitly excludes.

Syllabus coverage

CAMBRIDGE INTERNATIONAL AS & A LEVEL CHEMISTRY 9701 — A Level, Topic 26

26.1 Simple rate equations, orders of reaction and rate constants — explaining and using rate equation, order of reaction, overall order, rate constant, half-life, rate-determining step and intermediate; using rate equations of the form rate = k[A]ᵐ[B]ⁿ; deducing order from concentration-time graphs or experimental data; interpreting graphical data; calculating an initial rate; constructing a rate equation; using that a first-order half-life is independent of concentration; calculating a rate constant from initial rates or from half-life; for a multi-step reaction, suggesting a mechanism consistent with the rate equation, predicting order from a mechanism, deducing a rate equation from a mechanism, identifying an intermediate or catalyst, and identifying the rate-determining step; describing qualitatively the effect of temperature on the rate constant.

26.2 Homogeneous and heterogeneous catalysts — explaining that catalysts can be homogeneous or heterogeneous; describing the mode of action of a heterogeneous catalyst (adsorption, bond weakening, desorption), exemplified by iron in the Haber process and Pd/Pt/Rh in catalytic converters; describing the mode of action of a homogeneous catalyst (used in one step, reformed in a later step), exemplified by atmospheric NOₓ catalysing SO₂ oxidation and Fe²⁺/Fe³⁺ in the I⁻/S₂O₈²⁻ reaction.

Rate equations and orders of reaction

A rate equation expresses how reaction rate depends on the concentration of each reactant:

rate = k[A]ᵐ[B]ⁿ

where k is the rate constant, and m and n are the orders of reaction with respect to A and B (each 0, 1 or 2 at this level) — found only from experimental data, never from the stoichiometric equation. The overall order is m + n.

• Zero order (m = 0): changing [A] has no effect on rate; a concentration-time graph for A is a straight line (constant rate of loss).
• First order (m = 1): rate is directly proportional to [A]; doubling [A] doubles the rate.
• Second order (m = 2): rate is proportional to [A]²; doubling [A] quadruples the rate.

Deducing order from initial-rates data.

Worked example. The following initial rates were measured for A + B → products:

Experiment	[A] / mol dm⁻³	[B] / mol dm⁻³	Initial rate / mol dm⁻³ s⁻¹
1	0.10	0.10	2.0 × 10⁻³
2	0.20	0.10	4.0 × 10⁻³
3	0.20	0.20	1.6 × 10⁻²

Comparing experiments 1 and 2: [A] doubles, [B] constant, rate doubles (2.0 → 4.0 × 10⁻³) — first order with respect to A.

Comparing experiments 2 and 3: [B] doubles, [A] constant, rate quadruples (4.0 → 16 × 10⁻³) — second order with respect to B.

Rate equation: rate = k[A][B]²; overall order = 1 + 2 = 3.

Using experiment 1 to find k: 2.0 × 10⁻³ = k(0.10)(0.10)², so k = 2.0 × 10⁻³ / (0.10 × 0.010) = 2.0 × 10⁻³ / 1.0 × 10⁻³ = 2.0 mol⁻² dm⁶ s⁻¹

Half-life of a first-order reaction. For a first-order reaction, the time for the concentration to halve (t½) is constant, independent of the starting concentration — a distinctive test for first order directly from a concentration-time graph (equal time intervals for each successive halving). This links to the rate constant by:

k = 0.693 / t½

Worked example. A first-order reaction has t½ = 24 s. Calculate k.

k = 0.693 / 24 = 0.0289 s⁻¹

Effect of temperature on k. Increasing temperature increases the rate constant itself (not just the rate, which can also change with concentration) — this is the quantitative counterpart to the AS-level Boltzmann-distribution explanation: more particles have energy ≥ the activation energy at a higher temperature, which is reflected in a larger k.

Deducing mechanisms from rate equations

For a multi-step reaction, the overall rate equation is determined only by the rate-determining step (the slowest step) and any steps before it — species produced after the rate-determining step don’t appear in the rate equation.

Worked example. The reaction 2NO(g) + Br₂(g) → 2NOBr(g) is proposed to proceed by:

Step 1 (fast, reversible): NO + Br₂ ⇌ NOBr₂

Step 2 (slow): NOBr₂ + NO → 2NOBr

Deduce the rate equation implied by this mechanism, and identify the intermediate.

