An expression for the overall oxygen isotope fractionation between the sum of dissolved inorganic carbon and water

Stable oxygen isotope fractionation factors ( alpha's) between individual dissolved carbonate species (CO2(aq.), H2CO3, HCO3-, CO32-) and water, and their sum (S = [ CO2(aq.)] + [ H2CO3] + [ HCO3-] + [CO32-]) and water are fundamental geochemical parameters. While values of a(CO2(aq.)-H2O), (alpha) (HCO3--H2O), and (alpha)(CO32--H2O) have recently been examined, an overall mass balance for stable oxygen isotopes in the carbonate system still needs to be derived. The theoretical treatment of this mass balance is not trivial ( in contrast to, e. g., stable carbon isotopes) because (1) oxygen is exchanged with H2O and (2) complications arise from the nature of the oxygen mole fractions. I use the recently reported individual alpha's to derive an expression for the overall oxygen isotope fractionation between S and water. This allows the calculation of (alpha)(S-H2O) at any given pH of the solution. The result differs from a relationship published earlier, and implications for previous studies are discussed. Numerical routines in MATLAB and Excel for the present calculation have been developed and are available as auxiliary material (Software S1). Applications of the expression include, for example, examination of biomineralization mechanisms and corrections to isotopic paleotemperature equations. The latter application can significantly alter reconstructions of Phanerozoic climate change.