Kinetics - The Maxwell–Boltzmann Distribution and Catalysts (A-Level Chemistry)

The Maxwell–Boltzmann Distribution and Catalysts

Molecules in a Gas

Understanding the Maxwell-Boltzmann Distribution

If you consider all the molecules in a gas, not all of the particles will have the same amount of kinetic energy. Some will have lots of kinetic energy, whilst some will have less kinetic energy. We can therefore plot a Maxwell-Boltzmann Distribution to show the distribution of energies between different molecules.

In terms of its definition, the Maxwell-Boltzmann Distribution represents the distribution of molecular energies in gases. It is a plot of the number of particles, where each particle has a particular energy.

Plotting a Maxwell-Boltzmann Distribution

You should be able to draw, label and interpret a Maxwell-Boltzmann distribution plot like the one below.

Here are some rules you need to know before you interpret a Maxwell-Boltzmann distribution:

1. Area under curve – the area under the curve is a measure of the total number of particles present.
2. Activation energy – A dotted line or straight line is used to represent the activation energy.
3. Shaded region – the shaded region to the right of the activation energy line represents the only particles that will react when they collide. These are the particles that have sufficient energy that is more than the activation energy.
4. Median (most common) particle energy – the peak of the curve represents the most common energy of any single particle in the reaction.
5. Mean particle energy – there is a line to the right of the peak, which shows the mean particle energy. This is higher than the median, because often very high energy particles are present, which distort the mean.

The Maxwell-Boltzmann Distribution and Temperature Changes

As we saw on the previous chapter, increasing the temperature of a system will increase the kinetic energy of reactant particles so that a larger proportion of the particles have at least in the system will have enough energy to undergo successful collisions.

This can be represented on a Mazwell-Boltzmann Distribution curve and you should also be able to draw and interpret Maxwell-Boltzmann Distribution curves for different temperatures:

According to this Maxwell-Boltzmann distribution:

• When the temperature is increased from T1 to T2, the shape of the Maxwell Boltzmann distribution changes. The peak lowers and shifts to the right.
• According to the Maxwell Boltzmann distribution, increasing the temperature increases the proportion of particles that have sufficient energy (at least the activation energy) to react. This can be observed from the shaded region which increases in area when the temperature is increased.
• As a result of there being a greater proportion of particles having sufficient energy to react, the rate of reaction increases.
• The graph shows that even a small increase in temperature can lead to a large increase in rate.

Catalysts and Rate of Reaction

Mechanism of Catalysts

A catalyst is a substance that increases the rate of a chemical reaction without being changed in chemical composition or amount.

The catalyst works by providing an alternative route to a reaction which has a lower activation energy, which means that a smaller amount of energy is needed to start a reaction.

The way catalysts achieve this depends on whether they are heterogeneous or homogeneous catalysts.

Heterogeneous Catalysts

A heterogeneous catalyst is in a different physical state (or phase) from the reactants. They provide a surface for the reaction to take place on, which facilitates reactant molecules to react with each other at a lower activation energy.

The process by which heterogeneous catalyst work involves three steps:

1. Adsorption – Reactant molecules arrive at the surface of the solid heterogeneous catalyst and form weak bonds with it by a process known as adsorption.
2. Reaction – Intermolecular bonds in the reagent particles weaken and eventually break, resulting in the formation of free radicals with unpaired electrons. These can then form new bonds with each other to form the product of the reaction.
3. Desorption – The newly formed products detach from the surface of the catalyst.

An example of a heterogeneous catalyst would be solid iron used as a catalyst for the formation of ammonia in the Haber Process.

Homogeneous Catalysts

A homogeneous catalyst is in the same physical state (or phase) as the reactants.

Homogeneous catalysts work by forming intermediate species with the reactant particles, which then react to form the products and reform the catalyst. The activation energies of this stepwise reaction are overall lower than the activation energy for the uncatalysed reaction.

Effect of Catalysts on the Rate of Reaction

Re-Use of Catalysts

If a catalyst is present at the start of a reaction, it will also be present at the end of the reaction. This means that catalysts can be re-used in several reactions.

You should be able to explain the qualitative effect of using a catalyst on the rate of reaction using a Maxwell Boltzmann distribution:

According to this Maxwell-Boltzmann distribution:

• Only the particles that are represented by the area to the right of the activation energy will react when they collide.
• When the catalyst is used, an alternative route is provided with a lower activation energy. This is represented by the shift in the line, labelled activation energy, to the left.
• According to the Maxwell Boltzmann distribution, using a catalyst increases the proportion of particles that have sufficient energy (at least the activation energy) to react. This can be observed from the shaded region which increases in area when the catalyst is used.
• As a result of there being a greater proportion of particles having sufficient energy to react, the rate of reaction increases.

Catalyst Use in Industry

The Haber Process mentioned previously is an example of how catalysts can be used in industry.

Catalysts are very widely used in industrial processes for their multiple economic benefits:

1. Catalyst use lowers production costs. By allowing for the reaction to take place at a lower temperature and pressures, which decreases energy demands; as well as by allowing more product to be formed in less time.
2. Catalyst use can improve the properties of reaction products. For example, poly (ethene) made in the presence of a catalyst is much denser, more rigid and withstands heat better than if produced without.

The use of catalysts in industrial processes also has environmental benefits:

1. Catalyst use makes industrial processes more sustainable. If industrial processes can operate at lower temperatures and pressures, less fossil fuels have to be burned and CO2 emissions are reduced.
2. Catalyst use reduces waste production. Using catalysts improves at the atom economy of the reaction hence producing less unwanted by-products.

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