Kinetics of CO_(2(g))–H_2O_((1)) isotopic exchange, including mass 47 isotopologues

The analysis of mass 47 isotopologues of CO_2 (mainly ^(13)C^(18)O^(16)O) is established as a constraint on sources and sinks of environmental CO_2, complementary to δ^(13)C and δ^(18)O constraints, and forms the basis of the carbonate clumped isotope thermometer. This measurement is commonly reported using the Δ_(47) value — a measure of the enrichment of doubly substituted CO_2 relative to a stochastic isotopic distribution. Values of Δ_(47) for thermodynamically equilibrated CO_2 approach 0 (a random distribution) at high temperatures (≥ several hundred degrees C), and increase with decreasing temperature, to ≈ 0.9% at 25 °C. While the thermodynamic properties of doubly substituted isotopologues of CO_2 (and, similarly, carbonate species) are relatively well understood, there are few published constraints on their kinetics of isotopic exchange. This issue is relevant to understanding both natural processes (e.g., photosynthesis, respiration, air–sea or air–groundwater exchange, CO_2 degassing from aqueous solutions, and possibly gas–sorbate exchange on cold planetary surfaces like Mars), and laboratory handling of CO_2 samples for Δ_(47) analysis (e.g., re-equilibration in the presence of liquid water, water ice or water adsorbed on glass or metal surfaces). We present the results of an experimental study of the kinetics of isotopic exchange, including changes in Δ_(47) value, of CO_2 exposed to liquid water between 5 and 37 °C. Aliquots of CO_2 gas were first heated to reach a nearly random distribution of its isotopologues and then exposed at low pressure for controlled periods of time to large excesses of liquid water in sealed glass containers. Containers were held at 5, 25 and 37 °C and durations of exchange ranging from 5 min to 7 days. To avoid the formation of a boundary layer that might slow exchange, the tubes were vigorously shaken during the period of exchange. At the end of each experiment, reaction vessels were flash frozen in liquid nitrogen. CO_2 gas was then recovered from the head space of the reaction vessel, purified and analyzed for its Δ_(47), δ^(13)C and δ^(18)O by gas source isotope ratio mass spectrometry. Equilibrium was reached for both δ^(18)O and Δ_(47) after durations of a few hours to tens of hours. Δ^(18)O values at equilibrium were consistent with known fractionation factors for the CO_2–H_2O system. The evolution of δ^(18)O and Δ_(47) with experiment duration were consistent with first-order reactions, with rate constants equal to each other (within error), averaging 0.19 h^(−1) at 5 °C, 0.38 h^(−1) at 25 °C and 0.65 h^(−1) at 37 °C. We calculate an activation energy for this isotopic exchange reaction of 26.2 kJ/mol. By comparison, Mills and Urey (1940) measured the rate of ^(18)O exchange between CO_2(aq) and water to have a rate of 11 h^(−1) at 25 °C and an activation energy of 71.7 kJ/mol. Our finding of a slower rate and lower activation energy is consistent with the rate limiting step of our experiment being the CO_2(g)–CO_2(aq) exchange, even when samples are shaken during the partial equilibration. Our results broadly resemble those from the study of (Affek, 2013), though this prior study found a lower rate constant for Δ_(47). We propose that the difference is due to analytical uncertainties and explore the theoretical consequences of unequal reaction rates between ^(12)C^(18)O^(16)O and ^(13)C^(18)O^(16)O with a forward model