When `(+)` sucrose is hydrolysed, the `D`-glucose mutarotates downward to `+52.7^(@)`. What does this indicate about the structures of `(+)`-sucrose?

Answer

To analyze the hydrolysis of (+) sucrose and its implications for the structure of sucrose, we can follow these steps:

### Step-by-Step Solution

1. **Understanding Sucrose**:
Sucrose is a disaccharide composed of glucose and fructose. It is known to be a non-reducing sugar because it does not have a free aldehyde or ketone group.

2. **Hydrolysis of Sucrose**:
When sucrose undergoes hydrolysis, it breaks down into its constituent monosaccharides: D-glucose and D-fructose. This reaction is typically catalyzed by an acid or an enzyme.

3. **Mutarotation of D-Glucose**:
D-glucose can exist in two anomeric forms: alpha (α) and beta (β). Mutarotation refers to the change in optical rotation that occurs when an anomer of a sugar converts to another form in solution. For D-glucose, the specific rotations are:
- α-D-glucose: +112.2°
- β-D-glucose: +18.7°

4. **Observation of Downward Mutarotation**:
The question states that upon hydrolysis, D-glucose mutarotates downward to +52.7°. This indicates that the equilibrium between the α and β forms is shifting towards a mixture that is lower than the specific rotation of α-D-glucose but higher than that of β-D-glucose.

5. **Implications for Sucrose Structure**:
The fact that the mutarotation leads to a specific rotation of +52.7° suggests that the sucrose molecule has a configuration that allows for the formation of D-glucose in its pyranose form. This indicates that the glycosidic bond in sucrose is likely linking the anomeric carbon of glucose to the hydroxyl group of fructose.

6. **Conclusion**:
The downward mutarotation of D-glucose after hydrolysis of (+) sucrose indicates that sucrose is a disaccharide formed from the α-D-glucose and β-D-fructose, and that the hydrolysis results in the formation of D-glucose predominantly in the pyranose form.