Question #44433

An optically active compound $\textbf{X}$ ($\ce{C16H14O4}$) is treated with exactly one equivalent of periodic acid ($\ce{HIO4}$) at 298 K to yield two moles of a single compound $\textbf{Y}$. Compound $\textbf{Y}$ gives a positive Tollens' test (silver mirror) but fails to produce a red precipitate when heated with Fehling's solution. Instead, the strongly basic conditions of Fehling's solution cause $\textbf{Y}$ to undergo a rapid rearrangement to an intermediate that, upon careful acidification, yields compound $\textbf{Z}$. Let $C_{sp^2}$ be the number of $sp^2$ hybridized carbon atoms and $C_{sp^3}$ be the number of $sp^3$ hybridized carbon atoms in a single molecule of $\textbf{Z}$. What is the value of $(C_{sp^2} - C_{sp^3})$?