Statement I is correct because \( S_8 \) can indeed undergo disproportionation in alkaline medium:
\[ S_8 + 12 \text{OH}^- \rightarrow 4 S^{2-} + 2 S_2O_3^{2-} + 6 H_2O. \]
Statement II is incorrect because \( \text{ClO}_4^- \) cannot undergo disproportionation as chlorine is already in its highest oxidation state.
Given below are two statements:
Statement (I): The first ionization energy of Pb is greater than that of Sn.
Statement (II): The first ionization energy of Ge is greater than that of Si.
In light of the above statements, choose the correct answer from the options given below:
Let \( y = f(x) \) be the solution of the differential equation
\[ \frac{dy}{dx} + 3y \tan^2 x + 3y = \sec^2 x \]
such that \( f(0) = \frac{e^3}{3} + 1 \), then \( f\left( \frac{\pi}{4} \right) \) is equal to:
Find the IUPAC name of the compound.
If \( \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p \), then \( 96 \ln p \) is: 32