Kinetic and equilibrium mass-dependent isotope fractionation laws in nature and their geochemical and cosmochemical significance

The mass-dependent fractionation laws that describe the partitioning of isotopes are different for kinetic and equilibrium reactions. These laws are characterized by the exponent relating the fractionation factors for two isotope ratios such that α _2/1 = α _3/1^β. The exponent β for equilibrium exchange is (1/m ₁ - 1/m ₂)/(1/m ₁ - 1/m ₃), where m _i are the atomic masses and m ₁ < m ₂ < m ₃. For kinetic fractionation, the masses used to evaluate β depend upon the isotopic species in motion. Reduced masses apply for breaking bonds whereas molecular or atomic masses apply for transport processes. In each case the functional form of the kinetic β is ln(M ₁/M ₂)/ln(M ₁/M ₃), where M _i are the reduced, molecular, or atomic masses. New high-precision Mg isotope ratio data confirm that the distinct equilibrium and kinetic fractionation laws can be resolved for changes in isotope ratios of only 3‰ per amu. The variability in mass-dependent fractionation laws is sufficient to explain the negative Δ ¹⁷O of tropospheric O ₂ relative to rocks and differences in Δ ¹⁷O between carbonate, hydroxyl, and anhydrous silicate in Martian meteorites. (For simplicity, we use integer amu values for masses when evaluating β throughout this paper.)