For a bimolecular reaction in the gas of liquid state the rate constant can be expressed by:
Where:
- Z: The frequency of collisions between two molecules A and B that posses enough energy to overcome the energy barrier for a reaction to occur. .
- p: The fraction of molecules that have the correct orientation for a reaction. (To get the upper limit of the rate coefficient we assume that p = 1)
- Ea: The minimum activation energy for reaction.
Frequency of collisions Z:
The frequency Z can be correlated a number of ways:
- Maxwell-Boltzman distribution curve is a plot of the fraction of particles with a particular kinetic energy against kinetic energy values. Z can be calculated by taking the area under the curve that is greater than the minimum activation energy. Increasing the temperature of a reaction increases this area under the curve, which results in a greater Z.
- Z can also be calculated by:
Where:
- N: Avogadro’s number
- DA: Diffusion coefficient of molecule A
- DB: Diffusion coefficient of molecule B
- rA: Radii of molecule A
- rB: Radii of molecule B
- Z can also be expressed in terms of fluid viscosity, temperature, and radii of reacting species by the Stokes-Einstein equation:
Where:
- kb: Boltzmann constant
- h : Fluid viscosity
Substitution yields a new equation for Z:
Where R is the universal gas constant.