Collision Theory

Enzymes are biological catalysts that enhance the rate of a reaction by several mechanisms. Making a clear determination of the predominant mechanism is difficult. One may wonder if there is a physical limit to the rate of a chemical reaction? There is indeed such an upper limit; and two theories provide an estimate of the rate constant.

Collision Theory

Collision theory basically states for a bimolecular reaction to occur, molecules must:
  1. Collide with one another to initiate a reaction.
  2. Collide with a sufficient amount of energy.
  3. Collide in a specific orientation.

      Click to view a reaction:


      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.