Collision theory, activation energy, the Maxwell-Boltzmann distribution, and the effects of temperature, concentration, surface area and catalysts on the rate of reaction.

What this topic is asking

Edexcel Topic 9 wants you to use collision theory and the Maxwell-Boltzmann distribution to explain reaction rates, and to explain the effects of temperature, concentration, pressure, surface area and catalysts. The marks come from precise language ("proportion of molecules with $E \ge E_a$", "frequency of successful collisions") rather than loose phrases.

The answer

Collision theory

For a reaction to occur, particles must collide, with energy at or above the activation energy ($E_a$) and with the correct orientation (geometry that lets the right bonds break and form). Most collisions are unsuccessful because they are too gentle or wrongly oriented. The rate of reaction depends on the frequency of successful collisions per unit time.

The Maxwell-Boltzmann distribution

Raising the temperature shifts the curve to the right and lowers and broadens its peak (the total area, the number of molecules, is unchanged). The crucial effect is on the shaded area beyond $E_a$: because $E_a$ sits on the steep tail, even a modest temperature rise sharply increases the proportion of molecules with $E \ge E_a$. Adding a catalyst does not change the curve at all; it moves $E_a$ to a lower value, so a larger area of the same curve now lies beyond the (lower) barrier.

Factors affecting rate

• Temperature. A higher temperature increases the proportion of molecules with $E \ge E_a$ and makes collisions slightly more frequent, so the rate of successful collisions rises sharply. This energy effect dominates the frequency effect.
• Concentration (or pressure for gases). More particles per unit volume means collisions are more frequent, so successful collisions per second increase.
• Surface area. Breaking a solid into smaller pieces exposes more particles at the surface, increasing the frequency of collisions with the other reactant.

Catalysts

On a reaction profile the catalysed route has a lower hump; on the Maxwell-Boltzmann diagram the lower $E_a$ means a greater proportion of molecules can react. Catalysts can be heterogeneous (different phase, e.g. iron in the Haber process, working by adsorption) or homogeneous (same phase, e.g. acid catalysis of esterification).

Examples in context

Example 1. Catalytic converters in cars. A catalytic converter contains platinum, palladium and rhodium on a honeycomb support. It catalyses the conversion of toxic $\text{CO}$ and $\text{NO}$ into $\text{CO}_2$ and $\text{N}_2$, for example $2\text{CO} + 2\text{NO} \rightarrow 2\text{CO}_2 + \text{N}_2$. The metals work heterogeneously: gases adsorb onto the surface, bonds weaken, the reaction proceeds with a much lower $E_a$, and the products desorb. The catalyst is not consumed, which is why a converter lasts the life of the car (provided it is not poisoned by lead).

Example 2. Why flour mills risk dust explosions. Solid flour burns slowly, but finely dispersed flour dust has an enormous surface area, so collisions between fuel and oxygen are vastly more frequent. The initial rate becomes so high that combustion is effectively instantaneous, which is why grain silos and flour mills enforce strict dust control. This is the surface-area factor from collision theory taken to an industrial extreme.

Try this

Q1. State the two conditions needed for a successful collision. [2 marks]

• Cue. Energy at or above $E_a$, and the correct orientation.

Q2. Explain why increasing temperature increases the rate of reaction. [3 marks]

• Cue. The Maxwell-Boltzmann distribution shifts right, so a greater proportion of molecules have energy at or above $E_a$, and collisions are more frequent, giving more successful collisions per second.