Non-canonical mass laws in equilibrium isotopic fractionations: Evidence from the vapor pressure isotope effect of SF_6

Abstract

We report experimental observations of the vapor pressure isotope effect, including ^(33)S/^(32)S and ^(34)S/^(32)S ratios, for SF_6 ice between 137 and 173 K. The temporal evolution of observed fractionations, mass-balance of reactants and products, and reversal of the fractionation at one temperature (155 K) are consistent with a subset of our experiments having reached or closely approached thermodynamic equilibrium. That equilibrium involves a reversed vapor pressure isotope effect; i.e., vapor is between 2‰ and 3‰ higher in ^(34)S/^(32)S than co-existing ice, with the difference increasing with decreasing temperature. At the explored temperatures, the apparent equilibrium fractionation of ^(33)S/^(32)S ratios is 0.551 ± 0.010 times that for ^(34)S/^(32)S ratios—higher than the canonical ratio expected for mass dependent thermodynamic fractionations (∼0.515). Two experiments examining exchange between adsorbed and vapor SF_6 suggest the sorbate–vapor fractionation at 180–188 K is similar to that for ice–vapor at ∼150 K. In contrast, the liquid–vapor fractionation at 228–300 K is negligibly small (∼0.1‰ for ^(34)S/^(32)S; the mass law is ill defined due to the low amplitude of fractionation). We hypothesize that the observed vapor pressure isotope for SF_6 ice and sorbate is controlled by commonly understood effects of isotopic substitution on vibrational energies of molecules, but leads to both an exotic mass law and reversed fractionation due to the competition between isotope effects on intramolecular vibrations, which promote heavy isotope enrichment in vapor, and isotope effects on intermolecular (lattice) vibrations, which promote heavy isotope enrichment in ice. This explanation implies that a variety of naturally important compounds having diverse modes of vibration (i.e., varying greatly in frequency and particularly, reduced mass) could potentially exhibit similarly non-canonical mass laws for S and O isotope fractionations. We examined this hypothesis using a density function model of SF_6 vapor and lattice dynamic model of SF_(6(ice)). These models support the direction of the measured vapor pressure isotope effect, but do not quantitatively agree with the magnitude of the fractionation and poorly match the phonon spectrum of SF_6 ice. A strict test of our hypothesis must await a more sophisticated model of the isotopic dependence of the phonon spectrum of SF_6 ice.

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