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Learn7405Paper 1 · Paper 1: Physical and inorganic chemistryKineticsRates and the Boltzmann distribution
Kinetics · Subtopic 1 of 1

Rates and the Boltzmann Distribution

Rate = change in concentration per unit time (gradient of a concentration–time graph). The Boltzmann distribution shows the spread of molecular energies: it starts at the origin, rises to a peak (most probable energy) and tails off without touching the axis. Only molecules with E≥EaE\ge E_a react. At higher temperature the curve flattens and shifts right; the area beyond EaE_a grows a lot, so rate increases significantly. A catalyst gives a pathway with lower EaE_a, so more molecules exceed it. Homogeneous catalysts are in the same phase as reactants; heterogeneous catalysts are in a different phase (adsorption on surfaces).

Cambridge 9701 Paper 1Cambridge 9701 Paper 2Edexcel YCH11 WCH12AQA 7405 Paper 1≈ 45 minRevision 1 · updated 2026-10-30
Section 1 of 14

Learning objectives

  • Calculate rates from graphs.
  • Describe and sketch the Boltzmann distribution.
  • Explain the effect of temperature and catalysts using the distribution.
  • Distinguish homogeneous and heterogeneous catalysis.
Pause and think

A 10 °C rise only increases the average speed of molecules by about 2%, yet it often doubles the rate. How?

Section 2 of 14

Core idea

Start hereWhy 10 degrees matters

Milk goes off in a day on a summer bench but lasts a week in the fridge. A small temperature change makes a large difference to how many molecules have enough energy to react.

The big idea

Molecular energies follow the Boltzmann distribution. Only those with at least EaE_a react. Temperature shifts the distribution; catalysts lower EaE_a.

1. The Boltzmann distribution

Two ways to increase rate

Raise temperature or lower activation energy.

Worked exampleReading a rate from a graph

A tangent to a [product]–time curve passes through (0 s, 0.10) and (40 s, 0.50) mol dm⁻³.

Goal
Rate.
Strategy
Gradient.
  1. 0.50−0.1040−0\frac{0.50-0.10}{40-0}
    Rise over run.
  2. =0.010 mol dm−3 s−1=0.010\ \text{mol dm}^{-3}\text{ s}^{-1}
    With units.
Answer0.0100.010 mol dm⁻³ s⁻¹.
✓ CheckPositive for a product ✓.
Key takeawayHeterogeneous catalysis Adsorption onto surface sites weakens bonds; reaction; desorption of products. Too strong adsorption blocks sites; too weak gives no effect.
Pause and think

Why are catalytic converters "poisoned" by leaded petrol?

Summary

  • Rate = gradient.
  • Boltzmann: only E≥EaE\ge E_a react.
  • Homogeneous vs heterogeneous catalysts.
Key words
Activation energy
Minimum energy for a collision to lead to reaction.
Boltzmann distribution
Spread of molecular energies at a given temperature.
Adsorption
Molecules attaching to a surface.
HistoryMaxwell and Boltzmann. James Clerk Maxwell and Ludwig Boltzmann developed the statistical distribution of molecular speeds in the 1860s–70s. Boltzmann's entropy equation is carved on his tombstone.
Fun factFireflies and temperature. Fireflies flash faster on warm nights; the enzyme reactions controlling their light speed up with temperature, just like the Boltzmann tail predicts.
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