https://doi.org/10.1351/goldbook.T06470
A theory of the rates of @[email protected] which assumes a special type of equilibrium, having an @[email protected] \(K^{\ddagger }\), to exist between reactants and activated complexes. According to this theory the @[email protected] is given by: \[k=\frac{k_{\text{B}}\ T}{h}\ K^{\ddagger }\] where \(k_{B}\) is the @[email protected] and \(h\) is the @[email protected] The @[email protected] can also be expressed as: \[k=\frac{k_{\text{B}}\ T}{h}\ \exp (\frac{\Delta ^{\ddagger }S^{\,\unicode{x26ac}}}{R})\ \exp (- \frac{\Delta ^{\ddagger }H^{\,\unicode{x26ac}}}{R\ T})\] where \(\Delta ^{\ddagger}S^{\,\unicode{x26ac}}\), the @[email protected], is the standard molar change of @[email protected] when the @[email protected] is formed from reactants and \(\Delta ^{\ddagger}H^{\,\unicode{x26ac}}\), the @[email protected], is the corresponding standard molar change of @[email protected] The quantities \(E_{a}\) (the @[email protected]) and \(\Delta ^{\ddagger}H^{\,\unicode{x26ac}}\) are not quite the same, the relationship between them depending on the type of reaction. Also: \[k=\frac{k_{\text{B}}\ T}{h}\ \exp (- \frac{\Delta ^{\ddagger }G^{\,\unicode{x26ac}}}{R\ T})\] where \(\Delta ^{\ddagger}G^{\,\unicode{x26ac}}\), known as the @[email protected], is the standard molar Gibbs energy change for the conversion of reactants into @[email protected] A plot of standard molar Gibbs energy against a @[email protected] is known as a [email protected]@; such plots, unlike @[email protected], are temperature-dependent. In principle the equations above must be multiplied by a @[email protected], \(\kappa \), which is the @[email protected] that an @[email protected] forms a particular set of products rather than reverting to reactants or forming alternative products. It is to be emphasized that \(\Delta ^{\ddagger}S^{\,\unicode{x26ac}}\), \(\Delta ^{\ddagger}H^{\,\unicode{x26ac}}\) and \(\Delta ^{\ddagger}G^{\,\unicode{x26ac}}\) occurring in the former three equations are not ordinary thermodynamic quantities, since one degree of freedom in the @[email protected] is ignored. Transition-state theory has also been known as absolute rate theory, and as activated-complex theory, but these terms are no longer recommended.
Source:
PAC, 1996, 68, 149. (A glossary of terms used in chemical kinetics, including reaction dynamics (IUPAC Recommendations 1996)) on page 190 [Terms] [Paper]