https://doi.org/10.1351/goldbook.E02142
The standard @[email protected] of @[email protected] \(\Delta ^{\ddagger}H^{\,\unicode{x26ac}}\) is the @[email protected] change that appears in the thermodynamic form of the rate equation obtained from conventional @[email protected] This equation is only correct for a first order reaction, for which the @[email protected] has the dimension reciprocal time. For a second order reaction, for which the @[email protected] 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 @[email protected] (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 @[email protected], and care must be taken with standard states. In this equation \(k_{\text{B}}\) is the @[email protected], \(T\) the absolute temperature, \(h\) the @[email protected], and \(R\) the @[email protected] The @[email protected] of @[email protected] is approximately equal to the @[email protected]; the conversion of one into the other depends on the @[email protected] The @[email protected] of @[email protected] 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 \(H\).
Sources:
Green Book, 2nd ed., p. 56 [Terms] [Book]
PAC, 1993, 65, 2291. (Nomenclature of kinetic methods of analysis (IUPAC Recommendations 1993)) on page 2294 [Terms] [Paper]
PAC, 1994, 66, 1077. (Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994)) on page 1113 [Terms] [Paper]
PAC, 1996, 68, 149. (A glossary of terms used in chemical kinetics, including reaction dynamics (IUPAC Recommendations 1996)) on page 164 [Terms] [Paper]