Reaction kinetics

The rate of reaction and how it is measured

The rate of reaction is the change in concentration of a reactant or a product per unit time. Concentration is measured in mol dm-3 and time in seconds, so a rate is usually quoted in mol dm-3 s-1; when a gas is collected instead, the rate may be quoted in cm3 s-1 or cm3 min-1. A rate is only meaningful if you say when it was measured, because the rate of a reaction is not constant: it is fastest at the very beginning, when the reactants are most concentrated, and it falls steadily as they are used up.

To follow a rate you need a property that changes measurably as the reaction proceeds. You can collect the gas produced in a gas syringe or over water, follow the loss in mass on a balance when a gas escapes, time how long a mixture takes to become cloudy enough to hide a cross on paper, or measure the change in colour with a colorimeter. Each method gives you a set of readings of the same kind: how much of something is there at known times.

From a graph of concentration (or volume, or mass) against time, the rate at any instant is the gradient of the curve at that point. Because the curve is not a straight line, you draw a tangent at the point you want and find the gradient of the tangent: rate = change in concentration / change in time. The gradient at t = 0 is the initial rate, which is the value chemists usually compare when they study how a change in conditions affects a reaction.

Collision theory: frequency and effectiveness of collisions

For a reaction to happen at all, the reacting particles must collide. Collisions in a liquid or a gas are extremely frequent, but almost all of them come to nothing: the particles simply bounce apart. A collision that does not lead to reaction is a non-effective collision, and it fails because the particles were not carrying enough energy when they met (and, in a molecule with a complicated shape, sometimes because they met the wrong way round).

A collision in which the particles do react is an effective collision. For a collision to be effective, the particles must collide with at least a certain minimum energy; anything less and they rebound unchanged. The frequency of collisions is simply how many collisions happen per unit time; what matters for the rate is the frequency of effective collisions, because only those change the reactants into products.

This gives the two levers that control the rate of any reaction. You can increase how often the particles meet, which is what raising the concentration or the pressure does, or you can increase the fraction of those collisions that are effective, which is what raising the temperature or adding a catalyst does. Every rate effect in this topic is one of these two ideas, so say which one you are using before you explain it.

• Collision: two particles meet. Most collisions in a gas or solution are frequent but useless.
• Non-effective collision: the particles rebound unchanged, because there was not enough energy (or the orientation was wrong).
• Effective collision: the collision leads to reaction, which requires energy greater than or equal to the activation energy.
• Rate depends on the frequency of effective collisions per unit time, not on the total number of collisions.

Concentration and pressure: getting the particles closer together

Increasing the concentration of a reactant means putting more of its particles into the same volume. The particles are closer together, they meet more often, and the frequency of collisions rises. Because collisions in general are more frequent, the number of collisions per second that carry at least the activation energy also rises, so the frequency of effective collisions rises and the reaction goes faster.

The same argument covers pressure. For a reaction between gases, raising the pressure squeezes the same number of molecules into a smaller volume, which is exactly the same as increasing the concentration. Doubling the pressure of a gaseous reactant doubles its concentration and makes the collisions between its molecules more frequent, so the rate increases.

Two things are worth pinning down. First, concentration and pressure change the rate only; they do not change the activation energy, and they do not change the position of equilibrium, so they cannot be used to raise a yield at equilibrium. Second, in a reaction between two different substances, changing the concentration of one reactant often changes the rate much more than changing the concentration of the other by the same amount, so a rate experiment has to test the two reactants separately.

Activation energy and the Boltzmann distribution

The activation energy, EA, is the minimum energy required for a collision to be effective. It is the energy barrier that the colliding particles must overcome, and it is a property of the reaction: the bonds in the reactants must be stretched and broken far enough for the rearrangement to begin, and that costs energy. A reaction with a high activation energy is slow at room temperature because very few collisions carry that much energy; a reaction with a low activation energy is fast.

The Boltzmann distribution shows how the energies of the molecules of a gas or liquid are spread at a fixed temperature. Plot the number of molecules (or the fraction of molecules) on the vertical axis against kinetic energy on the horizontal axis, and you get a curve with a characteristic shape: it starts at the origin, because no molecule has zero energy; it rises steeply to a single maximum; it then falls away smoothly to the right; and it approaches the horizontal axis without ever touching it, because a tiny number of molecules always have very high energies.

The curve is not symmetrical, and it moves with the temperature. At a higher temperature the maximum becomes lower, the curve becomes flatter, the peak moves to the right, and the tail at high energy gets much fatter. The important quantity is an area: mark the activation energy on the horizontal axis and shade the area under the curve to the right of it. That shaded area is the fraction of collisions that have enough energy to react, and it is the reason activation energy has its significance. For a typical reaction at room temperature only a very small fraction of collisions is found in that shaded region, so only a small fraction is effective, however many collisions there are.

