Equilibrium mass-dependent fractionation relationships for triple oxygen isotopes

With a growing interest in small ¹⁷O-anomaly, there is a pressing need for the precise ratio, ln¹⁷α/ln¹⁸α, for a particular mass-dependent fractionation process (MDFP) (e.g., for an equilibrium isotope exchange reaction). This ratio (also denoted as “θ”) can be determined experimentally, however, such efforts suffer from the demand of well-defined process or a set of processes in addition to high precision analytical capabilities. Here, we present a theoretical approach from which high-precision ratios for MDFPs can be obtained. This approach will complement and serve as a benchmark for experimental studies. We use oxygen isotope exchanges in equilibrium processes as an example.We propose that the ratio at equilibrium, θ^E ≡ ln¹⁷α/ln¹⁸α, can be calculated through the equation below: