The volume of activation… This is one of those parameters we rarely think about… It represents the difference in the partial molar volume of the transition state compared to that of the reagents. The value of volume of activation provides information about the structural changes that take place in the transition state. Here is a good example: the Baylis-Hillman reaction.
Baylis-Hillman reactions can be really slow (a week to go to completion is not unusual, which is really atrocious). The calculated volume of activation in a prototypical Baylis-Hillman process is approximately -70 cm3/mol. This is a fairly high negative number, indicating a volume reduction when reagents are transformed into the transition state. It can be inferred that an increase in pressure would result in rate acceleration. Indeed, an increase in pressure from 1 bar to 1000 bar provides approximately 15-fold increase in the reaction rate. Please note that no gases are employed here (and pressure still matters)!
One can anticipate that reactions that are accompanied by an increase in the volume of activation should be accelerated when performed in vacuo. Elimination reactions belong to this class. We typically don’t think of vacuum as a means of driving reactions to completion, save for a few rare cases. By the way, volume of activation can be easily measured. Here is a classic paper: