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Activation Energy And Boltzmann Distribution

Learn and apply Activation Energy And Boltzmann Distribution in the published Chemistry course sequence.

  • GCE A-Level H1 Chemistry 8873-2027
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Activation Energy and Boltzmann Distribution: Orientation

Temperature and catalysts are the two “rate boosters” examiners love to test. The mark-scheme phrases are very specific: you must talk about the fraction of molecules with E ≥ Eₐ and the area beyond Eₐ on a Maxwell–Boltzmann distribution.

Link this page to Rate Equations, Orders, and Rate Constant and the Reaction Kinetics hub to keep mechanism and data interpretation consistent.

Definitions (Must Know)

A. Activation energy, Eₐ

The activation energy, Eₐ, is the minimum energy required for reactant particles to react successfully (reach the transition state).

B. Successful collision

A successful collision is a collision with energy at least Eₐ (and correct orientation, where relevant).

C. Maxwell–Boltzmann distribution

A Maxwell–Boltzmann distribution shows how the energies of particles are distributed at a given temperature. The area under the curve represents the total number (or fraction) of particles.

D. Catalyst (in kinetics)

A catalyst increases reaction rate by providing an alternative pathway with a lower activation energy, Eₐ.

Detailed Explanations

A. What to say about the distribution

With higher temperature, the most probable energy moves to the right, the curve becomes broader and its peak becomes lower. The total area stays the same for the same number of particles, but the area beyond Eₐ increases.

Maxwell–Boltzmann energy distributions at two temperatures

A lower-temperature curve has a taller peak at lower energy. A higher-temperature curve is lower and broader. Uncatalysed and catalysed activation-energy thresholds mark the fractions energetic enough to react.

Scroll across the graph to read all labels.

A lower-temperature curve has a taller peak at lower energy. A higher-temperature curve is lower and broader. Uncatalysed and catalysed activation-energy thresholds mark the fractions energetic enough to react.A lower-temperature curve has a taller peak at lower energy. A higher-temperature curve is lower and broader. Uncatalysed and catalysed activation-energy thresholds mark the fractions energetic enough to react.
Schematic Maxwell–Boltzmann distributions for the same number of particles. Higher temperature makes the curve broader with a lower peak and increases the area beyond Ea; a catalyst lowers Ea without changing either curve.
Open full-size graph
View figure data
Values for Maxwell–Boltzmann energy distributions at two temperatures
Particle energy (relative units)Lower temperatureHigher temperature
000
0.50.22890.0974
10.30180.1516
1.50.29840.1771
20.26230.1839
2.50.21620.1791
30.1710.1673
3.50.13150.1521
40.09910.1353
4.50.07350.1186
50.05380.1026
5.50.0390.0879
60.02810.0747
6.50.02010.063
70.01420.0528
7.50.01010.0441
80.00710.0366
8.50.0050.0303
90.00350.025
9.50.00240.0205
100.00170.0168

B. Why the area statement matters

Temperature does not increase every molecule’s energy by the same amount. Some particles lose energy in collisions while others gain it. The key change is that the fraction in the tail beyond Eₐ grows, so more particles are energetic enough to react.

C. Catalyst on the distribution

At the same temperature, the distribution curve stays the same, but the catalyst lowers Eₐ, so the “Eₐ line” moves left and the area beyond Eₐ increases.

Worked Examples

Modelled example 1

Explain the strong temperature effect on rate

Core

Problem

Explain why raising temperature can increase reaction rate substantially even if collision frequency increases only slightly.
Study the worked solution

  1. Describe the energy distribution

    Method

    State that higher temperature shifts the distribution toward higher energies.

    Reason

    Particle energies are redistributed rather than every particle receiving the same energy increase.

    Working

    A larger fraction of particles lies in the high-energy tail.

  2. Compare with Ea

    Method

    Identify the increased area where E ≥ Eₐ.

    Reason

    Those particles have enough energy for successful collisions.

    Working

    Fraction with E ≥ Eₐ increases significantly.

  3. Link to rate

    Method

    State that successful collisions per unit time increase.

    Reason

    The energetic-fraction effect can be much larger than the modest collision-frequency increase.

    Working

    More successful collisions → faster reaction.

Guided practice 2

Describe a higher-temperature distribution

About 7 min

Problem

State the principal changes to a Maxwell–Boltzmann distribution when temperature increases, then link the changed area beyond Eₐ to reaction rate.

Try this before viewing the solution

Hints

Hint 1: describe the curve
The most probable energy moves right; the distribution becomes broader and its peak becomes lower.
Hint 2: preserve and partition area
For the same number of particles, total area stays constant, but more area lies to the right of the unchanged Eₐ line.
View solution step by step

  1. Describe the new curve

    Method

    State that the curve broadens, lowers and shifts toward higher energies.

