enthalpy of activation, \(\Delta ^{\ddagger}H^{\,\unicode{x26ac}}\)

The standard enthalpy of activation \(\Delta ^{\ddagger}H^{\,\unicode{x26ac}}\) is the enthalpy change that appears in the thermodynamic form of the rate equation obtained from conventional transition state theory. This equation is only correct for a first order reaction, for which the rate constant has the dimension reciprocal time. For a second order reaction, for which the rate constant has the dimension (reciprocal time) × (reciprocal concentration), the left hand side should be read as \(k\ c^{\,\unicode{x26ac}}\), where \(c^{\,\unicode{x26ac}}\) denotes the standard concentration (usually \(1\ \text{mol dm}^{-3}\)). \[k = \frac{k_{\text{B}}\ T}{h}\ \text{e}^{\frac{\Delta ^{\ddagger }S^{\,\unicode{x26ac}}}{R}}\ \mathrm{e}^{\frac{-\Delta ^{\ddagger }H^{\,\unicode{x26ac}}}{R\ T}}\] The quantity \(\Delta ^{\ddagger}S^{\,\unicode{x26ac}}\) is the standard entropy of activation, and care must be taken with standard states. In this equation \(k_{\text{B}}\) is the Boltzmann constant, \(T\) the absolute temperature, \(h\) the Planck constant, and \(R\) the gas constant. The enthalpy of activation is approximately equal to the activation energy; the conversion of one into the other depends on the molecularity. The enthalpy of activation is always the standard quantity, although the word standard and the superscript \(^{\unicode{x26ac}}\) on the symbol are often omitted. The symbol is frequently (but incorrectly) written \(\Delta H^{\ddagger }\), where the standard symbol is omitted and the \(\ddagger \) is placed after the \(H\).
Green Book,2nd ed., p. 56 (https://www.cintegrado.com.br/site/documentos/green_book_2ed.pdf)
PAC, 1993, 65, 2291. 'Nomenclature of kinetic methods of analysis (IUPAC Recommendations 1993)' on page 2294 (https://doi.org/10.1351/pac199365102291)
PAC, 1994, 66, 1077. 'Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994)' on page 1113 (https://doi.org/10.1351/pac199466051077)
PAC, 1996, 68, 149. 'A glossary of terms used in chemical kinetics, including reaction dynamics (IUPAC Recommendations 1996)' on page 164 (https://doi.org/10.1351/pac199668010149)