Rate of Reaction

Chemists can find out many different pieces of information about particular reactions. The most useful are the enthalpy changes associated with reactions and information about how fast a reaction will occur. Controlling reaction rates and understanding the processes by which reactants change into products are essential skills for a chemist.

You will be familiar with many everyday uses of the term ‘rate’. For example the rate kinetics of movement of a car is referred to as speed: the distance travelled by the car in relation to the time taken for the journey. The rate of a chemical reaction is measured as the amount of product made or reactant used up in a certain time.

\[Rate = \frac{{increase{\kern 1pt} \,in\,concentration}}{{time}}\]

Collision theory

When a chemical reaction takes place the reactant particles must collide. The theory which explains the reactions that take place as the result of collisions is called collision theory. Imagine a gaseous substance in which the particles are in constant random motion. The particles are continuously colliding with each other and with the walls of their container. Not all of the collisions between the gaseous particles result in a reaction.

The diagram shows that in order for a reaction occur:

• the correct particles must collide
• the collision must be of the correct energy

In order to maximize the energy of the collision the particles must be moving quickly and collide head on. Reaction conditions can be altered to maximize the probability of a collision occurring or to increase the energy with which particles collide. The factors that affect the rates of chemical reactions are:

• the temperature of the reactants
• the concentration of the reactants and products
• the surface area of reactants
• the presence of any catalysts

Activation energy

The minimum energy with which particles must collide in order for a reaction to occur is referred to as the ‘activation energy’. If the particles collide with energy less than the activation energy then the particles will simply bounce off each other and no reaction will occur. If the particles collide with energy equal to or greater than the activation energy the collision is described as successful and a reaction will take place.

Activation energy and enthalpy changes

The diagrams shows the relationship between the activation energy, E_a, of a reaction and the enthalpy change of the reaction.

The reaction profiles for (a) an exothermic reaction and (b) an endothermic reaction. E_a is the activation energy barrier that reactants must overcome before they can change into products. ΔH indicates the overall enthalpy change for the reaction.

For the reaction of calcium carbonate with hydrochloric acid, the rate can be monitored by collecting the carbon dioxide gas released.

CaCO₃(s) + 2HCl(aq) --> CaCl₂(aq) + H₂O(l) + CO₂(g)

The graph obtained will be a curve until the reaction is finished. The gradient or slope at any point on the curve will give us the rate of reaction at that particular point in time.

Temperature is used as a measure of the amount of energy of the particles in a substance. For example if a sample of gas is heated up to a higher temperature this tells us that the average amount of energy each particle possesses has increased. You know that whether a reaction takes place or not is dependent on:

• the energy of the colliding particles
• the number of collisions Maxwell–Boltzmann distribution of molecular energies

In a sample of gas at a given temperature, the molecules do not all have the same energy. They are all moving at different speeds. At any instant some of the particles have a very low energy, a small proportion have a very high energy while the majority of the particles have an intermediate energy.

In 1859 the Scottish physicist James Clerk Maxwell calculated this distribution of energies in a sample of gas. His ideas were applied by the Austrian physicist Ludwig Edward Boltzmann in 1871. The resulting graph showing the distribution of molecular energies is known as the Maxwell–Boltzmann distribution.

Note the following features of the curve:

• Only very small fractions of the molecules have extremely high or extremely low energies.
• The curve is not symmetrical; the average energy is to the right of the peak of the curve.
• The curve passes through the origin.
• The curve does not touch the x (horizontal) axis on the right hand side. It is an asymptote, a line or curve which approaches another but never touches it.

The shaded area under the right of the curve shows the proportion of molecules that possess the activation energy (the minimum energy with which particles must collide in order to react). Only molecules in this portion of the curve are able to react. Each reaction has its own activation energy. At a given temperature a reaction with higher activation energy will be slower than one with lower activation energy.

Effect of temperature

The shape of the Maxwell-Boltzmann distribution changes as temperature is altered. As the temperature increases the energy distribution moves to the right and the height of the peak decreases. The total area under the curve is constant as this represents the total number of particles.

For a small increase in temperature the shape of the graph remains broadly the same but note that the area of the shaded portion has increased, so more molecules have energy greater than or equal to the activation energy.

For a large increase in temperature the shape of the graph alters more dramatically.

Note that altering the temperature does not have any effect on the value of the activation energy; this is constant for a given reaction. Increasing the temperature does not influence this value it increases the energy with which particles collide so that more of these collisions possess the activation energy.

Catalysis

Many of the reactions essential for our everyday life would not occur without the presence of catalysts. They can be recovered at the end of the reaction and used many times over. Industrially, catalysts are used in the manufacture of ammonia, sulphuric acid, margarines, plastics, and fertilizers. Without the presence of enzymes (biological catalysts) our bodies would not function, we would not have biological washing powder, nor have bread to eat or alcohol to drink.

Catalysts

A catalyst can be described as a substance that alters the rate of a chemical reaction and remains unchanged at the end of the reaction. The catalyst acts by providing an alternative route of lower activation energy. This reduction in activation energy enables many more of the collisions between reactants to achieve this minimum requirement for a reaction to take place. Therefore the rate of the reaction increases.

Catalysts and the Maxwell–Boltzmann distribution

The addition of a catalyst to a reaction has no effect on the energies of the reactant molecules or on the total number of molecules in the reaction system. It therefore has no effect on the shape or size of the Maxwell–Boltzmann distribution. The activation energy line is marked further to the left hand side of the curve to show the reduction in its value. This has a significant effect on the number of particles that are found in the shaded area of the curve and can therefore take part in the reaction.

Adding a catalyst to a reaction lowers the activation energy. This means more molecules can collide with enough energy to react.

Heterogeneous and homogeneous catalysts

There are two important classes of catalysts: heterogeneous and homogeneous.

Heterogeneous catalysts

A heterogeneous catalyst is in a different phase from the reactants. For example in the hardening of vegetable oils for the production of margarine a nickel catalyst is used to reduce the activation energy for the reaction of two gases: hydrogen and an alkene. The reactant molecules attach themselves to the nickel surface breaking the C=C in the alkene as they attach. The reaction then takes place on the surface and the alkane molecules formed detach from the surface. You will learn about the catalytic converter, an important use of heterogeneous catalysts, when you study the combustion of fossil fuels.

Catalytic converters in the exhaust systems of modern cars show all the main features of a heterogeneous catalyst. The catalyst consists of about 2g of finely divided platinum/rhodium, on a rigid ceramic support. The primary effect is to catalyse the conversion of the pollutants carbon monoxide and nitrogen monoxide to carbon dioxide and nitrogen.

2CO(g) + 2NO(g) --> 2CO₂(g) + N₂(g)

 Note that leaded petrol will rapidly poison a catalytic converter.

Homogeneous catalysts

A homogeneous catalyst is in the same phase as the reactants. Chlorine radicals act as a homogeneous catalyst in the upper atmosphere, and have a devastating effect on the sequence of reactions which take place constantly making and destroying ozone. One chlorine radical can catalyse as many as one hundred thousand reactions. The series of reactions that take place is complex and you will study them in more detail elsewhere. Some of them are given here:

Cl^• + O₃ --> ClO^• + O₂

ClO^• + O3 --> Cl^• + 2O₂

The chlorine radical is represented by Cl^•. It destroys ozone in the first reaction and is regenerated in the second.

Another example is the bombardier beetle:

The bombardier beetle stores hydrogen peroxide, water, and noxious substances in an abdominal sac. When threatened, it injects a catalyst into this mixture. The almost instantaneous exothermic decomposition of hydrogen peroxide generates steam, which ejects the contents of the sac as a hot and highly offensive spray.