Pressure dependence of rate and equilibrium constants in solution. A guide to analytical equations

Most of the equations proposed since 1940 to express the isothermal pressure dependence of rate and equilibrium constants in solution are critically reviewed. Purely empirical, mechanical compression and model-based approaches are identified for constructing analytical equations. The original equations are rewritten in the form -[RT/(p-p(o))] In (K-p/K-po = phi(p), so that Delta V-po = phi(p(o)) and Delta V-infinity = phi(infinity). This analysis, highlighting similarities and differences, revealed that mathematically equivalent equations have been derived in the past by different authors using different approaches. Special attention is paid to equations predicting finite values for Delta V-infinity. It is concluded that in general phi p should contain at least three independent parameters related to volume changes arising respectively, from intramolecular rearrangements, activation or reaction solvating power, and the nature of the solvent. If one of these volume changes is inoperative (as the intramolecular term in some ionization equilibria), then the number of adjustable parameters may be reduced accordingly. Finally, it is shown that most of the equations can be represented by InK = a(0) + a(1)p + a(2)f(p) + a(3)pf(p) which comprises three distinct classes corresponding to f(p) = p(2), f(g) = 1/(1+a(4)p) and f(p) = ln(1+a(4)p).