The Boltzmann distribution

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

  In a sample of a gas or liquid :

  • some molecules move fast + have high energy
  • some molecules move slow + have low energy
  • the majority of the molecules have an average energy
• The Boltzmann distribution is the distribution of energies of molecules at a particular temperature, often shown as a graph

  
• Important features :

  • the area under the curve is equal to the total number of molecules in the sample - area doesn't change with conditions
  • there are no molecules in the system with zero energy - the curve starts at the origin
  • there is no maximum energy for a molecule - the curve gets close to, but does not touch or cross, the energy axis
  • only the molecules with an energy greater than the activation energy, Ea, are able to react
• The effect of temperature on reaction rate

  • at higher temperatures, the kinetic energy of all the molecules increases + the Boltzmann distribution flattens + shifts to the right + the number of molecules in the system does not change, so the area under the curve remains the same

  
• The effect of temperature on reaction rate 2

  as the temperature increases , the rate of reaction increases

  • due to more collisions take place in a certain length of time - the molecules are moving faster + more kinetic energy
  • a higher proportion of molecules have an energy that is greater than the activation energy - more collisions will lead to a chemical reaction

  - > on collision more molecules in the system will overcome the activation energy of the reaction + there will be more successful collisions in a certain length of time + rate of reaction will increase
• the effect on catalyst on reaction rate

  • by lowering the activation energy, more particles will automatically be above the activation energy barrier
  • on collision, more molecules in the system will overcome the new lower activation energy of the reaction. there will be more successful collisions in a certain length of time + rate of reaction will increase