Disclosed herein are acid-base leaching methods and systems. Specifically, the systems and methods can include supplying an iron and/or aluminum feed material and an acid to a first reaction chamber; supplying a first leachate comprising iron and/or aluminum salts or cations from the first reaction chamber and a calcium feed material to a second reaction chamber to form a solid comprising iron and/or aluminum; supplying a second leachate from the second reaction chamber comprising alkaline earth metal salts or cations and a base to a third reaction chamber to form a precipitated alkaline earth metal product.

A process may involve digesting raw phosphate with concentrated sulfuric acid and converting the raw phosphate to calcium sulfate in the form of dihydrate and/or hemihydrate, and phosphoric acid, separating off calcium sulfate as solid from a liquid phase of a suspension that is obtained, treating the calcium sulfate that is separated off or from a stockpile with an acid to give a suspension with purified calcium sulfate and P.sub.2O.sub.5-containing acid solution, separating off the purified calcium sulfate as solid from a liquid phase of a suspension obtained, using the P.sub.2O.sub.5-containing liquid phase as a portion of the sulfuric acid required for digesting the raw phosphate or as feedstock for treating phosphogypsum from the stockpile to give a suspension of purified calcium sulfate and P.sub.2O.sub.5-containing acid solution, which is thereafter processed.