Achievement of carbon isotope equilibrium in the system HCO3− (solution)-CO2(gas)

The magnitude of stable carbon isotope fractionation between dissolved bicarbonate and gaseous carbon dioxide as a function of isotope exchange time was measured in the temperature range 7 to 70°C at an initial partial pressure of CO2 of 26.7 kPa and from 7 to 60°C at a total initial pressure P(CO2 + H2O vapour) of 28 kPa. Isotope equilibrium was also examined at a temperature of 53.5°C and at an initial pressure of carbon dioxide that varied from 13.3 to 118.7 kPa. The permil fractionation, ϵ13C, as a function of exchange time, t, is given by the formula ϵ13C = ϵ∞13C(1 − e−tτ) where the carbon fractionation at isotopic equilibrium, ϵ∞13C, and relaxation time, τ, are calculated from the experimental data. It has been found that the relaxation time in a given experimental apparatus depends on two variables: (1) temperature and (2) the initial pressure. 13C value as a function of temperature is well described by the equation: ϵ∞13C = −(0.0954±0.0027) T[°C] + (10.41 ± 0.12). The relaxation time as a function of absolute temperature at a total initial pressure of 28 kPa is given by the equation: τ[hours] = (350 ± 35) T−12 − (18 ± 2), and as a function of the total initial pressure, P (in kPa), at temperature 53.5°C is well represented by the following dependence: τ[hours] = (0.03054 ± 0.00097)P.