Specific Rotation of Sugar Derivatives Produced by Nitric Acid Oxidation

When D-glucose is treated with concentrated $\text{HNO}_3$, both the terminal aldehyde group ($-\text{CHO}$) at $\text{C-1}$ and the primary alcohol group ($-\text{CH}_2\text{OH}$) at $\text{C-6}$ are oxidized to carboxylic acid ($-\text{COOH}$) groups. This forms an aldaric acid, specifically D-glucaric acid ($\mathbf{P}$).

The Fischer projection of D-glucose and its oxidation product $\mathbf{P}$ (D-glucaric acid) with $[\alpha]_D = +52.7^\circ$ is given by:

$\text{D-glucose} \xrightarrow{\text{HNO}_3} \mathbf{P} \quad ([\alpha]_D = +52.7^\circ)$

$$\begin{array}{c} \text{CHO} \\ | \\ \text{H} - \text{C} - \text{OH} \\ | \\ \text{HO} - \text{C} - \text{H} \\ | \\ \text{H} - \text{C} - \text{OH} \\ | \\ \text{H} - \text{C} - \text{OH} \\ | \\ \text{CH}_2\text{OH} \end{array} \xrightarrow{\text{HNO}_3} \begin{array}{c} \text{COOH} \\ | \\ \text{H} - \text{C} - \text{OH} \quad (\text{Right}) \\ | \\ \text{HO} - \text{C} - \text{H} \quad (\text{Left}) \\ | \\ \text{H} - \text{C} - \text{OH} \quad (\text{Right}) \\ | \\ \text{H} - \text{C} - \text{OH} \quad (\text{Right}) \\ | \\ \text{COOH} \end{array}$$

Thus, the spatial orientation of the $-\text{OH}$ groups from $\text{C-2}$ to $\text{C-5}$ in D-glucaric acid ($\mathbf{P}$) is $(\text{Right}, \text{Left}, \text{Right}, \text{Right})$.

To obtain a product with an optical rotation of $[\alpha]_D = -52.7^\circ$, the oxidation product must be the enantiomer of D-glucaric acid, which is L-glucaric acid ($\mathbf{P'}$).

The Fischer projection of L-glucaric acid ($\mathbf{P'}$) has the inverted configuration at all chiral centers:

$$\mathbf{P'} \quad ([\alpha]_D = -52.7^\circ) = \begin{array}{c} \text{COOH} \\ | \\ \text{HO} - \text{C} - \text{H} \quad (\text{Left}) \\ | \\ \text{H} - \text{C} - \text{OH} \quad (\text{Right}) \\ | \\ \text{HO} - \text{C} - \text{H} \quad (\text{Left}) \\ | \\ \text{HO} - \text{C} - \text{H} \quad (\text{Left}) \\ | \\ \text{COOH} \end{array}$$

The $-\text{OH}$ orientation sequence for $\mathbf{P'}$ from $\text{C-2}$ to $\text{C-5}$ is $(\text{Left}, \text{Right}, \text{Left}, \text{Left})$.

Since a $180^\circ$ rotation of a Fischer projection in the plane of the page yields an identical representation of a molecule:

• Top ($-\text{COOH}$) and Bottom ($-\text{COOH}$) swap places.
• $\text{C-2}$ swaps with $\text{C-5}$, and $\text{C-3}$ swaps with $\text{C-4}$.
• Left substituents move to the Right, and Right substituents move to the Left.

Under a $180^\circ$ in-plane rotation, the configuration sequence $(s_2, s_3, s_4, s_5)$ transforms to: $(s'_2, s'_3, s'_4, s'_5) = (\text{opp}(s_5), \text{opp}(s_4), \text{opp}(s_3), \text{opp}(s_2))$

Applying this to L-glucaric acid $(\text{Left}, \text{Right}, \text{Left}, \text{Left})$ gives: $(\text{opp}(\text{Left}), \text{opp}(\text{Left}), \text{opp}(\text{Right}), \text{opp}(\text{Left})) = (\text{Right}, \text{Right}, \text{Left}, \text{Right})$

Therefore, any substrate whose oxidation product has an $-\text{OH}$ configuration sequence of either $(\text{Left}, \text{Right}, \text{Left}, \text{Left})$ or $(\text{Right}, \text{Right}, \text{Left}, \text{Right})$ will produce L-glucaric acid ($\mathbf{P'}$), exhibiting $[\alpha]_D = -52.7^\circ$.

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Analysis of the Options:

1. Option (A):

   • Configuration from $\text{C-2}$ to $\text{C-5}$: $(\text{Left}, \text{Left}, \text{Right}, \text{Right})$.
   • Oxidation product sequence: $(\text{Left}, \text{Left}, \text{Right}, \text{Right})$.
   • This does not match L-glucaric acid.

2. Option (B):

   • Configuration from $\text{C-2}$ to $\text{C-5}$: $(\text{Left}, \text{Left}, \text{Right}, \text{Left})$ (L-gulose).
   • A $180^\circ$ rotation of its oxidized product gives $(\text{Right}, \text{Left}, \text{Right}, \text{Right})$, which is D-glucaric acid ($\mathbf{P}$), having $[\alpha]_D = +52.7^\circ$.

3. Option (C):

   • Configuration from $\text{C-2}$ to $\text{C-5}$: $(\text{Left}, \text{Right}, \text{Left}, \text{Left})$ (L-glucose).
   • Upon oxidation with $\text{HNO}_3$, it directly yields L-glucaric acid ($\mathbf{P'}$), which has $[\alpha]_D = -52.7^\circ$.
   • Correct option.

4. Option (D):

   • Configuration from $\text{C-2}$ to $\text{C-5}$: $(\text{Right}, \text{Right}, \text{Left}, \text{Right})$ (D-gulose).
   • Upon oxidation with $\text{HNO}_3$, the product has sequence $(\text{Right}, \text{Right}, \text{Left}, \text{Right})$. Rotating this product by $180^\circ$ in-plane yields $(\text{Left}, \text{Right}, \text{Left}, \text{Left})$, which is identical to L-glucaric acid ($\mathbf{P'}$), having $[\alpha]_D = -52.7^\circ$.
   • Correct option.

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Conclusion:

The compounds in options (C) and (D) yield a product with $[\alpha]_D = -52.7^\circ$.