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A member of the lanthanide element series, whose ionic-size and redox trends reflect the filling and incomplete shielding of the 4f shell.

Two bidentate bipyridine ligands provide four N donors and three terminal NCS ligands provide three more. Adding one water gives $n=1$ and coordination number eight:Eight-coordinate arrangements, distorted between familiar ideal polyhedra, are plausible for a sterically crowded Eu(III) centre. A second water would give coordination number nine, which is not forbidden for a lanthanide; the requested value is a chemically motivated prediction, not something fixed by charge balance. Diffraction or a direct hydration-number measurement is needed to establish it uniquely.

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 $4f$ 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.

Use the balanced aqueous-acid reactionA Hess cycle first atomizes the metal, then ionizes its gas-phase atoms, then hydrates the triply charged gas ions:Close the reference leg by combining the three electrons with $3{\mathrm{H}}^{+}(\mathrm{aq})$ to make $\frac{3}{2}{\mathrm{H}}_2(\mathrm{g})$. Calling that element-independent contribution $C_H$ givesA single-ion standard enthalpy of formation uses the conventional hydrogen-ion reference; it must not be treated as a balanced creation of net charge from neutral metal without an electron/reference term. The constant hydrogen leg does not affect comparisons along the lanthanide series.