for a gas mixture with gas A concentration 0.1 mol⋅L−1 and B concentration 0.2 mol⋅L−1, the number of density of A is 0.1×6.02×1023÷10−3 = 6.02×1025 m−3, the number of density of B is 0.2×6.02×1023÷10−3 = 1.2×1026 m−3. Z is the collision frequency in units of m−3⋅s−1. is the steric factor. Ea is the activation energy of the reaction, in units of J⋅mol−1. T is the temperature in units of K. R is the gas constant in units of J mol−1K−1. The unit of r(T) can be converted to mol⋅L−1⋅s−1, after divided by (1000×NA), where NA is the Avogadro constant. For a reaction between A and B, the collision frequency calculated with the hard-sphere model with the unit number of collisions per m3 per second is: where: σAB is the reaction cross section (unit m2), the area when two molecules collide with each other, simplified to , where rA the radius of A and rB the radius of B in unit m. kB is the Boltzmann constant unit J⋅K−1. T is the absolute temperature (unit K). μAB is the reduced mass of the reactants A and B, (unit kg). NA is the Avogadro constant. [A] is molar concentration of A in unit mol⋅L−1. [B] is molar concentration of B in unit mol⋅L−1. If all the units that are related to dimension are converted to dm, i.e. mol⋅dm−3 for [A] and [B], dm2 for σAB, dm2⋅kg⋅s−2⋅K−1 for the Boltzmann constant, then unit mol⋅dm−3⋅s−1. Quantitative insights Derivation 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 (σAB) 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