Identification of Non Reducing Disaccharide Structure Giving Laevorotatory Hydrolysis Product

To determine the identity of the disaccharide $\mathbf{X}$, we analyze its chemical properties step-by-step:

1. Reaction with Bromine Water (Non-reducing Sugar)

Bromine water ($\text{Br}_2/\text{H}_2\text{O}$) is a mild oxidizing agent that selectively oxidizes aldoses (free aldehyde or hemiacetal groups) to aldonic acids. Since disaccharide $\mathbf{X}$ cannot be oxidized by bromine water, it lacks a free hemiacetal or hemiketal group at its anomeric carbons.

This indicates that $\mathbf{X}$ is a non-reducing disaccharide, where the anomeric carbons of both monosaccharide units are mutually involved in the glycosidic linkage.

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2. Acid Hydrolysis and Optical Rotation

Upon acid hydrolysis, $\mathbf{X}$ yields an equimolar mixture of its constituent monosaccharides: $\mathbf{X} \xrightarrow{\text{H}_3\text{O}^+} \text{D-(+)-glucose} + \text{D-(-)-fructose}$

• The specific rotation of $\text{D-(+)-glucose}$ is $[\alpha]_D = +52.7^\circ$.
• The specific rotation of $\text{D-(-)-fructose}$ is $[\alpha]_D = -92.4^\circ$.

The net specific rotation of the hydrolyzed equimolar mixture (invert sugar) is calculated as: $[\alpha]_D^{\text{mixture}} = \frac{+52.7^\circ + (-92.4^\circ)}{2} = -19.85^\circ$

Since the resulting mixture is laevorotatory (a process known as the inversion of sugar), the disaccharide $\mathbf{X}$ must be sucrose.

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3. Structural Analysis of Sucrose

Sucrose is composed of an $\alpha$-D-glucopyranose unit and a $\beta$-D-fructofuranose unit connected by a $\text{C}_1-\text{O}-\text{C}_2$ glycosidic linkage:

• Left Unit ($\alpha$-D-glucopyranose): A 6-membered pyranose ring with the glycosidic oxygen attached at $\text{C}_1$ in the $\alpha$-configuration (pointing downwards in Haworth projection).
• Right Unit ($\beta$-D-fructofuranose): A 5-membered furanose ring with the glycosidic oxygen attached at its anomeric carbon $\text{C}_2$.

Comparing the given options:

• Option (A): Correctly shows the $\text{C}_1-\text{O}-\text{C}_2$ glycosidic linkage between $\alpha$-D-glucopyranose and $\beta$-D-fructofuranose without any free hemiacetal/hemiketal group.
• Options (B), (C), and (D): Represent reducing disaccharides with free hemiacetal OH groups at anomeric centers.

Thus, the correct structure of disaccharide $\mathbf{X}$ is given by (A).