The key is coupling redox equilibrium to hydrolysis and precipitation. Ce(IV) has a much greater tendency than Ce(III) to form a hydrated cerium dioxide solid. Raising pH therefore preferentially stabilizes the oxidized form. In the presence of dissolved oxygen a representative net reaction is
Removing drives this reaction towards Ce(IV). Writing the solid as hydrated oxide changes its water content, not this redox argument.
The Nernst equation makes the pH effect explicit. At , the reduction has a pH slope approximately per pH unit at fixed Ce(III) activity. The oxygen/water reduction has slope about per pH unit. Raising pH thus makes oxidation of Ce(III) by oxygen increasingly favourable within the relevant phase-stability region. Conversely strong acid favours soluble Ce(III) relative to the oxide and makes Ce(IV) a stronger oxidizing agent. pH changes the redox driving force; an electron acceptor or donor is still required, and slow oxygen evolution or oxidation kinetics can prevent immediate equilibration.
Not as a general aqueous separation reaction for the other lanthanides. Most strongly favour the trivalent state in ordinary water chemistry. Ce(IV) is unusually accessible because it has the empty shell and is strongly stabilized by oxide formation. Some other lanthanides have accessible alternative oxidation states, such as Eu(II), and higher oxides of Pr or Tb can exist under suitable conditions; this does not imply that they undergo the same Ce(III)/Ce(IV) pH-controlled aqueous oxidation.
A natural feed can contain thorium and uranium, as well as other lanthanides. Th(IV) hydrolyses readily and can accompany the cerium precipitate; uranium speciation depends on its oxidation state and the ligands present. Raising pH too far also precipitates other rare-earth hydroxides. Even before their bulk precipitation thresholds, adsorption and coprecipitation on a high-area hydrated cerium oxide can contaminate the solid. Local high-pH zones during base addition and incomplete Ce(III) oxidation make the separation less reproducible.
Thus a cerium-rich precipitate need not be pure cerium. A sensible test measures the Ce oxidation state, analyses both filtrate and washed solid, and includes thorium-containing and thorium-free mixtures; otherwise low dissolved cerium could be mistaken for selective purification.
A better controlled route is selective solvent extraction in acid, followed by selective stripping, rather than precipitating everything near overlapping hydrolysis thresholds. Oxidize Ce(III) to Ce(IV) in a controlled acidic nitrate medium, extract its nitrate complexes into an organic donor phase, and separate the phases. Then reduce the extracted Ce(IV) to Ce(III) and back-extract it into an aqueous phase. Trivalent rare earths are less strongly extracted under suitable conditions.
This still needs a thorium separation: tributyl phosphate can coextract Th(IV). One demonstrated strategy deliberately coextracts Ce(IV) and Th(IV), then uses reducing peroxide solution to strip Ce as Ce(III), followed by a separate thorium strip. The appropriate controls are distribution measurements for each ion at the chosen acid concentration, a cerium oxidation-state check, and a complete mass balance over extraction and stripping. Selectivity comes from combining oxidation state and complexation, not from assuming that one extraction removes every contaminant.[ref]

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