Maxwell-Boltzmann Distributions (Edexcel AS Chemistry)

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 gas, a few particles will have very low energy, a few particles will have very high energy, but most particles will have energy in between

The Maxwell-Boltzmann distribution curve shows the distribution of the energies and the activation energy

• The graph shows that only a small proportion of molecules in the sample have enough energy for an effective collision and for a chemical reaction to take place

Changes in temperature

• 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 Boltzmann distribution curve flattens and the peak shifts to the right

 

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

• Catalysis is the process in which the rate of a chemical reaction is increased, by adding a catalyst
• A catalyst increases the rate of a reaction by providing the reactants with an alternative reaction pathway which is lower in activation energy than the uncatalysed reaction
• Catalysts can be divided into two types:
  • Homogeneous catalysts
  • Heterogeneous catalysts

• Homogeneous means that the catalyst is in the same phase as the reactants
  • For example, the reactants and the catalysts are all in solution

• Heterogeneous means that the catalyst is in a different phase to the reactants
  • For example, the reactants are gases but the catalyst used is a solid

The diagram shows that the catalyst allows the reaction to take place through a different mechanism, which has a lower activation energy than the original reaction

Maxwell-Boltzmann distribution curve

• Catalysts provide the reactants another pathway which has a lower activation energy
• On the graph below, the original number of successfully reacting particles is shown by the dark shaded area
• By lowering E_a, a greater proportion of molecules in the reaction mixture have the activation energy, and therefore have sufficient energy for an effective collision
  • This is shown by the combined number of particles in the light and dark shaded areas
• As a result of this, the rate of the catalysed reaction is increased compared to the uncatalysed reaction

 

The diagram shows that the total shaded area (both dark and light shading) under the curve shows the number of particles with energy greater than the E_a 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 E_a without a catalyst