NOVELTY - Producing biodiesel comprising obtaining two electrolytic cells (12, 14) each comprising an alkali ion conductive ceramic membrane (16, 42) to selectively transport alkali ions and separate an anolyte compartment (18, 44) having an electrochemically active anode (22, 48) and a catholyte compartment (20, 46) having an electrochemically active cathode (24, 50); removing a mixture of biodiesel and alkali salt of glycerine (40) from first catholyte compartment and introducing into second anolyte compartment; and removing biodiesel and glycerine (66) from second anolyte compartment.    USE - For producing biodiesel.    ADVANTAGE - The method eliminates or limits the use of alkali hydroxides or alkali alkoxides as catalysts and combines biodiesel synthesis with the separation of alkali ions from glycerine byproducts.    DETAILED DESCRIPTION - Producing biodiesel comprises    (A) obtaining a first electrolytic cell comprising a first alkali ion conductive ceramic membrane which selectively transports alkali ions and separates a first anolyte compartment having an electrochemically active first anode and a first catholyte compartment having an electrochemically active first cathode;    (B) introducing an alkali hydroxide solution into the first anolyte compartment;    (C) introducing alcohol and a triglyceride (32) into the first catholyte compartment;    (D) applying an electric current to the first electrolytic cell to (i) oxidize hydroxide anions in the first anolyte compartment to form oxygen, gas and water; (ii) cause alkali ions to pass through the alkali ion conductive ceramic membrane from the first anolyte compartment to the first catholyte compartment; (iii) reduce the alcohol in the presence of alkali ions in the first catholyte compartment to form an alkali alkoxide and hydrogen gas; and (iv) react the alkali alkoxide and the triglyceride to form a mixture of biodiesel and an alkali metal salt of glycerine;    (E) obtaining a second electrolytic cell comprising a second alkali ion conductive ceramic membrane which selectively transports alkali ions and separates a second anolyte compartment having an electrochemically active second anode and a second catholyte compartment having an electrochemically active second cathode;    (F) removing the mixture of biodiesel and alkali salt of glycerine from the first catholyte compartment and introducing the mixture into the second anolyte compartment;    (G) introducing hydrogen gas into the second anolyte compartment;    (H) introducing water into the second catholyte compartment;    (I) applying an electric current to the second electrolytic cell to (i) oxidize hydrogen gas in the second anolyte compartment to form hydrogen ions and facilitate the reaction of alkali metal salt of glycerine with hydrogen ions (H+) to form glycerine (C3H5(OH)3) and alkali metal ions; (ii) cause alkali ions to pass through the alkali ion conductive ceramic membrane from the second anolyte compartment to the second catholyte compartment; and (iii) decompose water in the presence of alkali ions in the second catholyte compartment according to a reaction where alkali metal ions, water and electrons react to form alkali metal hydroxide and hydrogen; and    (J) removing biodiesel and glycerine from the second anolyte compartment.    INDEPENDENT CLAIMS are included for:    (1) a biodiesel production apparatus comprising two electrolytic cells each comprising an anolyte compartment having an electrochemically active anode and a catholyte compartment having an electrochemically active cathode separated from the anolyte compartment by an alkali ion conductive ceramic membrane; a fluid path for transporting a portion of the biodiesel and alkali metal salt of glycerine from the first catholyte compartment to the second anolyte compartment; and a fluid path for removing biodiesel and glycerine from the second anolyte compartment; and    (2) a method for converting alkali salts of glycerine into glycerine comprising obtaining an electrolytic cell comprising an alkali ion conductive ceramic membrane which selectively transports alkali ions and separates an anolyte compartment having an anode and a catholyte compartment having a cathode; introducing alkali metal salt of glycerine into the anolyte compartment; introducing hydrogen gas into the anolyte compartment; introducing water into the catholyte compartment; applying an electric current to the electrolytic cell to (i) oxidize hydrogen gas in the anolyte compartment to form hydrogen ions and facilitate the reaction of alkali metal salt of glycerine and hydrogen ions to form C3H5(OH)3 and alkali metal ions; (ii) cause alkali ions to pass through the alkali ion conductive ceramic membrane from the anolyte compartment to the catholyte compartment; and (iii) decompose water in the presence of alkali ions in the catholyte compartment where alkali metal ions, water and electrons react to form alkali metal hydroxide and hydrogen; and removing glycerine from the anolyte compartment.    DESCRIPTION OF DRAWING(S) - The figure shows a schematic view of an electrolytic apparatus for producing biodiesel.    Electrolytic cells (12, 14)    Alkali ion conductive ceramic membrane (16, 42)    Anolyte compartment (18, 44)    Catholyte compartment (20, 46)    Anode (22, 48)    Cathode (24, 50)    Alcohol and a triglyceride (32)    Water (36)    Hydrogen gas (38)    Mixture of biodiesel and alkali salt of glycerine (40)    Alkali ions (52)    Water (58)    Hydrogen gas (62, 64)    Biodiesel and glycerine (66)    Settling tank (68)    Biodiesel (70)    Clean glycerine (72)    Additional water (74)