• The curve starts at the origin: no molecule has zero kinetic energy.
• It rises to a single peak, then falls away to the right.
• It never meets the energy axis: a few molecules always have very high energies.
• The area under the curve to the right of EA is the fraction of molecules that can react.
• Raising the temperature lowers and flattens the peak and moves it to the right, so the area beyond EA grows.

Temperature: why a small rise can double the rate

Raising the temperature speeds a reaction up for two reasons, and Cambridge expects both. First, the molecules move faster, so they meet more often: the frequency of collisions increases. Second, and far more important, the particles have a higher average kinetic energy, so a much larger fraction of them has energy greater than or equal to the activation energy. Both effects increase the frequency of effective collisions, but the second dominates by a long way.

The Boltzmann distribution shows why a modest rise in temperature has such a large effect. At the original temperature the area to the right of EA is a thin sliver. Raise the temperature and the whole curve flattens and shifts to the right, and because the curve is falling steeply near EA, even a small shift to the right adds a large amount of area under the tail. A rise of only 10 K, taking the mixture from about 298 K to about 308 K, therefore produces a much bigger increase in the number of effective collisions than the small increase in collision frequency would explain on its own.

Keep the vocabulary straight in an answer. Temperature does not change the activation energy, and it does not give every molecule enough energy to react: the great majority of molecules still have less than EA. What changes is the proportion of molecules that has at least EA, and therefore the frequency of effective collisions. A common but wrong explanation says that raising the temperature lowers the activation energy; only a catalyst does that.

Catalysts: homogeneous and heterogeneous

A catalyst is a substance that increases the rate of a reaction by providing an alternative reaction pathway of lower activation energy. It is not used up in the reaction and is chemically unchanged at the end, although it may change physically, for example a lump of catalyst may break up into powder. A catalyst works because the new pathway takes the reaction over a lower energy barrier, and it is this new mechanism that is the definition worth remembering: in the presence of a catalyst the reaction has a different mechanism, one of lower activation energy.

The Boltzmann distribution explains the effect at once. The molecules still have the same spread of energies at a given temperature, because the temperature has not changed, but the activation energy on the horizontal axis moves to the left. The area under the curve beyond that smaller activation energy is much larger than before, so a much greater fraction of collisions is effective, and the rate rises. In an uncatalysed reaction the catalyst can be regenerated many times over, so a small amount of catalyst can speed up a very large amount of reaction.

In homogeneous catalysis the catalyst is in the same physical state as the reactants. Aqueous acid catalysing the hydrolysis of an ester is the standard example: the acid is in the same aqueous phase as the ester and it is regenerated at the end, and the new pathway goes through a protonated intermediate that breaks down more readily. Iron(II) and iron(III) ions catalysing the reaction between peroxodisulfate ions and iodide ions work in the same way, the iron ion being reduced and then reoxidised in two steps of lower activation energy than the single uncatalysed step.

In heterogeneous catalysis the catalyst is in a different physical state from the reactants, which is the usual arrangement in industry: a solid catalyst with gaseous or liquid reactants. The mechanism runs on the surface. The reactant molecules are adsorbed onto the active sites of the solid, they react there in a favourable orientation with the activation energy of the surface pathway, and the product molecules are desorbed back into the gas or liquid. Because the reaction happens on the surface, the rate depends on the surface area of the catalyst, which is why industrial catalysts are made as finely divided powders or spread thinly over a honeycomb support.

• Homogeneous catalysis: catalyst and reactants in the same physical state, often both in solution or both gases.
• Heterogeneous catalysis: catalyst in a different physical state, usually a solid with gaseous or liquid reactants.
• Heterogeneous mechanism: adsorption onto active sites, reaction on the surface, desorption of the products.
• A finely divided catalyst has a larger surface area, so more reactant can be adsorbed per unit time and the rate is greater.

Reaction pathway diagrams and what they show

A reaction pathway diagram (an energy profile) plots the energy of the reacting species on the vertical axis against the progress of the reaction on the horizontal axis. The reactants are marked at the left and the products at the right, and between them the curve rises to a maximum that represents the highest-energy arrangement along the way. The difference in energy between the reactants and the top of that barrier is the activation energy; the difference between the products and the reactants is the enthalpy change of the reaction.

Draw a second curve on the same axes for the catalysed reaction and the difference stands out. Both curves start at the same energy for the reactants and finish at the same energy for the products, because the catalyst does not change the reactants or the products; the catalysed curve simply takes a different route, usually in more than one step, so it may show two or more humps, and its highest point is lower. The activation energy is smaller with the catalyst, and because the catalyst lowers the barrier of the forward and the reverse reaction by the same amount, it is smaller for the backward reaction too.

That last point explains the behaviour of equilibrium systems. A catalyst changes neither the enthalpy change nor the position of equilibrium, because the products and reactants are unchanged and both directions are accelerated equally. What it does change is the time taken to reach that position: with a lower activation energy, equilibrium is established sooner. So when a question asks why an industrial catalyst such as iron in the Haber process is used, the answer is that it allows a workable rate at a lower temperature and pressure, not that it increases the yield.