Isotopic fractionations associated with phosphoric acid digestion of carbonate minerals: Insights from first-principles theoretical modeling and clumped isotope measurements

Phosphoric acid digestion has been used for oxygen- and carbon-isotope analysis of carbonate minerals since 1950, and was recently established as a method for carbonate ‘clumped isotope’ analysis. The CO_2 recovered from this reaction has an oxygen isotope composition substantially different from reactant carbonate, by an amount that varies with temperature of reaction and carbonate chemistry. Here, we present a theoretical model of the kinetic isotope effects associated with phosphoric acid digestion of carbonates, based on structural arguments that the key step in the reaction is disproportionation of H_2CO_3 reaction intermediary. We test that model against previous experimental constraints on the magnitudes and temperature dependences of these oxygen isotope fractionations, and against new experimental determinations of the fractionation of ^(13)C–^(18)O-containing isotopologues (‘clumped’ isotopic species). Our model predicts that the isotope fractionations associated with phosphoric acid digestion of carbonates at 25 °C are 10.72‰, 0.220‰, 0.137‰, 0.593‰ for, respectively, ^(18)O/^(16)O ratios (1000 lnα^*) and three indices that measure proportions of multiply-substituted isotopologues (Δ^*_(47), Δ^*_(48), Δ^*_(49). We also predict that oxygen isotope fractionations follow the mass dependence exponent, λ of 0.5281 (where α_(17)_O = α^λ_(18)_O). These predictions compare favorably to independent experimental constraints for phosphoric acid digestion of calcite, including our new data for fractionations of ^(13)C–^(18)O bonds (the measured change in Δ_(47) = 0.23‰) during phosphoric acid digestion of calcite at 25 °C. We have also attempted to evaluate the effect of carbonate cation compositions on phosphoric acid digestion fractionations using cluster models in which disproportionating H_2CO_3 interacts with adjacent cations. These models underestimate the magnitude of isotope fractionations and so must be regarded as unsucsessful, but do reproduce the general trend of variations and temperature dependences of oxygen isotope acid digestion fractionations among different carbonate minerals. We suggest these results present a useful starting point for future, more sophisticated models of the reacting carbonate/acid interface. Examinations of these theoretical predictions and available experimental data suggest cation radius is the most important factor governing the variations of isotope fractionation among different carbonate minerals. We predict a negative correlation between acid digestion fractionation of oxygen isotopes and of ^(13)C–^(18)O doubly-substituted isotopologues, and use this relationship to estimate the acid digestion fractionation of Δ^*_(47) for different carbonate minerals. Combined with previous theoretical evaluations of ^(13)C–^(18)O clumping effects in carbonate minerals, this enables us to predict the temperature calibration relationship for different carbonate clumped isotope thermometers (witherite, calcite, aragonite, dolomite and magnesite), and to compare these predictions with available experimental determinations. The success of our models in capturing several of the features of isotope fractionation during acid digestion supports our hypothesis that phosphoric acid digestion of carbonate minerals involves disproportionation of transition state structures containing H_2CO_3.