An electrolytic cell for oxidizing an alkali metal monosulfide or an alkali metal polysulfide comprising: an anolyte compartment configured with an anode and containing an anolyte solution comprising an alkali metal monosulfide, an alkali metal polysulfide, or a mixture thereof and an anolyte solvent that partially dissolves elemental sulfur, the anolyte compartment further comprising an anolyte solution inlet and an anolyte solution outlet; a catholyte compartment configured with a cathode and containing a catholyte, wherein the catholyte comprises a molten alkali metal, the catholyte compartment further comprising a catholyte outlet; an alkali ion conductive membrane configured to selectively transport alkali ions, wherein the alkali ion conductive membrane is substantially impermeable to anions, the anolyte solvent, and dissolved sulfur; a source of electric potential electrically coupled to the anode and the cathode and configured to: oxidize the alkali metal monosulfide or polysulfide in the anolyte compartment to form liquid elemental sulfur and alkali metal ions; cause the alkali metal ions to pass through the alkali ion conductive membrane from the anolyte compartment to the catholyte compartment; and reduce the alkali metal ions in the catholyte compartment to form liquid elemental alkali metal; and an elemental sulfur settling zone where the liquid elemental sulfur separates from the anolyte solution; and a sulfur outlet for removal of the liquid elemental sulfur from the electrolytic cell disposed at a location lower than the anolyte solution outlet. an anolyte compartment configured with an anode and containing an anolyte solution comprising an alkali metal monosulfide, an alkali metal polysulfide, or a mixture thereof and an anolyte solvent that partially dissolves elemental sulfur, the anolyte compartment further comprising an anolyte solution inlet and an anolyte solution outlet; a catholyte compartment configured with a cathode and containing a catholyte, wherein the catholyte comprises a molten alkali metal, the catholyte compartment further comprising a catholyte outlet; an alkali ion conductive membrane configured to selectively transport alkali ions, wherein the alkali ion conductive membrane is substantially impermeable to anions, the anolyte solvent, and dissolved sulfur; a source of electric potential electrically coupled to the anode and the cathode and configured to: oxidize the alkali metal monosulfide or polysulfide in the anolyte compartment to form liquid elemental sulfur and alkali metal ions; cause the alkali metal ions to pass through the alkali ion conductive membrane from the anolyte compartment to the catholyte compartment; and reduce the alkali metal ions in the catholyte compartment to form liquid elemental alkali metal; and oxidize the alkali metal monosulfide or polysulfide in the anolyte compartment to form liquid elemental sulfur and alkali metal ions; cause the alkali metal ions to pass through the alkali ion conductive membrane from the anolyte compartment to the catholyte compartment; and reduce the alkali metal ions in the catholyte compartment to form liquid elemental alkali metal; and an elemental sulfur settling zone where the liquid elemental sulfur separates from the anolyte solution; and a sulfur outlet for removal of the liquid elemental sulfur from the electrolytic cell disposed at a location lower than the anolyte solution outlet.