MediumChemistryHigh School (11–12)The d- and f-Block ElementsNumerical

The standard potentials of two couples are E°(Sm³⁺/Sm²⁺) = -1.55 V and E°(Yb³⁺/Yb²⁺) = -1.05 V…

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The standard potentials of two couples are $E^\circ(\text{Sm}^{3+}/\text{Sm}^{2+}) = -1.55\ \text{V}$ and $E^\circ(\text{Yb}^{3+}/\text{Yb}^{2+}) = -1.05\ \text{V}$ . Each 2+ ion can reduce hydrogen ions: $\text{M}^{2+}(aq) + \text{H}^+(aq) \rightarrow \text{M}^{3+}(aq) + \tfrac{1}{2}\text{H}_2(g)$ . Use $E^\circ(\text{H}^+/\text{H}_2) = 0.00\ \text{V}$ . Find the standard emf for samarium and for ytterbium, and the Gibbs energy change for each. One electron is transferred.

Need a reminder? The key ideaShow

The 3+ ion of a lanthanoid is $[\text{Xe}]\,4f^{n}$ with $n = Z - 57$ . Unpaired electrons: $n$ up to 7, then $14 - n$ . Spin-only moment: $\mu = \sqrt{n(n+2)}\ \text{BM}$ . An empty, half-full or full 4f subshell ( $4f^0$ , $4f^7$ , $4f^{14}$ ) makes an ion unusually stable. That explains $\text{Ce}^{4+}$ , $\text{Tb}^{4+}$ , $\text{Eu}^{2+}$ and $\text{Yb}^{2+}$ . For a cell, $\Delta G^\circ = -nFE^\circ$ with $F = 96.5\ \text{kJ/(V mol)}$ .

The worked solution

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