Collision Theory and Activation Energy

A more concentrated solution contains more dissolved reactant particles in a given volume. With more reacting particles in the same space, collisions between reactants become more frequent.

For example, magnesium reacts faster with a more concentrated acid, provided the other conditions are unchanged. More acid particles are available to collide with the magnesium surface each second. At the same temperature, the proportion of collisions with sufficient energy is unchanged, but the greater collision frequency means more successful collisions per second.

Diluting the acid has the opposite effect: fewer acid particles per unit volume lead to less frequent collisions and a slower reaction.

Gas pressure: bringing particles closer together

For reacting gases, increasing pressure by compressing them into a smaller volume brings the particles closer together. The number of particles has not increased, but there are now more particles per unit volume.

At constant temperature, this makes collisions more frequent without making the particles more energetic. More successful collisions occur per second, so the reaction rate increases. Reducing the pressure by allowing the gases to occupy a larger volume has the opposite effect.

Concentration and gas pressure therefore have a similar explanation: both can increase the number of reacting particles in a given volume.

Solid piece size: exposing more of the reactant

When a solid reacts with a solution or gas, collisions occur at its exposed surface. Particles inside a large lump are not initially accessible to the other reactant.

Breaking the same mass of solid into smaller pieces exposes more surface without changing the total volume of solid. Smaller pieces have a larger surface area to volume ratio. More solid particles are available for collisions, so successful collisions occur more frequently and the reaction is faster.

For example, powdered calcium carbonate reacts faster with acid than the same mass of large marble chips, when the acid and temperature are otherwise unchanged.

A cube shows why cutting matters. One cube with sides of 2 cm has a volume of 8 cm³ and a surface area of 24 cm². Cutting it into eight separate cubes with sides of 1 cm leaves the total volume at 8 cm³, but increases the total exposed surface area to 48 cm². The surface area per unit volume has doubled because previously internal surfaces are now exposed.

The smaller cubes must be separated so that the other reactant can reach their new surfaces. This model explains why a powder generally reacts faster than lumps of the same solid.

Temperature: more frequent and more energetic collisions

Heating gives particles more kinetic energy. They move faster, so they collide more frequently.

There is also a second important effect. Particles do not all have the same energy. At a higher temperature, a greater proportion of collisions have energy at least equal to the activation energy. A larger fraction of collisions is therefore successful.

Together, these effects produce more successful collisions per second and a faster reaction. Cooling reverses both effects: particles move more slowly, collisions are less frequent, and a smaller proportion have sufficient energy to react.

The activation energy itself does not fall when the reaction mixture is heated. Heating changes the particles’ energies, not the energy threshold they must reach.

Using simple proportionality

In a simple collision model, doubling the concentration of one reactant while keeping the other conditions unchanged can approximately double its collision frequency with the other reactant. If the fraction of successful collisions stays the same, the reaction rate approximately doubles too.

For this model:

$$\text{rate} \propto \text{concentration}$$

Direct proportionality means that halving the concentration halves the predicted rate, while tripling it triples the predicted rate. The explanation must still link the concentration change to particles per unit volume and then to successful collisions per second.

This is not a universal rule for every reaction. Use it when the question or data supports the simple relationship. In particular, temperature does not have this simple proportional effect: it changes both collision frequency and the proportion of collisions that are successful.

• Higher concentration: more reactant particles per unit volume → more frequent collisions → faster reaction.
• Higher gas pressure by compression: particles closer together → more frequent collisions → faster reaction, at constant temperature.
• Smaller solid pieces, same mass: larger surface area to volume ratio → more exposed particles → more frequent collisions → faster reaction.
• Higher temperature: faster particles → more frequent collisions; greater proportion of collisions have sufficient energy → faster reaction.

Decreasing these factors has the opposite effect. Heating does not lower activation energy.

Simple proportionality

Where the simple model applies:

$$\text{rate} \propto \text{concentration}$$

Doubling concentration approximately doubles rate if other conditions are unchanged. Do not apply this relationship automatically to every reaction or to temperature.