parameters, the enthalpy of activation ΔH‡ and the entropy of activation ΔS‡, based on the defining formula ΔG‡ = ΔH‡ − TΔS‡. In effect, the free energy of activation takes into account both the activation energy and the likelihood of successful collision, while the factor kBT/h gives the frequency of molecular collision. The factor (c⊖)1-M ensures the dimensional correctness of the rate constant when the transition state in question is bimolecular or higher. Here, c⊖ is the standard concentration, generally chosen based on the unit of concentration used (usually c⊖ = 1 mol L−1 = 1 M), and M is the molecularity of the transition state. Lastly, κ, usually set to unity, is known as the transmission coefficient, a parameter which essentially serves as a "fudge factor" for transition state theory. The biggest difference between the two theories is that Arrhenius theory attempts to model the reaction (single- or multi-step) as a whole, while transition state theory models the individual elementary steps involved. Thus, they are not directly comparable, unless the reaction in question involves only a single elementary step. Finally, in the past, collision theory, in which reactants are viewed as hard spheres with a particular cross-section, provided yet another common way to rationalize and model the temperature dependence of the rate constant, although this approach has gradually fallen into disuse. The equation for the rate constant is similar in functional form to both the Arrhenius and Eyring equations: where P is the steric (or probability) factor and Z is the collision frequency, and ΔE is energy input required to overcome the activation barrier. Of note, , making the temperature dependence of k different from both the Arrhenius and Eyring models. Comparison of models All three theories model the temperature dependence of k using an equation of the form for some constant C, where α = 0, , and 1 give Arrhenius theory, collision theory, and transition state theory, respectively, although the imprecise notion of ΔE, the energy needed to overcome the activation barrier, has a slightly different meaning in each theory. In practice, experimental data does not generally allow a determination to be made as to which is "correct" in terms of best fit. Hence, it must be remembered that all three are conceptual frameworks that make numerous assumptions, both realistic and unrealistic, in their derivations. As a result, they are capable of providing different insights into a