A method of purifying a Bayer process stream, comprising: providing a liquid phase that comprises an oxalate-extracting amount of an organic salt which is a mass fraction of at least 1%, based on the mass of the Bayer process stream, wherein the organic salt comprises a quaternary organic cation selected from the group consisting of: phosphonium, ammonium, imidazolium, pyrrolidinium, quinolinium, pyrazolium, oxazolium, thiazolium, isoquinolinium, and piperidinium, and the organic salt is selected: - from the group consisting of: trihexyltetradecylphosphonium chloride, tetrabutylphosphonium chloride, tetrabutylphosphonium hydroxide, tetradecyl(tributyl)-phosphonium chloride, tributyl (8-hydroxyoctyl)phosphonium chloride, octyl(tributyl)phosphonium chloride, and tetradecyl(tributyl)phosphonium chloride, - or from the group consisting of: tributylmethylammonium hydroxide, tetrabutylammonium hydroxide, tetrabutylammonium chloride, tetrapentylammonium hydroxide, stearamidopropyldimethyl-2-hydroxyethylammonium nitrate, ethyltetradecyldiundecyl ammonium chloride, tetrahexylammonium bromide, dodecyltrimethyl ammonium chloride, benzyldimethylcoco ammonium chloride, N,N-dimethyl-N-dodecylglycine betaine, dimethyl dicoco quaternary ammonium chloride, Aliquat® HTA-1, 1-octyl-2,3-dimethyl imidazolium chloride, and tallowalkyltrimethyl ammonium chloride; and wherein the liquid phase is at least partially immiscible with the Bayer process stream; intermixing the Bayer process stream with the liquid phase in an amount effective to form a biphasic liquid/liquid mixture, wherein the biphasic liquid/liquid mixture comprises a primarily Bayer process phase and a primarily organic salt phase; and at least partially separating the primarily Bayer process phase from the primarily organic salt phase to form a separated primarily Bayer process phase and a separated primarily organic salt phase; wherein the intermixing is effective to reduce the concentration of oxalate in the Bayer process stream. providing a liquid phase that comprises an oxalate-extracting amount of an organic salt which is a mass fraction of at least 1%, based on the mass of the Bayer process stream, wherein the organic salt comprises a quaternary organic cation selected from the group consisting of: phosphonium, ammonium, imidazolium, pyrrolidinium, quinolinium, pyrazolium, oxazolium, thiazolium, isoquinolinium, and piperidinium, and the organic salt is selected: - from the group consisting of: trihexyltetradecylphosphonium chloride, tetrabutylphosphonium chloride, tetrabutylphosphonium hydroxide, tetradecyl(tributyl)-phosphonium chloride, tributyl (8-hydroxyoctyl)phosphonium chloride, octyl(tributyl)phosphonium chloride, and tetradecyl(tributyl)phosphonium chloride, - or from the group consisting of: tributylmethylammonium hydroxide, tetrabutylammonium hydroxide, tetrabutylammonium chloride, tetrapentylammonium hydroxide, stearamidopropyldimethyl-2-hydroxyethylammonium nitrate, ethyltetradecyldiundecyl ammonium chloride, tetrahexylammonium bromide, dodecyltrimethyl ammonium chloride, benzyldimethylcoco ammonium chloride, N,N-dimethyl-N-dodecylglycine betaine, dimethyl dicoco quaternary ammonium chloride, Aliquat® HTA-1, 1-octyl-2,3-dimethyl imidazolium chloride, and tallowalkyltrimethyl ammonium chloride; - from the group consisting of: trihexyltetradecylphosphonium chloride, tetrabutylphosphonium chloride, tetrabutylphosphonium hydroxide, tetradecyl(tributyl)-phosphonium chloride, tributyl (8-hydroxyoctyl)phosphonium chloride, octyl(tributyl)phosphonium chloride, and tetradecyl(tributyl)phosphonium chloride, - or from the group consisting of: tributylmethylammonium hydroxide, tetrabutylammonium hydroxide, tetrabutylammonium chloride, tetrapentylammonium hydroxide, stearamidopropyldimethyl-2-hydroxyethylammonium nitrate, ethyltetradecyldiundecyl ammonium chloride, tetrahexylammonium bromide, dodecyltrimethyl ammonium chloride, benzyldimethylcoco ammonium chloride, N,N-dimethyl-N-dodecylglycine betaine, dimethyl dicoco quaternary ammonium chloride, Aliquat® HTA-1, 1-octyl-2,3-dimethyl imidazolium chloride, and tallowalkyltrimethyl ammonium chloride; and wherein the liquid phase is at least partially immiscible with the Bayer process stream; intermixing the Bayer process stream with the liquid phase in an amount effective to form a biphasic liquid/liquid mixture, wherein the biphasic liquid/liquid mixture comprises a primarily Bayer process phase and a primarily organic salt phase; and at least partially separating the primarily Bayer process phase from the primarily organic salt phase to form a separated primarily Bayer process phase and a separated primarily organic salt phase; wherein the intermixing is effective to reduce the concentration of oxalate in the Bayer process stream.