Alkaline oxidative fusion of \(MnO_2\) gives “A” which on electrolytic oxidation in alkaline solution produces B. A and B respectively are:
The process described involves the oxidative reactions of manganese compounds in alkaline solutions.
Alkaline Oxidative Fusion of \(MnO_2\): When \(MnO_2\) is subjected to oxidative fusion in an alkaline medium, it can form \(MnO_4^{2-}\) (manganate ion) under alkaline conditions. The reaction can be represented as:
\(2MnO_2 + 2OH^- + O_2 \rightarrow 2MnO_4^{2-} + H_2O\).
Electrolytic Oxidation of Product A: The product A formed from the oxidative fusion of \(MnO_2\) can be oxidized electrolytically in alkaline solution to form \(MnO_4^-\) (permanganate ion). The overall reaction is:
\(MnO_2 + 2e^- \rightarrow MnO_4^-\).
Thus, the products A and B formed in the given reaction sequence are: A = \(MnO_4^{2-}\) and B = \(MnO_4^-\).
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