AQA A-Level Chemistry: Rate equations (7405) – Revision Notes

These notes condense section 3.1.9 Rate equations of the AQA AS and A-level Chemistry specification (7404/7405), version 1.2, July 2026, for AS and A-level exams from June 2016 onwards. They cover 3.1.9.1, 3.1.9.2 and Required practical 7. Everything here is A-level only. The specification places 3.1.9 on A-level Paper 2, and Paper 3 can test any content.

For full explanations and worked examples, use the rate equations study guide. Test yourself with the rate equations practice questions. Collision theory and the Maxwell–Boltzmann distribution are in the kinetics revision notes. The course hub is AQA A-Level Chemistry, and the printable checklist lists every specification point.

Definitions to learn

• Rate equation: Rate = k[A]^m [B]^n, an experimentally determined relationship.
• Order of reaction with respect to a reactant: the power to which its concentration is raised in the rate equation (m for A, n for B). Orders here are 0, 1 or 2.
• Overall order: the sum of the orders, m + n.
• Rate constant, k: the constant of proportionality in the rate equation. It changes with temperature (or if a catalyst is added), never with concentration.
• Rate-determining step: the slowest step in a mechanism; it limits the overall rate.
• Initial rate: the rate at t = 0, the gradient of the tangent to a concentration–time curve at the start.

3.1.9.1 Key equations

Equation	Use it to	Watch out for
Rate = k[A]^m [B]^n	find rate, k or a concentration	square second-order concentrations
k = A e^(−Ea/RT)	find k, A, Ea or T	Ea in J mol⁻¹, T in K
ln k = −Ea/(RT) + ln A	plot ln k (y) against 1/T (x)	slope = −Ea/R, intercept = ln A

R = 8.31 J K⁻¹ mol⁻¹. The specification states that these equations and R will be given when required. A has the same units as k.

Units of k: method in steps

1. Write k = Rate ÷ (concentration terms).
2. Put in mol dm⁻³ s⁻¹ on top and (mol dm⁻³) raised to the overall order underneath.
3. Cancel, and write negative powers.

Overall order	Units of k
0	mol dm⁻³ s⁻¹
1	s⁻¹
2	mol⁻¹ dm³ s⁻¹
3	mol⁻² dm⁶ s⁻¹

Worked reminder: Rate = k[A]²[B]. Overall order 3, so k = (mol dm⁻³ s⁻¹) ÷ (mol dm⁻³)³ = mol⁻² dm⁶ s⁻¹.

Effect of concentration changes

Multiply each concentration factor raised to its order.

Order	×2 conc	×3 conc	×½ conc
0	×1	×1	×1
1	×2	×3	×½
2	×4	×9	×¼

Worked reminder: Rate = k[A][B]². Halve [A] and triple [B]: factor = ½ × 3² = 4.5.

Temperature and k

• Raising the temperature increases k; lowering it decreases k.
• Concentration changes the rate but never k.
• Reason (link to 3.1.5): at a higher temperature a much larger proportion of collisions have energy at or above Ea, so k and the rate rise sharply for a small temperature rise.

Method in steps: Ea from a graph

1. Convert each T to 1/T (keep 4 s.f.) and each k to ln k.
2. Plot ln k (y) against 1/T (x). Draw the best-fit straight line.
3. Gradient from two points far apart on the line (not data points off the line).
4. Ea = −gradient × R. Answer in J mol⁻¹; divide by 1000 for kJ mol⁻¹.
5. If you need A: ln A = ln k + Ea/RT for any point on the line, then A = e^(ln A).

3.1.9.2 Reading graphs

Graph	Zero order	First order	Second order
[A] against time	straight line, falling	curve, flattening	curve, flattening
Rate against [A]	horizontal line	straight line through origin	upward curve through origin
Rate against [A]²	—	—	straight line through origin

• Rate at time t = size of the gradient of the tangent to the concentration–time curve at t.
• Zero order: Rate = k, so k = −gradient of the concentration–time line. Units mol dm⁻³ s⁻¹.
• Tangents: draw them long and read two points far apart.

Method in steps: orders from initial rates

1. Find two experiments where only one concentration changes.
2. Find the factor change in that concentration and the factor change in rate.
3. Factor 1 → order 0; same factor → order 1; factor squared → order 2.
4. If no pair isolates a reactant, divide the rate change by the effect of the reactant you already know.
5. Write the rate equation with only reactants of order 1 or 2.
6. Rearrange for k using any one experiment; work out the units; check with a second experiment.

