1. The distribution and its axes
In a gas at a fixed temperature, molecules do not all have the same energy. Collisions constantly pass energy between them. The Maxwell–Boltzmann distribution shows how the molecules' kinetic energies are spread out.
| Axis | What it shows | Note |
|---|---|---|
| x-axis | Kinetic energy (energy) | Not speed. Starts at zero; there are no negative energies |
| y-axis | Number of molecules with a given energy | Strictly, the number in each small energy interval. Some books plot the fraction of molecules instead |
If y is the number of molecules, the total area under the curve is the total number of molecules, N. If y is the fraction, the total area is 1.
2. Key features of the curve
- Starts at the origin: no molecules have zero energy.
- Rises to a peak: the most probable energy.
- Is not symmetrical: the mean energy is to the right of the peak.
- Has a long tail on the high-energy side that gets closer and closer to the x-axis but never touches it: there is no maximum energy.
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Maxwell–Boltzmann distribution at one temperature
Labels to include:
- x-axis: Energy (kinetic energy)
- y-axis: Number of molecules (with that energy)
- Curve starts at the origin
- Peak labelled 'most probable energy'
- Mean energy marked slightly to the right of the peak
- Tail approaching but not touching the x-axis
- Vertical line labelled Ea well to the right of the peak
- Shaded area under the curve to the right of Ea, labelled 'molecules with E ≥ Ea'
One curve: up from the origin to a peak, then a long tail down towards the axis. Ea is far out in the tail, so only a small shaded area lies to its right.
3. What the area above Ea means
The area to the right of Ea shows the number (or fraction) of molecules with enough energy to react. These molecules are energetically able to react, but they still need to collide, and with the right orientation, for reaction to happen.
This is not a fixed lucky group. Energy is constantly redistributed by collisions, so individual molecules move in and out of the high-energy tail; the shape of the distribution stays the same at a fixed temperature.
4. Effect of temperature
For the same sample (same N) at a higher temperature:
- the peak moves right (higher most probable energy) and lower;
- the curve is broader, with more molecules at high energies;
- the total area is the same, because the number of molecules has not changed;
- the two curves cross once;
- Ea does not change.
The area to the right of Ea is much larger at the higher temperature. Many more molecules have energy ≥ Ea, so there are more successful collisions per unit time. Temperature does not lower Ea.
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Maxwell–Boltzmann distributions at two temperatures
Labels to include:
- x-axis: Energy; y-axis: Number of molecules
- Curve T₁ (lower temperature): taller, peak further left
- Curve T₂ (higher temperature): lower peak, shifted right, broader
- Both curves start at the origin and have tails approaching the x-axis
- Curves cross once (to the right of the T₁ peak)
- One vertical Ea line (the same for both)
- Area right of Ea shaded and labelled for T₁ (small) and T₂ (larger)
- Note: equal total areas under both curves
Both curves enclose the same area. The higher-temperature curve is flatter and further right, so it has a bigger area beyond the same Ea line.
5. Effect of a catalyst
At the same temperature, a catalyst does not change the distribution, and it does not give molecules more energy. It provides a pathway with a lower activation energy, so the Ea line moves left. A larger area lies to the right of the new Ea, so more molecules can react, and ΔH is unchanged.
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Catalyst on a Maxwell–Boltzmann distribution
Labels to include:
- x-axis: Energy; y-axis: Number of molecules
- One curve only (temperature unchanged)
- Vertical line Ea (uncatalysed) to the right
- Vertical line Ea (catalysed) to the left of it
- Area right of catalysed Ea shaded and labelled as larger
One curve, two activation-energy lines. The extra shaded strip between the two lines represents the extra molecules that can react by the catalysed route.
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Reaction profile: catalysed vs uncatalysed
Labels to include:
- Vertical axis: Enthalpy; horizontal axis: Progress of reaction
- Reactants and products levels the same for both routes
- Uncatalysed curve with a higher peak
- Catalysed curve (dashed) with a lower peak
- Ea (uncatalysed) and Ea (catalysed): vertical arrows from the reactants level to each peak
- ΔH arrow from reactants to products, the same for both
Both curves start and end at the same levels; only the peak height differs, so ΔH is unchanged.
