Why some reactions race and others crawl

What has to happen for particles to react

For two particles to react, bonds have to break and new bonds have to form, and that only happens when particles meet. Collision theory says a collision leads to a reaction only when three conditions are met:

1. the reactant particles collide;
2. they collide with at least a minimum amount of energy, the activation energy (E_a);
3. they collide with a suitable orientation, so the atoms that need to bond actually meet.

The activation energy is needed because existing bonds must be stretched and weakened before new ones can form. At the top of the energy hill the particles form a short-lived, high-energy arrangement called the activated complex (or transition state). A collision that has less energy than E_a simply bounces the particles apart, unchanged.

Most collisions fail. In a gas at room temperature each particle collides billions of times a second, yet many reactions take minutes or years. The rate of a reaction depends on the number of successful collisions per unit time.

Energy profiles

An energy profile diagram tracks the potential energy of the particles as the reaction proceeds. The reactants sit on the left, the products on the right, and the activated complex at the peak.

• The enthalpy change, ΔH, is the energy of the products minus the energy of the reactants. It is negative for an exothermic reaction (products lower, energy released to the surroundings) and positive for an endothermic reaction.
• The forward activation energy is measured from the reactants up to the peak.
• The reverse activation energy is measured from the products up to the same peak.

Because both barriers share the same peak, they are linked by \(E_\mathrm{a}(\text{reverse}) = E_\mathrm{a}(\text{forward}) – \Delta H\). For example, if \(E_\mathrm{a}(\text{forward}) = 75\) kJ mol⁻¹ and \(\Delta H = -120\) kJ mol⁻¹, then \(E_\mathrm{a}(\text{reverse}) = 75 – (-120) = 195\) kJ mol⁻¹. For an exothermic reaction the reverse barrier is always the larger one.

Energy profiles tell you about energy, not speed. A very exothermic reaction can still be extremely slow if its activation energy is high: a mixture of petrol vapour and air will sit unchanged until a spark supplies enough energy to get some particles over the barrier.

Temperature and the spread of particle energies

Particles in a sample do not all have the same energy. The Maxwell–Boltzmann distribution shows how many particles have each kinetic energy. A few are slow, most have moderate energies, and a long tail of particles have high energies. The area under the curve represents the total number of particles. Only the particles in the tail beyond E_a can react when they collide.

When the temperature rises, the average kinetic energy of the particles increases, so the curve flattens and shifts to the right. The area under the curve stays the same because the number of particles has not changed. Raising the temperature has two effects:

• particles move faster, so they collide more often. This is a small effect: a 10 °C rise near room temperature increases the collision frequency by only about 2%;
• a much larger fraction of collisions have at least E_a. This is the main effect, and it is why the rates of many reactions roughly double for a 10 °C rise.

The tail of the curve is where the action is, and the tail is very sensitive to temperature. The higher the activation energy, the further out in the tail E_a sits, and the greater the factor by which the rate increases for the same temperature rise.

The levers that control a reaction rate

Every factor that changes a rate works through one or both of two routes: it changes how often particles collide, or it changes the fraction of those collisions that succeed.

Surface area matters whenever one reactant is a solid, because only the particles on its surface can be hit. Breaking a lump into smaller pieces exposes particles that were buried. This is exactly what happened in the Washburn mill.

A catalyst provides an alternative reaction pathway with a lower activation energy. It takes part in the reaction but is regenerated, so it is not used up. Because it lowers the peak of the energy profile, it lowers the forward and reverse activation energies by the same amount and speeds up both directions. It does not change the energy of the reactants or the products, so ΔH is unchanged. Iron in the Haber process and the enzymes in your cells are both catalysts.

The nature of the reactants matters too. Reactions between oppositely charged ions in solution, such as the precipitation of silver chloride, are almost instantaneous because no strong bonds need to be broken. Reactions that must break strong covalent bonds tend to be slow at room temperature.

Reading rate graphs

A common way to follow a reaction is to measure a product as it forms, such as the volume of hydrogen released when magnesium reacts with hydrochloric acid. The gradient of the graph at any moment is the rate at that moment.

• The gradient is steepest at the start, when the concentration of reactants is highest.
• The gradient decreases as reactants are used up, because collisions become less frequent.
• The curve levels off when the limiting reactant is used up. The final volume depends only on the amount of limiting reactant, not on how fast the reaction went.

So curve B (warmer acid) is steeper but finishes at the same volume as A, while curve C (half the magnesium) finishes at half the volume. C also starts less steeply, because half the ribbon has half the surface area.