Collision Theory and Rates of Reaction

This lesson covers the fundamental principles of collision theory, the Maxwell-Boltzmann distribution, activation energy, and the quantitative and qualitative effects of temperature, concentration, pressure, surface area, and catalysts on rates of reaction.

Collision Theory

For a chemical reaction to occur, reactant particles must:

Collide with each other
With sufficient energy (equal to or greater than the activation energy, Ea)
With the correct orientation

Only collisions that satisfy all three conditions are called successful collisions (or effective collisions). Most collisions between particles do not lead to reaction.

Key Definition: The activation energy (Ea) is the minimum energy that colliding particles must possess in order for a reaction to occur.

The Maxwell-Boltzmann Distribution

The Maxwell-Boltzmann distribution describes the spread of molecular kinetic energies in a sample of gas at a given temperature.

Key Features of the Curve

The x-axis shows molecular kinetic energy; the y-axis shows the number (or fraction) of molecules with that energy.
The curve starts at the origin — no molecules have zero kinetic energy.
It rises to a peak (the most probable energy), then tails off asymptotically to the right.
The curve never touches the x-axis on the right — there is no upper limit to molecular energy.
The total area under the curve equals the total number of molecules.

A vertical line at Ea divides the curve. The shaded area to the right of Ea represents molecules with sufficient energy to react.

Effect of Temperature

At a higher temperature:

The peak of the curve shifts right and becomes lower (the distribution flattens and broadens).
The total area under the curve remains the same (same number of molecules).
The area to the right of Ea increases significantly — a much greater proportion of molecules now have energy ≥ Ea.
This is why even a small increase in temperature (e.g. 10°C) can roughly double the rate.

Exam Tip: When sketching two Maxwell-Boltzmann curves at different temperatures, ensure: (1) the higher-T curve has a lower, broader peak shifted right; (2) both curves start at the origin; (3) the total area under each curve is the same; (4) neither curve touches the x-axis on the right.

Effect of Concentration and Pressure

Increasing concentration (in solution) or increasing pressure (for gases) increases the number of particles per unit volume.
This increases the frequency of collisions, so more successful collisions occur per unit time.
The rate increases.

Note: changing concentration or pressure does not change the Maxwell-Boltzmann distribution or the proportion of molecules with energy ≥ Ea. It only affects collision frequency.

Effect of a Catalyst

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

The Maxwell-Boltzmann distribution does not change — the molecules have the same energies.
The Ea line shifts to the left (to a lower value, Ea').
A greater proportion of molecules now have energy ≥ Ea'.
More successful collisions per unit time → faster rate.

Key Definition: A catalyst is a substance that increases the rate of a chemical reaction without being consumed, by providing an alternative pathway with lower activation energy.

Homogeneous catalysts are in the same phase as the reactants (e.g. H⁺ ions catalysing ester hydrolysis). Heterogeneous catalysts are in a different phase (e.g. iron in the Haber process, vanadium(V) oxide in the Contact process).

Worked Examples

Example 1: In a Maxwell-Boltzmann diagram, the area to the right of Ea at 300 K represents 5% of molecules. At 310 K, this increases to 10%. Explain the effect on rate.

The proportion of molecules with energy ≥ Ea has doubled. Therefore, the frequency of successful collisions approximately doubles, and the rate approximately doubles.

Example 2: Explain why a catalyst increases the rate of both the forward and reverse reactions equally.

A catalyst lowers the activation energy for both the forward and reverse reactions by the same amount (it lowers the energy of the transition state). Therefore, both reactions speed up equally. The position of equilibrium is unchanged, but equilibrium is reached faster.

Example 3: A student increases the pressure on a gaseous reaction from 100 kPa to 200 kPa at constant temperature. Explain the effect on rate.

Doubling the pressure doubles the number of gas molecules per unit volume. The frequency of collisions increases, so there are more successful collisions per unit time. The rate increases. The proportion of molecules with energy ≥ Ea is unchanged.

Summary

Factor	Effect on rate	Mechanism
↑ Temperature	↑ Rate significantly	Greater proportion of molecules with E ≥ Ea
↑ Concentration	↑ Rate	Greater frequency of collisions
↑ Pressure (gases)	↑ Rate	Greater frequency of collisions
Catalyst	↑ Rate	Lower Ea, greater proportion of molecules with E ≥ Ea
↑ Surface area	↑ Rate	More exposed particles, greater collision frequency

Exam Tip: In exam answers, always state both what happens AND why (the mechanism). For temperature, the key point is the increased proportion of molecules exceeding Ea, not just "particles move faster".