Method of distilling mixtures comprising salts having a melting point of less than 200° C. at 1 bar (ionic liquids), wherein the cation of the ionic liquid comprises a heterocyclic ring system having at least one nitrogen atom and all nitrogen atoms of the heterocyclic ring system have an organic group as substituent, the anion of the ionic liquid is a compound having at least one carboxylate group (carboxylate for short) or at least one phosphate group (phosphate for short) and the distance from the surface via which the heat of distillation is introduced in the distillation (vaporizer surface) to the surface at which condensation takes place (condenser surface) is less than 50 cm at least one point, with the vaporizer surface and condenser surface themselves having at least one length dimension of greater than 50 cm.