The Hall-Heroult process is used for the extraction of aluminum from its oxide, Al_2O_3 (alumina). Let's evaluate each statement:
In the Hall-Heroult process, carbon anodes are used, and during the electrolysis, these anodes get oxidized, producing carbon dioxide (CO_2). Carbon monoxide (CO) can also be produced in smaller amounts. Therefore, this statement is correct.
In the Hall-Heroult process, Al_2O_3 is indeed mixed with cryolite (Na_3AlF_6) and calcium fluoride (CaF_2), which lowers the melting point and increases conductivity. Thus, this statement is correct.
During the electrolysis process, Al^{3+} ions are reduced at the cathode to form aluminum metal. This statement is correct.
Na_3AlF_6 (cryolite) serves as a solvent or a flux, not solely as the electrolyte. The electrolyte in the Hall-Heroult process is primarily molten alumina dissolved in molten cryolite. Thus, this statement is incorrect and is the false statement among the options.
Therefore, the false statement regarding the Hall-Heroult process is: Na_3AlF_6 serves as the electrolyte.