Maxwell-Boltzmann distribution and catalystsEdexcel International A Level Chemistry: Revision notes

Section 1

The Maxwell–Boltzmann distribution

The molecules in a gas have a spread of energies, shown by a Maxwell–Boltzmann distribution: a curve of the number of molecules against energy.

The curve starts at the origin (no molecules have zero energy) and has a long tail to high energy that never touches the axis.
The area under the curve equals the total number of molecules.
Only molecules with energy equal to or greater than the activation energy ( $E_a$ ) can react: this is the area to the right of the $E_a$ line.

Key termsMaxwell–Boltzmann distributionhigh-energy tail

Section 2

Effect of temperature

At a higher temperature the peak moves to a higher energy and is lower, and the curve is flatter and wider. The total area stays the same because the number of molecules is unchanged.

The area beyond $E_a$ is much larger, so a greater proportion of molecules can react. More collisions are successful each second, so the rate increases sharply even though the mean energy rises only slightly.

Key termsproportion of molecules

Common mistake

Do not draw the higher-temperature curve with a larger area, or let it cross the energy axis. The area is constant and the curve never touches the axis.

Section 3

Catalysts and activation energy

A catalyst speeds up a reaction by providing an alternative route with a lower activation energy. It is not used up and does not change the enthalpy change or the position of equilibrium.

On a Maxwell–Boltzmann diagram the distribution stays the same but the $E_a$ line moves left. A greater proportion of molecules then have enough energy at the same temperature, so there are more successful collisions per second.

Key termscatalyst

Exam tip

Say 'alternative route with lower activation energy', not 'lowers the activation energy of the same route'.

Section 4

Reaction profiles with a catalyst

A reaction profile plots energy against the progress of reaction. The uncatalysed profile has one peak at $E_a$ . With a catalyst, the reactants often bond to the catalyst to form an intermediate, so the profile shows two lower peaks with a dip (the intermediate) between them.

Reactants and products are at the same energy in both profiles, so $\Delta H$ is unchanged. The highest peak gives the rate-determining step.

Example: peaks at +80 and +60 kJ mol⁻¹ with an intermediate at +30 kJ mol⁻¹: step 1 has $E_a = 80$ kJ mol⁻¹ and step 2 has $E_a = 60 - 30 = 30$ kJ mol⁻¹.

Key termsreaction profileintermediate

Section 5

Catalysts and sustainability

Catalysts make industrial processes more sustainable by:

allowing lower temperatures and pressures, so less energy is used and less fuel burned
enabling routes with a higher atom economy, so less waste

$\text{atom economy} = \frac{\text{M}_r \text{ of desired product}}{\text{sum of M}_r \text{ of all reactants}} \times 100$

Key termsatom economysustainable

That's the notes covered.

Carry on to the next subtopic.

Exam questions on Maxwell-Boltzmann distribution and catalysts

A chemist sketches Maxwell–Boltzmann distributions of molecular energies for the same sample of gas at 300 K and at 310 K. She notes that the mean kinetic energy of the molecules rises by only about 3% over this range, yet the rate of a reaction in the gas roughly doubles.
Explain, using the Maxwell–Boltzmann distribution, why a rise in temperature of only 10 K can double the rate even though the mean kinetic energy rises very little.2 marks
Hydrogen peroxide solution decomposes slowly at room temperature to form water and oxygen. When a small amount of solid manganese(IV) oxide is added, oxygen is released rapidly, and the manganese(IV) oxide can be recovered unchanged at the end.
Describe how the reaction profile for the catalysed route differs from the profile for the uncatalysed route, given that the catalyst forms an intermediate.2 marks
Ethanol can be made industrially by the catalysed hydration of ethene with steam, using phosphoric acid on a silica support at about 570 K. A laboratory alternative is to react bromoethane with aqueous sodium hydroxide, which gives sodium bromide as the only other product. A company wants to know which route is more sustainable.
Explain, in terms of activation energy, how a catalyst allows a process to be carried out at a lower temperature, and why this makes the process more sustainable.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).