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.
Let one focus of the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ be at $ (\sqrt{10}, 0) $, and the corresponding directrix be $ x = \frac{\sqrt{10}}{2} $. If $ e $ and $ l $ are the eccentricity and the latus rectum respectively, then $ 9(e^2 + l) $ is equal to:
The largest $ n \in \mathbb{N} $ such that $ 3^n $ divides 50! is: