Trajectory and timescale of oxygen and clumped isotope equilibration in the dissolved carbonate system under normal and enzymatically-catalyzed conditions at 25 °C

Abstract

The abundance of ¹⁸O isotopes and ¹³C-¹⁸O isotopic “clumps” (measured as δ¹⁸O and Δ₄₇, respectively) in carbonate minerals have been used to infer mineral formation temperatures. An inherent requirement or assumption for these paleothermometers is mineral formation in isotopic equilibrium. Yet, apparent disequilibrium is not uncommon in biogenic and abiogenic carbonates formed in nature and in synthetic carbonates prepared under laboratory settings, as the dissolved carbonate pool (DCP) from which minerals precipitate is often out of δ¹⁸O and Δ₄₇ equilibrium. For this, a complete understanding of both equilibrium and kinetics of isotopic partitioning and ¹³C-¹⁸O clumping in DCP is crucial. To this end, we analyzed Δ₄₇ of inorganic BaCO₃ samples from Uchikawa and Zeebe (2012) (denoted as UZ12), which were quantitatively precipitated from NaHCO₃ solutions at various times over the course of isotopic equilibration at 25 °C and pH_(NBS) of 8.9. Our data show that, although the timescales for δ¹⁸O and Δ₄₇ equilibrium in DCP are relatively similar, their equilibration trajectories are markedly different. As opposed to a simple unidirectional and asymptotic approach toward δ¹⁸O equilibrium (first-order kinetics), Δ₄₇ equilibration initially moves away from equilibrium and then changes its course towards equilibrium. This excess Δ₄₇ disequilibrium is manifested as a characteristic “dip” in the Δ₄₇ equilibration trajectory, a feature consistent with an earlier study by Staudigel and Swart (2018) (denoted as SS18). From the numerical model of SS18, the non-first-order kinetics for Δ₄₇ equilibration can be understood as a result of the difference in the exchange rate for oxygen isotopes bound to ¹²C versus ¹³C, or an isotope effect of ~25‰. We also developed an independent model for the Exchange and Clumping of ¹³C and ¹⁸O in DCP (ExClump38 model) to trace the evolution of singly- and doubly-substituted isotopic species (i.e., δ¹³C, δ¹⁸O and Δ₄₇). The model suggests that the dip in the Δ₄₇ equilibration trajectory is due largely to kinetic carbon isotope fractionation for hydration and hydroxylation of CO₂. We additionally examined the BaCO₃ samples prepared from NaHCO₃ solutions supplemented with carbonic anhydrase (CA), an enzyme known to facilitate δ¹⁸O equilibration in DCP by catalyzing CO₂ hydration (UZ12). These samples revealed that, while CA effectively shortens the time required for Δ₄₇ equilibrium in DCP, the overall pattern and magnitude of the dip in the Δ₄₇ equilibration trajectory remain unchanged. This suggests no additional isotope effects due to the CA enzyme within the tested CA concentrations. With the ExClump38 model, we test various physicochemical scenarios for the timescales and trajectories of isotopic equilibration in DCP and discuss their implications for the Δ₄₇ paleothermometry.