Question #44476

An organic compound $\textbf{P}$ ($C_4H_6$) exhibits terminal acidity. Two separate experiments are performed on 1 mole of $\textbf{P}$:

\textbf{Experiment 1:} $\textbf{P}$ is subjected to vigorous oxidation with hot acidic $KMnO_4$, yielding a carboxylic acid $\textbf{Q}$ and a gas. The reaction consumes $x$ moles of $KMnO_4$.

\textbf{Experiment 2:} $\textbf{P}$ is treated with $HgSO_4 / H_2SO_4$ to undergo complete hydration, forming a stable tautomer $\textbf{R}$. Compound $\textbf{R}$ is then subjected to vigorous oxidation with hot acidic $KMnO_4$, yielding exclusively the major product $\textbf{S}$ as dictated by Popoff's rule. This oxidation step consumes $y$ moles of $KMnO_4$.

Assuming complete conversion in all steps, what are the values of $x$ and $y$, and the identity of $\textbf{S}$?