Pressure Effects and the Volume of Activation

The same partial derivative of AG with respect to pressure provides an equation for the pressure dependence of the rate constant, or 

This form assumes that the effect of pressure on the molar volume of the solvent, which accelerates reactions of order 1 by increasing the concentrations when they are expressed on the molar scale, has been allowed for. This effect is usually small, ignored but in the most precise work. Equation (7-41) shows that In k will vary linearly with pressure. We shall refer to this graph as the pressure profile. The value of A V is easily calculated from its slope. The values of A V may be nearly zero, positive, or negative. In the first case, the reaction rate shows little if any pressure dependence in the second and third, the applied hydrostatic pressure will cause k to decrease or increase, respectively. A positive value of the volume of activation means that the molar volume of the transition state is larger than the combined molar volume of the reactant(s), and vice versa. 

If necessary, one can avoid making the assumption that AV is independent of pressure by introducing a further quantity termed the compressibility, 

The expression for the rate constant then becomes a power series, 

Returning to the simpler form of Eq. (7-40), let us ask first how great the effect of pressure is. A cursory survey of the literature tells us that a reaction having AV = - 5.0 cm3 mol 1 at 298 K is not atypical. Let us calculate the pressure needed to change the rate by a factor of two from its value at atmospheric pressure. In SI units, where atmospheric pressure is 105 N m-2, we have 

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