volume of activation
/ delta-V double-dagger /
Squeeze a sponge and it shrinks; let it spring back and it grows. Reactions have a similar give as they pass over their highest-energy point, the transition state. The volume of activation asks a simple physical question: at the very top of the barrier, does the reacting system take up less room or more room than it did at the start? That single measurement turns out to be one of the most direct windows we have into how a substitution actually happens.
Written as delta-V double-dagger, the volume of activation is the difference in volume between the transition state and the starting materials. You measure it by running the reaction at several pressures and seeing how the rate responds: squeezing the system with high pressure favours whichever side takes up less volume. If raising the pressure speeds the reaction up, the transition state is more compact than the reactants, so delta-V double-dagger is negative — the signature of an associative pathway, where an extra ligand is being pulled in and the system is contracting. If raising the pressure slows the reaction down, the transition state is more expanded, so delta-V double-dagger is positive — the signature of a dissociative pathway, where a bond is stretching and breaking and the system is swelling.
This is the cleanest experimental criterion for placing a substitution on the A-to-D continuum, and it is what let chemists move beyond merely reading rate laws. A modestly negative value (a few cubic centimetres per mole) points to associative interchange Ia; a modestly positive value points to dissociative interchange Id; large magnitudes approach the limiting A and D mechanisms. The honest caveat is that the measured volume change includes not just the metal-ligand bond but also rearrangements of the surrounding solvent, especially when charged species form or vanish — so for reactions involving ions, the solvent contribution must be untangled before reading the number as pure bond-making or bond-breaking.
Water exchange on [Cr(H2O)6]3+ has delta-V double-dagger of about -9 cubic centimetres per mole (associative, Ia), whereas on [Fe(H2O)6]3+ it is about -5 and on later, smaller ions it turns positive, tracking the shift toward dissociative interchange.
Measuring rates under pressure gives the activation volume, the most direct probe of associative versus dissociative character.
A measured activation volume mixes the intrinsic change in the metal coordination sphere with solvent reorganization. For reactions that create or destroy charge, the large solvent (electrostriction) term can swamp the bond-making or bond-breaking part and must be accounted for.