Question #44989

D-Glyceraldehyde is subjected to the Kiliani-Fischer synthesis. The intermediate cyanohydrins are hydrolyzed and heated to yield a mixture of two stable cyclic compounds, $\mathbf{L_1}$ and $\mathbf{L_2}$. Reduction of $\mathbf{L_1}$ and $\mathbf{L_2}$ with $\ce{Na(Hg)}$ in water at pH 3-5 yields a mixture of two aldotetroses, $\mathbf{X}$ and $\mathbf{Y}$. The mixture of $\mathbf{X}$ and $\mathbf{Y}$ is then treated with excess $\ce{CH_3OH}$ in the presence of catalytic dry $\ce{HCl}$ to yield a mixture of major products $\mathbf{Z}$.

Let $x$ be the number of compounds in the mixture $\mathbf{L_1} + \mathbf{L_2}$ that exhibit mutarotation in aqueous solution. Let $y$ be the number of compounds in the mixture $\mathbf{X} + \mathbf{Y}$ that give a positive Tollens' test. Let $z$ be the total number of major stereoisomers present in the mixture $\mathbf{Z}$.

Determine the correct set of values for $(x, y, z)$.