Past exam of the chemistry A course of the University of Cambridge / 2024 / Paper 2 / A7 / c / ii / Solution

At fixed temperature, differentiating the Eyring equation with a pressure-independent prefactor and fixed concentration convention givesSince $\mathrm{d}G=V\mathrm{d}p-S\mathrm{d}T$, the derivative is the difference between the activated complex's partial molar volume and the sum for the reactants:If activation volume is approximately constant over the pressure range, integration givesThus plot $\ln k_2$ against pressure: its slope is $-\Delta V^{‡\circ }/RT$. Use pressure in pascals for a volume in ${\mathrm{m}}^3\mathrm{mo}{\mathrm{l}}^{-1}$. The model neglects pressure dependence of the transmission coefficient, substantial changes in mechanism, and strong curvature from a pressure-dependent activation volume. Fixed concentration-unit conventions and compression corrections matter for non-first-order rates.^[ref]