Maxwell-Boltzmann Distribution Curves
What is a Maxwell-Boltzmann distribution curve?
- A Maxwell-Boltzmann distribution curve is a graph that shows the distribution of energies at a certain temperature
- In a sample of a substance:
- A few particles will have very low energy
- A few particles will have very high energy
- Many particles will have energy in between
Maxwell-Boltzmann distribution curve
The Maxwell-Boltzmann distribution curve shows the distribution of energies and the activation energy
- The graph shows that only a small proportion of particles in the sample have enough energy for an effective or successful collision and for a chemical reaction to take place
- The most probable energy of a particle is represented by the highest point on the curve's peak
- This is sometimes written as EMP
Effect of changes in temperature on the Maxwell-Boltzmann distribution curve
- When the temperature of a reaction mixture is increased, the particles gain more kinetic energy
- This causes the particles to move around faster, resulting in more frequent collisions
- Furthermore, the proportion of successful collisions increases, meaning a higher proportion of the particles possess the minimum amount of energy (activation energy) to cause a chemical reaction
- With higher temperatures, the Maxwell-Boltzmann distribution curve flattens and the peak shifts to the right
Graph of the effect of temperature on the Maxwell-Boltzmann distribution curve
The Maxwell-Boltzmann distribution curve at T oC and when the temperature is increased by 10 oC
- Therefore, an increase in temperature causes an increased rate of reaction due to:
- There being more effective collisions as the particles have more kinetic energy, making them move around faster
- A greater proportion of the molecules having kinetic energy greater than the activation energy
Exam Tip
- When drawing Maxwell-Boltzmann distribution curves at different temperatures, make sure that:
- The peak of the curve of the higher temperature is lower and to the right of the peak of the curve of the lower temperature
- The two curves should only cross each other once
- The tail of the curve of the higher temperature should be higher than that of the lower temperature
- Careful: Examiners currently prefer to ask about the effect of reducing the temperature of a reaction, rather than increasing the temperature
- The underlying theory is still the same but you need to apply it in the opposite direction
Effect of a catalyst on the Maxwell-Boltzmann distribution curve
- A catalyst provides the reactants with another reaction pathway which has a lower activation energy
- By lowering Ea, a greater proportion of molecules in the reaction mixture will have sufficient energy for a successful collision
- As a result of this, the rate of the catalysed reaction is increased compared to the uncatalysed reaction
Maxwell-Boltzmann distribution curve with a catalyst
The total shaded area (both dark and light shading) under the curve shows the number of particles with energy greater than the Ea when a catalyst is present. This area is much larger than the dark shaded area which shows the number of particles with energy greater than the Ea without a catalyst. The light-shaded area shows the extra particles which have enough energy to react with a catalyst.
Exam Tip
- Make sure you know how to sketch and label the axes in Maxwell-Boltzmann distribution curves
- The curve must start at the origin and it approaches, but never touches the x-axis.
- If you are asked to show the area that represents the particles with an energy greater than the activation energy with a catalyst, make sure you highlight the total shaded area, not just the light-shaded area.