A process may involve treating calcium sulfate separated from phosphoric acid with acid to obtain a suspension comprising purified calcium sulfate, separating the purified calcium sulfate in solid form from a liquid phase of the suspension, treating the purified calcium sulfate with water or with a salt- and/or chelate ligand-containing aqueous solution to leach rare earths out of the calcium sulfate, separating the further-purified calcium sulfate in solid form from the liquid phase of the suspension, mixing the purified calcium sulfate that is separated off with admixtures and reducing agents to obtain a raw meal mixture for cement clinker production, burning the raw meal mixture to obtain the cement clinker and thereby forming sulfur dioxide as offgas, and feeding the sulfur dioxide as raw material to sulfuric acid production to produce the sulfuric acid.