Orders and the rate-determining step

• Species in the rate equation are involved in the rate-determining step (or a step before it).
• The order tells you how many of that particle are involved up to and including that step.
• Zero-order reactants react after the rate-determining step.
• A valid mechanism must fit the rate equation and its steps must add up to the overall equation.

Required practical 7

Initial rate (clock) method

• Iodine clock: iodine formed reacts with a small fixed amount of thiosulfate; when that runs out, iodine turns starch blue-black.
• Vary the volume of one reactant; add water so total volume stays constant.
• Same amount of product forms each run, so rate ∝ 1/t.
• Keep temperature and all other concentrations constant.

Continuous monitoring method

• One run, followed over time: gas volume, mass loss, colorimeter readings, or samples quenched and titrated.
• Plot concentration against time; tangents give rates at several concentrations.

Apparatus and techniques: AT a, k and l. Wear eye protection and handle chemicals by their hazards.

Must-know distinctions

• Rate vs rate constant: rate changes as concentrations fall; k stays fixed at a given temperature.
• Order vs coefficient: orders come from experiment, coefficients from the balanced equation.
• Initial rate vs mean rate: initial rate is a tangent gradient at t = 0, not a change over an interval.
• ln vs log: the Arrhenius straight line uses natural logs (ln).
• Zero order vs not reacting: a zero-order reactant is used up; it just does not affect the rate.

Quick self-test

1. Give the units of k for a reaction with overall order 3.
2. Rate = k[A]². By what factor does the rate change when [A] is tripled?
3. Describe the graph of rate against concentration for a first-order reactant.
4. A plot of ln k against 1/T has gradient −5.5 × 10³ K. Calculate Ea in kJ mol⁻¹ (R = 8.31 J K⁻¹ mol⁻¹).
5. Rate = k[A][B]. Rate = 3.0 × 10⁻³ mol dm⁻³ s⁻¹ when [A] = 0.10 and [B] = 0.25 mol dm⁻³. Calculate k with units.
6. A reactant is zero order. Is it involved in the rate-determining step?
7. A zero-order concentration–time line has gradient −2.5 × 10⁻⁴ mol dm⁻³ s⁻¹. State k.
8. State the effect of raising the temperature on k.
9. In k = Ae^(−Ea/RT), what units must Ea and T be in?
10. Rate = k[X][Y]². [X] is halved and [Y] is doubled. Find the rate factor.
11. A = 1.0 × 10¹⁰ s⁻¹, Ea = 50 kJ mol⁻¹, T = 300 K. Calculate k (R = 8.31 J K⁻¹ mol⁻¹).

Answers

1. mol⁻² dm⁶ s⁻¹
2. ×9 (3²)
3. A straight line through the origin.
4. Ea = 5.5 × 10³ × 8.31 = 4.57 × 10⁴ J mol⁻¹ = 45.7 kJ mol⁻¹
5. k = 3.0 × 10⁻³ ÷ (0.10 × 0.25) = 0.12 mol⁻¹ dm³ s⁻¹
6. No. It reacts in a step after the rate-determining step.
7. k = 2.5 × 10⁻⁴ mol dm⁻³ s⁻¹
8. k increases.
9. Ea in J mol⁻¹ and T in K.
10. ½ × 2² = ×2
11. k = 1.0 × 10¹⁰ × e^(−50 000 / (8.31 × 300)) = 19.5 s⁻¹

Where marks are usually lost

• Taking orders from the balanced equation instead of the data.
• Giving units of k from memory and getting them wrong for overall order 3.
• Leaving Ea in kJ mol⁻¹ in the Arrhenius equation, or using °C.
• Dropping the minus sign so that Ea comes out negative.
• Using log₁₀ instead of ln when plotting.
• Taking a gradient between two data points that lie off the best-fit line.
• Quoting a negative rate from a falling concentration–time gradient.
• Saying a temperature rise increases rate “because k increases” without the energy explanation, when the question asks you to explain.
• Choosing a mechanism whose slow step fits but whose steps do not add up to the overall equation.
• Forgetting to keep total volume constant in a clock-reaction plan.

Next steps

Work through the practice questions, and go back to the study guide for any step that felt shaky. The free 10-minute diagnostics show which topics to revise next.

Official syllabus

AQA, AS and A-level Chemistry specification (7404/7405), version 1.2, July 2026, for AS and A-level exams June 2016 onwards: section 3.1.9 Rate equations (3.1.9.1 and 3.1.9.2, A-level only), with Required practical 7.