Phase equilibrium isotope effects in molecular solids and liquids. Vapor pressures of the isotopic carbon dioxide molecules

The vapor pressures of samples of ${\mathrm{CO}}_2$ enriched in ${}^{13}\mathrm{C}$ and ${}^{18}\mathrm{O}$ have been compared with normal ${\mathrm{CO}}_2$ over the temperature range 154−217°K. Over the entire temperature range the order of the vapor pressures is $P_{{13}_{{\mathrm{CO}}_2}}{\mathrm{>\; P}}_{{12}_{{\mathrm{CO}}_2}}{\mathrm{>\; P}}_{{\mathrm{C}}^{18}{\mathrm{O}}_2}.$ The results are explained by the small shift in the internal vibrations, which dominate the carbon isotope effect, and hindered rotation in the solid and liquid. While the isotope effect on melting is small for carbon substitution, it is found to be large for oxygen substitution. Hindered rotation is the major contribution to the oxygen isotope effect in the solid, while the hindered translation is the most important contribution to the oxygen isotope effect in the liquid. Model calculations of the logarithm of the reduced partition function ratios of the solid and liquid, $\ln {\mathrm{(f}}_c{\mathrm{/f}}_g\mathrm{),}$ are made in an anharmonic version of the Stern−Van Hook−Wolfsberg cell model. These calculations give good agreement with the experimentally determined $\ln {\mathrm{(f}}_c{\mathrm{/f}}_g)$ values for the solid, liquid−vapor isotope fractionation measurements of Grootes, Mook, and Vogel, and lattice dynamic calculations.