A method of precipitating arsenic and heavy metal out of acidic process water, especially containing sulfuric acid, and containing both arsenic and heavy metals, where the method comprises a method step of precipitation with a sulfide precipitation stage in which arsenic and at least one primary heavy metal are coprecipitated, by adding a sulfide precipitation reagent to the process water such that arsenic precipitates out as arsenic sulfide and the at least one primary heavy metal as the metal sulfide, wherein a) the sulfide precipitation stage comprises a first sulfide precipitation step (C.1) in which sulfide precipitation reagent is added to the process water in a first sulfide precipitation reactor, producing an intermediate liquid still containing arsenic or still containing arsenic and primary heavy metal; b) the intermediate liquid, after the first sulfide precipitation step (C.1), is transferred into a second sulfide precipitation reactor; c) the sulfide precipitation stage comprises a second sulfide precipitation step (C.2) in which sulfide precipitation reagent is added to the intermediate liquid in the second precipitation reactor, producing a residual liquid that has been largely freed of arsenic; wherein d) after the first sulfide precipitation step (C.1) at least one separation stage is conducted, in which precipitated sulfides are separated from the intermediate liquid; and/or e) after the second sulfide precipitation step (C.2) at least one separation stage is conducted, in which precipitated sulfides are separated from the residual liquid; characterized in that f) the first sulfide precipitation reactor and/or the second precipitation reactor and/or one or more separation stages (D, E) are supplied with air, especially conditioned air; g) output air that arises in the first sulfide precipitation reactor is monitored for the presence of hydrogen sulfide by means of a measurement device. a) the sulfide precipitation stage comprises a first sulfide precipitation step (C.1) in which sulfide precipitation reagent is added to the process water in a first sulfide precipitation reactor, producing an intermediate liquid still containing arsenic or still containing arsenic and primary heavy metal; b) the intermediate liquid, after the first sulfide precipitation step (C.1), is transferred into a second sulfide precipitation reactor; c) the sulfide precipitation stage comprises a second sulfide precipitation step (C.2) in which sulfide precipitation reagent is added to the intermediate liquid in the second precipitation reactor, producing a residual liquid that has been largely freed of arsenic; wherein d) after the first sulfide precipitation step (C.1) at least one separation stage is conducted, in which precipitated sulfides are separated from the intermediate liquid; and/or e) after the second sulfide precipitation step (C.2) at least one separation stage is conducted, in which precipitated sulfides are separated from the residual liquid; characterized in that f) the first sulfide precipitation reactor and/or the second precipitation reactor and/or one or more separation stages (D, E) are supplied with air, especially conditioned air; g) output air that arises in the first sulfide precipitation reactor is monitored for the presence of hydrogen sulfide by means of a measurement device.