Process for purifying crude synthesis gas with methanol as a physical absorption medium, wherein an acid gas comprising at least hydrogen sulfide (H 2 S) is produced and the process comprises the following process steps: - treating crude synthesis gas comprising at least carbon monoxide, hydrogen (H 2), hydrogen sulfide (H 2 S) and hydrogen cyanide and/or ammonia (NH 3) with methanol in an absorption apparatus to obtain a methanol laden with at least H 2 S and HCN and/or NH 3; - hot-regenerating the methanol laden with H 2 S and HCN and/or NH 3 in a hot regenerator to obtain a gas mixture comprising at least methanol, H 2 S and HCN and/or NH 3 which is withdrawn from the hot regenerator; - cooling the gas mixture withdrawn from the hot regenerator and transferring the cooled gas mixture into an acid gas separator, wherein the acid gas separator comprises an absorption region and a condensation region, wherein the absorption region and the condensation region are separated from one another by a gas-permeable tray; - condensing methanol from the gas mixture in the condensation region of the acid gas separator, withdrawing the condensed methanol from the acid gas separator and transferring it to the hot regenerator; - withdrawing a first acid gas substream comprising H 2 S and HCN and/or NH 3 from the acid gas separator; - passing a second acid gas substream comprising H 2 S and HCN and/or NH 3 through the absorption region of the acid gas separator, wherein HCN and/or NH 3 are absorbed by cryogenic methanol supplied to the absorption region of the acid gas separator, cryogenic methanol laden with HCN and/or NH 3 collects in the region of the gas-permeable tray and a second acid gas substream at least partially freed of HCN and/or NH 3 is obtained; - withdrawing the second acid gas substream at least partially freed of HCN and/or NH 3 from the acid gas separator; - withdrawing the cryogenic methanol laden with HCN and/or NH 3 from the region of the gas-permeable tray of the acid gas separator and transferring the cryogenic methanol laden with HCN and/or NH 3 to the hot regenerator. - treating crude synthesis gas comprising at least carbon monoxide, hydrogen (H 2), hydrogen sulfide (H 2 S) and hydrogen cyanide and/or ammonia (NH 3) with methanol in an absorption apparatus to obtain a methanol laden with at least H 2 S and HCN and/or NH 3; - hot-regenerating the methanol laden with H 2 S and HCN and/or NH 3 in a hot regenerator to obtain a gas mixture comprising at least methanol, H 2 S and HCN and/or NH 3 which is withdrawn from the hot regenerator; - cooling the gas mixture withdrawn from the hot regenerator and transferring the cooled gas mixture into an acid gas separator, wherein the acid gas separator comprises an absorption region and a condensation region, wherein the absorption region and the condensation region are separated from one another by a gas-permeable tray; - condensing methanol from the gas mixture in the condensation region of the acid gas separator, withdrawing the condensed methanol from the acid gas separator and transferring it to the hot regenerator; - withdrawing a first acid gas substream comprising H 2 S and HCN and/or NH 3 from the acid gas separator; - passing a second acid gas substream comprising H 2 S and HCN and/or NH 3 through the absorption region of the acid gas separator, wherein HCN and/or NH 3 are absorbed by cryogenic methanol supplied to the absorption region of the acid gas separator, cryogenic methanol laden with HCN and/or NH 3 collects in the region of the gas-permeable tray and a second acid gas substream at least partially freed of HCN and/or NH 3 is obtained; - withdrawing the second acid gas substream at least partially freed of HCN and/or NH 3 from the acid gas separator; - withdrawing the cryogenic methanol laden with HCN and/or NH 3 from the region of the gas-permeable tray of the acid gas separator and transferring the cryogenic methanol laden with HCN and/or NH 3 to the hot regenerator.