Isotope effects on the vapor phase second virial coefficients of the deuterated methanes

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Abstract
Isotope effects on the second virial coefficients of CH4, CH3D, CH2D2, CHD3, and CD4 have been measured between 110 and 300°K, by a differential expansion technique. The isotope effects obeyed the law of the mean to within the experimental precision (about ±0.2 cc/mole). That for CD4/CH4 is given by B(CD4) − B(CH4) = (2.08±0.14) +(399.8±24.2)/T. ΔB/B amounts to approximately 2% at 110°K increasing to 9% at 300°K. Our analysis indicates that the most important contribution to the virial coefficient isotope effect is due to the isotope effect on the molecular polarizability. The value for this effect extracted from the data is consistent with that derived by other methods. The effects correspond to isotopic differences on the Lennard‐Jones constants of (σCH4 − σCD4)/ξCH4 = −0.013 ± 0.005 and (εCH4 − εCD4)/εCH4 = 0.005 ± 0.005. These are shown to be consistent with isotope effects on intramolecular C–H and CD bond lengths via a simple model calculation. Consistency with condensed phase molar volume isotope effects is also demonstrated.