Review concepts of reduction potentials, stability of oxidation states in d-block elements, and the relationship between unpaired electrons and magnetic moment
The reduction potential for the M3+/M2+ couple for manganese is greater than that for iron:
\[ E^\circ_{\text{Mn}^{3+}/\text{Mn}^{2+}} = +1.57 \, \text{V}, \, E^\circ_{\text{Fe}^{3+}/\text{Fe}^{2+}} = +0.77 \, \text{V} \]
Therefore, this statement is incorrect.
Higher oxidation states of first-row d-block elements are stabilized by oxide ions (O2−) due to the formation of strong metal-oxygen bonds. This statement is correct.
Chromium in the Cr2+ oxidation state can reduce H+ to H2 in aqueous solution:
\[ \text{Cr}^{2+} + \text{H}^+ \rightarrow \text{Cr}^{3+} + \frac{1}{2}\text{H}_2 \]
The reduction potential \( E^\circ_{\text{Cr}^{3+}/\text{Cr}^{2+}} = -0.26 \, \text{V} \) confirms this. This statement is correct.
V2+ has three unpaired electrons, resulting in a magnetic moment of approximately 3.87 BM, which is not within the range of 4.4-5.2 BM. This statement is incorrect.
If the system of equations \[ x + 2y - 3z = 2, \quad 2x + \lambda y + 5z = 5, \quad 14x + 3y + \mu z = 33 \] has infinitely many solutions, then \( \lambda + \mu \) is equal to:}
The equilibrium constant for decomposition of $ H_2O $ (g) $ H_2O(g) \rightleftharpoons H_2(g) + \frac{1}{2} O_2(g) \quad (\Delta G^\circ = 92.34 \, \text{kJ mol}^{-1}) $ is $ 8.0 \times 10^{-3} $ at 2300 K and total pressure at equilibrium is 1 bar. Under this condition, the degree of dissociation ($ \alpha $) of water is _____ $\times 10^{-2}$ (nearest integer value). [Assume $ \alpha $ is negligible with respect to 1]