A method is described for producing sulfur that contains less than 1.3×10-5 mole fraction of liquid-soluble, solid-insoluble impurities as determined by the freezing point depression. This corresponds to a purity of 99.999 mole percent. Many of the impurities, including organic matter, are removed by oxidation with sulfuric and nitric acids. The nonvolatile impurities are removed on distilling the sulfur. The residual sulfuric acid is removed by a special extraction with distilled water. Methods are described for determining small amounts of the following impurities: Selenium, tellurium, arsenic, iron, carbon, sulfuric acid, and residue after ignition.