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Variability of total alkalinity in sea ice of the high-latitudinal Arctic from November 2005 to May 2006 is considered. For the bulk of one- and two-year sea ice, alkalinity dependence on salinity is described as TA = k x Sal, where k is salinity/alkalinity ratio in under-ice water. The given relationship is valid within a wide range of salinity from 0.1 psu in desalinated fraction of two-year ice to 36 psu in snow on the young ice surface. Geochemically significant deviations from the relationship noted were observed exclusively in snow and the upper layer of one-year ice. In the upper layer of one-year ice, deficiency of alkalinity is observed ( delta TA ~= -0.07 mEq/kg, or -15%). In snow on the surface of the one-year ice, alkalinity excess is formed under desalination ( delta TA is as high as 1.3 mEq/kg, or 380%). Deviations registered are caused by possibility of carbonate precipitation in form of CaCO3 x 6H2O under seawater freezing. It is shown that ice formation and the following melting might cause losses of atmospheric CO2 of up to 3 x 10**12 gC/year.