Collision Theory and Boltzmann Constant

The Collision theory, proposed by Max Trautz and William Lewis in 1916 and 1918, qualitatively explains how chemical reactions occur and why reaction rates differ for different reactions. This theory is based on the idea that reactant particles must collide for a reaction to occur, but only a certain fraction of the total collisions have the energy to connect effectively and cause the reactants to transform into products. This is because only a portion of the molecules have enough energy and the right orientation (or "angle") at the moment of impact to break any existing bonds and form new ones. The minimal amount of energy needed for this to occur is known as activation energy. Particles from different elements react with each other by releasing activation energy as they hit each other. If the elements react with each other, the collision is called successful, but if the concentration of at least one of the elements is too low, there will be fewer particles for the other elements to react with and the reaction will happen much more slowly. As temperature increases, the average kinetic energy and speed of the molecules increases but this only slightly increases the number of collisions. The rate of the reaction increases with temperature increase because a higher fraction of the collisions overcome the activation energy.
Collision theory is closely related to chemical kinetics.
The Boltzmann constant (k or k_B) is the physical constant relating energy at the particle level with temperature observed at the bulk level. It is the gas constant R divided by the Avogadro constant N_A. It has the same units as entropy. It is named after the Austrian physicist Ludwig Boltzmann.

History

Although Boltzmann first linked entropy and probability in 1877, it seems the relation was never expressed with a specific constant until Max Planck first introduced k , and gave an accurate value for it (1.346 × 10⁻²³ J/K, about 2.5% lower than today's figure), in his derivation of the law of black body radiation in 1900–1901. Before 1900, equations involving Boltzmann factors were not written using the energies per molecule and Boltzmann's constant, but rather using a form of the gas constant R, and macroscopic energies for macroscopic quantities of the substance. The iconic terse form of the equation S = k log W on Boltzmann's tombstone is in fact due to Planck, not Boltzmann.
As Planck wrote in his Nobel Prize lecture in 1920,

This constant is often referred to as Boltzmann's constant, although, to my knowledge, Boltzmann himself never introduced it — a peculiar state of affairs, which can be explained by the fact that Boltzmann, as appears from his occasional utterances, never gave thought to the possibility of carrying out an exact measurement of the constant.

This "peculiar state of affairs" can be understood by reference to one of the great scientific debates of the time. There was considerable disagreement in the second half of the nineteenth century as to whether atoms and molecules were "real" or whether they were simply a heuristic, a useful tool for solving problems. Nor was there agreement as to whether "chemical molecules" (as measured by atomic weights) were the same as "physical molecules" (as measured by kinetic theory). To continue the quotation from Planck's 1920 lecture:

Nothing can better illustrate the positive and hectic pace of progress which the art of experimenters has made over the past twenty years, than the fact that since that time, not only one, but a great number of methods have been discovered for measuring the mass of a molecule with practically the same accuracy as that attained for a planet.