Reaction Rates

Collision theory

The rate of a chemical reaction depends on two things:

1. How often the reactant particles are colliding

2. How many of those collisions are successful

For reactants to collide successfully, they need to:

• Collide in the correct orientation and

• Collide with enough energy (more than the activation energy).  

The more frequent and successful the collisions are, the faster the rate of reaction. The rate of reaction depends on the following factors:

• Concentration (for liquids) / pressure (for gases) – increasing the concentration or pressure means you have more reactant particles in a given volume, meaning there are more frequent collisions.

• Surface area – increasing the surface area of a solid reactant means that more particles will be exposed, so there are more frequent collisions.

• Temperature – increasing the temperature causes particles to move faster, so they collide more frequently. The particles also have more energy, so a greater proportion of the collisions will be successful.

• Catalyst – adding a catalyst will reduce the activation energy for the reaction. Dropping the energy barrier means that more particles will have sufficient energy to react, so there will be more successful collisions, increasing the rate of reaction.

You can calculate the rate of reaction by dividing the change in the amount of reactant or product over time. For example, in a reaction where solid products are being converted into gases, you could measure how much mass of solid was lost in a given amount of time. Or you could measure the volume of gas formed in a given time.

You can calculate the rate of a reaction from a graph by calculating its gradient. The steeper the gradient, the faster the rate of reaction.

To calculate the gradient from a straight-line graph, pick two points on the line that are easy to read and draw vertical and horizontal lines to form a triangle. The gradient of the line is equal to the change in y over the change in x.

Catalysts

A catalyst speeds up the rate of a chemical reaction without being used up — or chemically altered — in the process. It works by providing an alternative reaction pathway that requires less activation energy. It’s a bit like finding a shortcut from your house to the park: you start and end in the same place, but the simpler route requires less energy.

Since less energy is required, more particles will have sufficient energy to react. There will be more successful collisions and therefore a faster rate of reaction.

This is shown in energy profile diagrams, where the upwards curve to get from the reactants to the products is smaller.

Homogeneous and heterogeneous catalysts

Homogenous catalysts are catalysts which are in the same state (or phase) as the reactants. For example, if the reactants are all aqueous, then a homogenous catalyst will also be aqueous.

Heterogeneous catalysts are in a different state/phase to the reactants. Using a solid catalyst to catalyse a reaction between gases is an example of heterogeneous catalysis.

The reaction will happen on the surface of the catalyst, which means that increasing the surface area of the solid catalyst will increase the reaction rate. Things like catalytic converters will have a honeycomb structure to provide as much surface area as possible.

For a heterogeneous reaction, the surface area of the catalyst may act as a limiting factor for rate of reaction. For instance, if the active sites of a solid catalyst are already saturated, then increasing the pressure of the gaseous reactants will not be able to increase the rate any further.

Benefits of using catalysts

Using catalysts isn’t just a time-saver but has huge benefits for industrial processes and environmental sustainability. For example:

• Catalysts are used to make industrial processes cheaper and faster. For example, iron catalysts are used in the production of ammonia for fertilisers. In the absence of a catalyst, high temperatures and a lot of energy would be required to make the reaction happen at a reasonable pace. Less ammonia would be produced and the manufacturers would have to make their product more expensive.

• Since catalysts allow reactions to take place at lower temperatures, less fuel needs to be burned and less carbon dioxide is emitted, making the reaction more sustainable.

• Catalysts can reduce waste by providing an alternative reaction pathway with a higher atom economy. For the synthesis of ibuprofen, adding a catalyst increases the atom economy for the reaction by 45%. The production of less waste is better for the environment.

Boltzmann distribution

Within a reaction, not all particles will have the same amount of energy — some have a little energy, some have lots but most will have an intermediate amount.

We can represent the proportions of particles with different amounts of energies in a Boltzmann distribution graph. The y-axis tells us the number of molecules with a particular amount of energy, with kinetic energy increasing as you go along the x-axis.

From the graph below, we can see that a small number of molecules have a low amount of energy while most molecules have a moderate amount of energy. The downhill slope of the graph shows that a few molecules have a very high amount of energy.

We can add the activation energy for a reaction to our Boltzmann distribution to give us an idea of the proportion of molecules with enough kinetic energy to collide successfully with other molecules. Any particles that lie to the right of the activation energy barrier will have enough energy to react.

Since catalysts work by lowering the activation energy, this increases the proportion of particles in the reaction mixture with sufficient energy to react successfully.

Boltzmann distribution graphs can also be used to show how higher temperatures increase reaction rate. At hotter temperatures, the particles will have more kinetic energy and start moving faster. This means that a greater proportion of particles will exceed the activation energy ‘barrier’ to react, so more of them will lie to the right hand side of our activation energy line.

The shape of the Boltzmann distribution curve changes as temperature increases – it has a smaller peak and shifts over to the right. The total number of particles hasn’t changed, so the area under the curve should be equal to our curve at a lower temperature.