volume of activation, \(\Delta ^{\ddagger}V\)

A quantity derived from the pressure dependence of the @O04322@ of a reaction (mainly used for reactions in solution), defined by the equation: \[\Delta ^{\ddagger }V=- R\ T\ (\frac{\partial (\ln k)}{\partial p})_{T}\] providing that the rate constants of all reactions (except first-order reactions) are expressed in pressure-independent concentration units, such as \(\text{mol dm}^{-3}\) at a fixed temperature and pressure. The volume of @A00093@ is interpreted, according to @T06470@, as the difference between the partial molar volumes of the @T06468@ (\(V\)) and the sums of the partial volumes of the reactants at the same temperature and pressure, i.e. \[\Delta ^{\ddagger}V = ^{\ddagger}V- \sum \left(r\ V_{\text{R}}\right)\] where \(r\) is the order in the reactant R and \(V_{\text{R}}\) its partial molar volume.
PAC, 1994, 66, 1077. (Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994)) on page 1175 [Terms] [Paper]
See also:
Green Book, 2nd ed., p. 56 [Terms] [Book]
PAC, 1996, 68, 149. (A glossary of terms used in chemical kinetics, including reaction dynamics (IUPAC Recommendations 1996)) on page 191 [Terms] [Paper]