3.5.3 The Boltzmann Distribution

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
• The energy distribution should go through the origin because there are no molecules with no energy
• The energy distribution should never meet the x axis, as there is no maximum energy for molecules
• The area underneath the curve represents the total number of particles present

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

Effect of catalysts

• Catalysts provide the reactants another pathway which has a lower activation energy
• 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
• 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