text: Consider the bimolecular elementary reaction:
  :A + B → C
  In collision theory it is considered that two particles A and B will collide if their nuclei get closer than a certain distance. The area around a molecule A in which it can collide with an approaching B molecule is called the cross section (σ) of the reaction and is, in simplified terms, the area corresponding to a circle whose radius () is the sum of the radii of both reacting molecules, which are supposed to be spherical. 
  A moving molecule will therefore sweep a volume  per second as it moves, where  is the average velocity of the particle. (This solely represents the classical notion of a collision of solid balls. As molecules are quantum-mechanical many-particle systems of electrons and nuclei based upon the Coulomb and exchange interactions, generally they neither obey rotational symmetry nor do they have a box potential. Therefore, more generally the cross section is defined as the reaction probability of a ray of A particles per areal density of B targets, which makes the definition independent from the nature of the interaction between A and B. Consequently, the radius  is related to the length scale of their interaction potential.)
  From kinetic theory it is known that a molecule of A has an average velocity (different from root mean square velocity) of , where  is the Boltzmann constant, and  is the mass of the molecule.
  The solution of the two-body problem states that two different moving bodies can be treated as one body which has the reduced mass of both and moves with the velocity of the center of mass, so, in this system  must be used instead of .
  Thus, for a given molecule A, it travels  before hitting a molecule B if all B is fixed with no movement, where  is the average traveling distance. Since B also moves, the relative velocity can be calculated using the reduced mass of A and B.
  Therefore, the total collision frequency, of all A molecules, with all B molecules, is
  From Maxwell–Boltzmann distribution it can be deduced that the fraction of collisions with more energy than the activation energy is . Therefore, the rate of a bimolecular reaction for ideal gases will be
  : in unit number of molecular reactions s⋅m,
  where:
  * Z is the collision frequency with unit s⋅m. The z is Z without [A][B].
  *  is the steric factor, which will be discussed in detail in the next section,
  * E is the activation energy (per mole) of the reaction in unit J/mol,
  *T is the absolute temperature in unit K,
  * R is the gas constant in unit J/mol/K.
  * [A] is molar concentration of A in unit mol/L,
  * [B] is molar concentration of B in unit mol/L.
  The product zρ is equivalent to the preexponential factor of the Arrhenius equation.