On the time required to establish chemical and isotopic equilibrium in the carbon dioxide system in seawater

Dissolved inorganic carbon in sea water plays a key role in understanding the properties of the oceanic carbon reservoir within the global carbon cycle. For instance, fluxes between the atmosphere and the ocean are estimated using the stable carbon isotopes 12C and 13C of atmospheric CO2 and its dissolved forms within the ocean. Likewise, the investigation of carbon uptake by marine phytoplankton or the reconstruction of past oceans via stable isotope analysis demand a sound understanding of the sea water chemistry and associated carbon isotope fractionation. Chemical and isotopic disequilibrium is of particular interest when small length and time scales are considered. For example, within the microenvironment of marine plankton or within the surface boundary layer of the ocean (gas exchange atmosphere-ocean) the seawater carbonate chemistry deviates appreciably from equilibrium. It can be shown that a time-dependent description of the carbonate system is indispensable when time scales smaller than 90 s are involved (length scale of the diffusive boundary layer 10−4 m). Properties of the equilibrium state of the carbonate system in sea water are well known. However, hitherto there is little detailed work on the disequilibrium state of the chemical and in particular on the isotopic properties of the system. Here we present analytical and numerical techniques to determine the relaxation time of the chemical system including νCO2, HνCO−3, νCO2−3, H+, OH−, B(OH)3, and B(OH)4−, where ν=12, 13, and 14. The calculated relaxation time for chemical equilibrium at a temperature of 25°C and a salinity of 35 at pH 8.2 is 15.9 s (only 12C species), while the time calculated for isotopic equilibrium is 17.5 s (all carbon isotopes considered).