NOVELTY - A fuel cell system comprises a fuel cell containing an anode (1), a cathode (2), the fuel cell operating with a fuel (9) and an oxidant (10) reactant, at least one of the fuel and the oxidant reactant containing carbon, and a liquid (17), where carbon dioxide (CO2) or a carbon-containing oxidation product in the fuel cell reacts or dissolves in the liquid; and a source of group II metal ions (20) for converting the reacted or dissolved CO2 or carbon-containing oxidation product into an insoluble carbonate to regenerate the liquid.    USE - As a fuel cell system for capturing carbon (claimed).    ADVANTAGE - The fuel cell system prevents gaseous CO2 from being released to the atmosphere during the electrochemical oxidation of carbon-containing fuel and the simultaneous sequestration of the CO2 in a mineral precipitate.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are included for the following:    (1) operating a fuel cell comprising an anode, a cathode, fuel, and oxidant reactant, at least one of the fuel and the oxidant reactant containing carbon, involving introducing a liquid into the fuel cell, CO2 or a carbon-containing oxidation product in the fuel cell reacting with or dissolving in the liquid, and converting the reacted or dissolved CO2 or carbon-containing oxidation product into an insoluble carbonate by reaction with group II metal ions;    (2) capturing carbon using a fuel cell comprising an anode, a cathode, fuel, and oxidant reactant, at least one of the fuel and oxidant reactant containing carbon, involving introducing a liquid into the fuel cell, CO2 or a carbon-containing oxidation product in the fuel cell reacting with or dissolving in the liquid; and sequestering the reacted or dissolved CO2 or carbon-containing oxidation product by reaction with group II metal ions to form a stable solid carbonate;    (3) a sequestration apparatus for use with a fuel cell comprising a reaction vessel having an input configured for connection to the outlet of the fuel cell to receive reagents from the fuel cell, the reaction vessel containing a source of group II metal ions, and an output configured to supply liquid back to the fuel cell.    DESCRIPTION OF DRAWING(S) - The figure shows a schematic diagram of a fuel cell system.    Anode (1)    Cathode (2)    Fuel (9)    Oxidant (10)    Liquid (17)    Group II metal ions (20)