    Reason

    Higher temperature changes the spread and most probable particle energy.

    Working

    Lower peak; broader curve; most probable energy further right.

  2. Track the relevant area

    Method

    State that the area beyond the fixed Eₐ line increases.

    Reason

    A larger fraction of particles now has at least the activation energy.

    Working

    Fraction with E ≥ Eₐ increases.

  3. Conclude

    Method

    Link that fraction to successful collisions per unit time.

    Reason

    More collisions meet the energy requirement.

    Working

    Successful-collision frequency and reaction rate increase.

Common misconception 3

Correct a temperature–Ea claim

Find and correct the mistake

Learner claim

A learner says, “Heating speeds the reaction because temperature lowers the activation energy, moving the Eₐ line left.” Diagnose the error and describe the correct diagram change.

Choose what changes

Heating at unchanged pathway changes

View solution step by step

  1. Keep the threshold fixed

    Method

    State that Eₐ is unchanged when only temperature changes.

    Reason

    The reaction pathway has not been replaced.

    Working

    The Eₐ line stays in the same energy position.

  2. Change the distribution

    Method

    Broaden and lower the curve, shifting its most probable energy right.

    Reason

    This increases the area beyond the unchanged threshold.

    Working

    Larger fraction with E ≥ Eₐ → faster rate.

Examiner practice 4

Explain a catalyst on a Boltzmann diagram

4 marks

Problem

On a Maxwell–Boltzmann diagram, explain what changes when a catalyst is added at the same temperature and why the rate increases. [4 marks]

Try this before viewing the solution

View solution step by step

  1. Preserve the distribution

    1 mark

    Method

    State that the Maxwell–Boltzmann curve remains unchanged.

    Reason

    Temperature and particle number are unchanged.

    Working

    Same distribution curve.

  2. Lower the threshold

    1 mark

    Method

    Move the activation-energy line left.

    Reason

    The catalyst provides an alternative pathway with lower Eₐ.

    Working

    E_(a,cat) < E_(a,uncat).

  3. Increase successful fraction

    1 mark

    Method

    Identify the larger area beyond the lower threshold.

    Reason

    More particles now meet the energy requirement.

    Working

    Fraction with E ≥ E_(a,cat) increases.

  4. Link to rate

    1 mark

    Method

    State that successful collisions per unit time increase.

    Reason

    A larger eligible fraction can react.

    Working

    Reaction rate increases.

Challenge 5

Separate cooling and catalyst effects

Minimal support

Problem

A reacting mixture is cooled while a catalyst is added. Explain the separate changes on a Maxwell–Boltzmann diagram and decide whether the overall rate change can be predicted qualitatively without further data.

Try this before viewing the solution

Hints

Hint 1: separate curve and threshold
Cooling changes the distribution; the catalyst changes the activation-energy threshold.
Hint 2: compare directions
Cooling reduces the energetic fraction, while lowering Eₐ increases it. No sizes are supplied.
View solution step by step

  1. Analyse cooling

    Method

    Shift the distribution toward lower energies, making it narrower with a higher peak.

    Reason

    A smaller fraction lies beyond the original Eₐ.

    Working

    Cooling alone lowers the successful-collision fraction and rate.

  2. Analyse the catalyst

    Method

    Move the activation-energy threshold left without attributing that move to temperature.

    Reason

    The alternative pathway has lower Eₐ.

    Working

    Catalyst alone increases the fraction above the threshold and rate.

  3. Judge the combined outcome

    Method

    State that the two changes have opposing rate effects.

    Reason

    The qualitative diagram does not quantify which change dominates.

    Working

    The net rate change cannot be determined without further quantitative information.

Mind Stretchers

Mind stretcher 1Extension

Two reactions at the same temperature have different activation energies: E_(a,1) > E_(a,2). Without doing calculations, explain which reaction is faster and why, using Maxwell–Boltzmann language.

Show Hint

Temperature changes the distribution; a catalyst changes the threshold. Distinguish those two diagrams.

Show Answer

Mark scheme:

  • For the lower Eₐ reaction (E_(a,2)), the Eₐ threshold is smaller.
  • Therefore the area under the distribution curve with E ≥ Eₐ is larger.
  • A larger fraction of molecules have enough energy for successful collisions, so the rate is higher.

Mind stretcher 2: Same rate increase, different causeExtension

Question. Two changes each increase rate. Change X moves the Eₐ line left without changing the distribution; change Y broadens and lowers the distribution peak while keeping Eₐ fixed. Identify each change and explain the larger successful fraction.

Show Hint

A catalyst changes the pathway. Temperature changes the particles’ energy distribution.

Show Answer

X is adding a catalyst: its alternative pathway has lower Eₐ. Y is increasing temperature: a larger area lies beyond the unchanged Eₐ. In both cases a larger fraction of collisions can overcome the activation barrier.