maxwell boltzman distribution

• Sally adds 10 gas molecules to a container at constant temperature


  Illustrate this scenario using a particle model diagram
• Sally believes all 10 gas molecules will have the same kinetic energy
• I disagree with Sally because some gas molecules will have:
• There is a distribution of kinetic energies:
• Boltzmann distribution


  The distribution of molecular energies of a gas at constant temperature
• Boltzmann distribution


  • The area under the curve represents the total number of molecules in the sample
  • No molecules have zero energy
  • There is no maximum energy for a molecule
  • Only a small proportion of molecules are able to react
• The Boltzmann distribution curve is also commonly known as the Maxwell-Boltzmann distribution
• James Maxwell statistically calculated the distribution of kinetic energies in 1859 and Ludwig Boltzmann applied the distribution to gases in 1871
• Boltzmann distribution


  • The most probable (most likely) energy of the molecules
  • The average energy of the gas molecules
• At higher temperatures


  The kinetic energy of all the molecules will increase
• At higher temperatures, the graph will lower and shift to the right, the area above Ea will be greater, and the overall area under the curve will remain the same because the number of molecules in the sample doesn't change
• At higher temperatures the rate of reaction will increase because the kinetic energy of the molecules will increase, increasing the proportion of molecules that will collide with an energy equal to or greater than the activation energy, increasing the frequency of successful collisions
• When a catalyst is added there is no change in the number or distribution of energy within molecules, so the shape and area under the graph remains the same
• Catalysts increase the rate of reaction by providing an alternative route with a lower activation energy, which increases the proportion of molecules that will collide with an energy equal to or greater than the activation energy, increasing the frequency of successful collisions
• The mean energy of the molecules is represented by the letter Z
• Some molecules in the sample have very low energies due to collisions causing some molecules to slow down or lose energy
• Only a small percentage of particles have an energy that is greater than the activation energy, even in a fast reaction
• The value of the most probable energy does not change as the total number of molecules is increased at constant temperature
• The number of molecules with the most probable energy increases as the temperature is decreased without changing the total number of molecules
• The number of molecules with energy greater than the activation energy increases as the temperature is increased without changing the total number of molecules
• The area under the molecular energy distribution curve does not change as a catalyst is introduced without changing the temperature or the total number of molecules
• A small increase in temperature has a large effect on the initial rate of a reaction because many more/a lot more molecules/particles collide with sufficient energy to react (with E ≥ Ea)
• Addition of a catalyst increases the rate of reaction because it provides an alternative route with a lower activation energy, increasing the number of molecules that will collide with an energy greater than (or equal to) the activation energy, leading to an increase in frequency of successful collisions