Activation Energy and Boltzmann Distribution

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.

Use your course’s Reaction Kinetics topic navigation to connect the distribution to collision theory and catalysts. For further H2 study, Rate Equations, Orders, and Rate Constant connects rate measurements to quantitative models.

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.

Key Ideas (What Earns Marks)

• Increasing temperature increases average kinetic energy and collision frequency, but the main mark is:
  • a larger fraction of molecules have E ≥ Eₐ
  • so there are more successful collisions per unit time
• On the Maxwell–Boltzmann curve, higher temperature:
  • shifts the distribution to higher energies and flattens it
  • increases the area to the right of Eₐ
• A catalyst:
  • lowers Eₐ (moves the Eₐ threshold left)
  • increases the fraction with E ≥ Eₐ
  • does not change the Maxwell–Boltzmann distribution at a fixed temperature

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.

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Values for Maxwell–Boltzmann energy distributions at two temperatures

Particle energy (relative units)	Lower temperature	Higher temperature
0	0	0
0.5	0.2289	0.0974
1	0.3018	0.1516
1.5	0.2984	0.1771
2	0.2623	0.1839
2.5	0.2162	0.1791
3	0.171	0.1673
3.5	0.1315	0.1521
4	0.0991	0.1353
4.5	0.0735	0.1186
5	0.0538	0.1026
5.5	0.039	0.0879
6	0.0281	0.0747
6.5	0.0201	0.063
7	0.0142	0.0528
7.5	0.0101	0.0441
8	0.0071	0.0366
8.5	0.005	0.0303
9	0.0035	0.025
9.5	0.0024	0.0205
10	0.0017	0.0168

Values for Maxwell–Boltzmann energy distributions at two temperatures

Particle energy (relative units)	Lower temperature	Higher temperature
0	0	0
0.5	0.2289	0.0974
1	0.3018	0.1516
1.5	0.2984	0.1771
2	0.2623	0.1839
2.5	0.2162	0.1791
3	0.171	0.1673
3.5	0.1315	0.1521
4	0.0991	0.1353
4.5	0.0735	0.1186
5	0.0538	0.1026
5.5	0.039	0.0879
6	0.0281	0.0747
6.5	0.0201	0.063
7	0.0142	0.0528
7.5	0.0101	0.0441
8	0.0071	0.0366
8.5	0.005	0.0303
9	0.0035	0.025
9.5	0.0024	0.0205
10	0.0017	0.0168

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.

Test these statements on moving particles: the simulation counts every collision and how many have at least Eₐ, beside the distribution for the same temperature.

Worked Examples

Common Mistakes

• Saying ‘temperature increases Eₐ’ (it doesn’t; it changes the fraction above Eₐ).
• Saying catalysts increase collision frequency as the main mechanism (the key mark is lower Eₐ pathway).
• Describing Maxwell–Boltzmann curves without mentioning ‘area beyond Eₐ’.

Use the topic check in Practise and check below to practise and check your understanding.

Exam Tips

• For Maxwell–Boltzmann, don’t say ‘molecules have more energy’ — say ‘a larger fraction has E ≥ Eₐ’.
• Catalyst questions: catalyst lowers Eₐ; it does not change Δ H or the position of equilibrium.
• Temperature increase shifts the distribution to higher energies and increases collision frequency.

Mind Stretchers