The rate-determining step is step 2, so the rate equation is based on its reactants: rate = k[NOBr₂][NO]. Since NOBr₂ doesn’t appear in the overall equation, it’s an intermediate, formed in step 1 and consumed in step 2 — its own concentration can be re-expressed using the fast pre-equilibrium of step 1, but at this level it’s enough to identify it and write the rate equation directly in terms of the species present in the rate-determining step and any before it.

This works in reverse too: given an experimental rate equation, a proposed mechanism is only consistent with it if the rate-determining step’s reactants (and only those) match the species in the rate equation. A species appearing in the rate equation with a lower order than its stoichiometric coefficient in the overall equation is a strong sign it’s involved before the rate-determining step, not in it directly.

Homogeneous and heterogeneous catalysts

A catalyst can be homogeneous (same physical state as the reactants, typically forming a genuine intermediate step within the reaction) or heterogeneous (different physical state, typically acting via surface adsorption).

Heterogeneous catalysis proceeds by: adsorption of reactant molecules onto active sites on the catalyst’s surface; bond weakening within the adsorbed molecules as they interact with the surface, lowering the activation energy for the reaction between them; and desorption of the product molecules, freeing the active site for further reactant molecules.

• Iron in the Haber process: N₂ and H₂ adsorb onto the iron surface, where the N≡N and H–H bonds are weakened, allowing them to react to form NH₃, which then desorbs.
• Pd, Pt and Rh in catalytic converters: NO and CO (from car exhaust) adsorb onto the precious-metal surface, where bond weakening allows the reaction 2CO + 2NO → 2CO₂ + N₂ to proceed with a much lower activation energy than the uncatalysed gas-phase reaction, before the products desorb.

Homogeneous catalysis proceeds by the catalyst being consumed in one step of the mechanism and regenerated in a later step — never appearing in the overall balanced equation, but genuinely taking part in the reaction pathway.

• Atmospheric oxides of nitrogen catalysing SO₂ oxidation: NO reacts with O₂ to form NO₂, which then oxidises SO₂ to SO₃ while being reduced back to NO — the NO is regenerated and can catalyse further SO₂ oxidation, contributing to acid rain formation.
• Fe²⁺/Fe³⁺ in the I⁻/S₂O₈²⁻ reaction: the direct reaction between I⁻ and S₂O₈²⁻ is slow, since both ions are negatively charged and repel each other. Fe²⁺ reduces S₂O₈²⁻ to give Fe³⁺ (which, being a cation, doesn’t face that repulsion problem), and Fe³⁺ then oxidises I⁻ back to Fe²⁺ — regenerating the catalyst while avoiding the slow anion-anion step entirely.

Common mistakes

Reading orders of reaction off the balanced stoichiometric equation. Orders can only be found from experimental data (initial rates, concentration-time graphs, or a given mechanism) — never assumed from stoichiometric coefficients.

Forgetting that half-life being constant is unique to first-order reactions. For zero-order or second-order reactions, successive half-lives are not equal — this is precisely why a constant half-life is used as a diagnostic test for first order.

Including a homogeneous catalyst’s formula in the overall equation. By definition, a catalyst is regenerated and cancels out — it appears in the mechanism steps but never in the final balanced equation.

Confusing a reaction intermediate with a catalyst. Both are produced in one step and consumed in another, but an intermediate is produced then consumed later in the same overall reaction sequence (forward-moving); a catalyst is consumed then regenerated, ending the reaction sequence unchanged and available to react again.

Quick revision checklist

• rate = k[A]ᵐ[B]ⁿ; orders found from data only, never from stoichiometry
• Doubling a reactant: rate ×2 (order 1), ×4 (order 2), unchanged (order 0)
• First-order half-life is constant; k = 0.693/t½
• Rate equation reflects the rate-determining step (and any step before it)
• Intermediate: made then consumed within the mechanism, absent from the overall equation
• Heterogeneous catalysis: adsorption → bond weakening → desorption (different phase from reactants)
• Homogeneous catalysis: consumed in one step, regenerated in a later step (same phase as reactants)

Related resources

• Reaction Kinetics: Collision Theory and Catalysis — the qualitative AS foundation this topic quantifies
• Transition Elements: Properties, Complexes and Redox Chemistry — the Fe²⁺/Fe³⁺ catalytic cycle in transition-metal context
• Nitrogen and Sulfur — atmospheric NOₓ chemistry and acid rain this topic’s catalysis example connects to
• Cambridge AS & A Level Chemistry hub

Written against Cambridge International AS & A Level Chemistry 9701, 2025–2027 series. Always check the current syllabus for your examination year.