6. Concentration and the curve
Whether the curve changes depends on what the y-axis counts:
- Fraction of molecules: unchanged by concentration at the same temperature.
- Number of molecules, more reactant added to the same volume: the curve is scaled up vertically at every energy. The peak stays at the same energy and the area increases with N.
- Number of molecules, gas compressed (same N, smaller volume): the curve is unchanged; what changes is the number of particles per unit volume, which the curve does not show.
So “higher concentration always makes the curve higher” is an overgeneralisation: it depends on the axis and on whether the number of molecules in the sample has changed.
7. Worked numbers
8. Building a complete answer
“Explain why a small temperature rise greatly increases the rate.”
| Answer | What's missing |
|---|---|
| “The particles have more energy so they collide more.” | Doesn't mention Ea; focuses on collision frequency, the smaller effect |
| “More particles have energy above the activation energy.” | Doesn't link to successful collisions per unit time |
| “Many more particles have energy ≥ Ea, so there are more successful collisions per unit time.” | Complete chain |
Quick checks
These are Finesse practice questions. The step-by-step answers are indicative worked solutions, not official AQA mark allocations.
Q1. A gas sample has 5.0 × 105 molecules. A fraction 0.0040 have E ≥ Ea. How many molecules are energetically able to react?Show answer
Step 1: number = fraction × N.
Step 2: 0.0040 × 5.0 × 105 = 2.0 × 103 molecules.
Q2. The fraction with E ≥ Ea rises from 0.0030 to 0.012 when the temperature is raised. By what factor does the number of eligible molecules increase (same N)? What can you not conclude?Show answer
Step 1: 0.012 ÷ 0.0030 = 4.0.
Step 2: you cannot conclude the rate is exactly 4.0 times faster without a stated model; it shows the eligible molecules increase by that factor.
Q3. Describe how the Maxwell–Boltzmann curve for a fixed sample of gas changes when the temperature is lowered.Show answer
The peak moves to the left (lower most probable energy) and becomes higher.
The curve is narrower; the total area is unchanged; it still starts at the origin.
The area to the right of Ea becomes smaller; Ea itself does not move.
Q4. More reactant gas is added to a fixed-volume container at constant temperature, doubling the number of molecules. The y-axis is “number of molecules”. How does the curve change?Show answer
Every point on the curve is doubled vertically; the peak stays at the same energy.
The area doubles, and the number of molecules with E ≥ Ea doubles. The fraction with E ≥ Ea is unchanged.
Q5. A student writes: “A catalyst works by giving particles more energy, so more of them have energy above Ea.” Correct this.Show answer
A catalyst does not change the energies of particles or the distribution at the same temperature.
It provides an alternative pathway with a lower Ea, so the Ea line moves left and more molecules have energy ≥ the new Ea, giving more successful collisions per unit time.
Sources
Sources and examiner guidance (reviewed 1 October 2026)
- Chemrevise — AQA 1.5 Reaction kinetics revision guide (N. Goalby) — Checklist for the distribution; its 'concentration makes the curve higher' line is qualified here by axis and sample size.
- AQA 7405 specification — 3.1.5 Kinetics (incl. Required Practical 3) — 3.1.5.2 Maxwell–Boltzmann distribution; 3.1.5.3 temperature; 3.1.5.5 catalysts.
- AQA 7404/2 mark scheme, June 2023 — Q08: curve features and temperature comparison.
- AQA 7404/2 examiner report, June 2023 — Q08: linking area above Ea to rate.
- AQA 7404/2 mark scheme, June 2022 — Q01.6: many more eligible particles and successful collisions.
Finesse Tuition is not endorsed by AQA or Chemrevise. All explanations and examples here are our own.