Give Reasons:
(I) \( \text{Ce}^{4+} \) in aqueous solution is a good oxidising agent.
(II) The actinoid contraction is greater from element to element than lanthanoid contraction.
(III) \( E^\circ_{\text{M}^{2+}/\text{M}} \) value is more negative than expected, whereas \( E^\circ_{\text{Cu}^{2+}/\text{Cu}} \) is positive.
(I) \( \text{Ce}^{4+} \) in aqueous solution is a good oxidising agent.
Reason: \( \text{Ce}^{4+} \) is a strong oxidising agent because it has a high tendency to accept an electron and reduce to \( \text{Ce}^{3+} \). The high charge on \( \text{Ce}^{4+} \) (a +4 oxidation state) and the relatively small ionic radius of \( \text{Ce}^{4+} \) compared to its reduced form \( \text{Ce}^{3+} \) give it a high electron affinity, making it an effective oxidant in aqueous solutions.
(II) The actinoid contraction is greater from element to element than lanthanoid contraction.
Reason: The actinoid contraction is greater than the lanthanoid contraction because the 5f-electrons in actinides experience poor shielding by other f-electrons, resulting in a greater increase in effective nuclear charge as the atomic number increases. In contrast, lanthanides with 4f-electrons experience better shielding; therefore, the contraction is less significant. This explains why the atomic sizes in the actinide series decrease more significantly across the series than in the lanthanide series.
(III) \( E^\circ_{\text{M}^{2+}/\text{M}} \) value is more negative than expected, whereas \( E^\circ_{\text{Cu}^{2+}/\text{Cu}} \) is positive.
Reason: The \( E^\circ_{\text{M}^{2+}/\text{M}} \) value is more negative than expected due to the large increase in ionization energy as we remove electrons from the second ionization state, leading to a stronger pull by the nucleus. On the other hand, \( E^\circ_{\text{Cu}^{2+}/\text{Cu}} \) is positive because copper has a stable electronic configuration with a filled 3d10 subshell, making it more resistant to oxidation and thus having a positive electrode potential. Copper, being a transition metal, has a more favorable reduction potential than other elements like iron, leading to a positive standard electrode potential for the Cu2+/Cu system.
Complete and balance the following chemical equations: (a) \[ 2MnO_4^-(aq) + 10I^-(aq) + 16H^+(aq) \rightarrow \] (b) \[ Cr_2O_7^{2-}(aq) + 6Fe^{2+}(aq) + 14H^+(aq) \rightarrow \]