Equimolar mixture of `alpha`-D(+)-glucose has specific `([alpha]_(D))` is

Options

A. `-92.4^@`
B. `+112.5^@`
C. `+52.5^@`
D. `-19.2^@`

Answer

To solve the question regarding the specific rotation of an equimolar mixture of α-D(+)-glucose, we will follow these steps:

### Step-by-Step Solution:

1. **Understand the Components**:
- The equimolar mixture consists of α-D(+)-glucose and another sugar, which is typically sucrose. Upon hydrolysis, sucrose breaks down into glucose and fructose.

2. **Identify the Specific Rotations**:
- The specific rotation of α-D(+)-glucose is +52.5°.
- The specific rotation of fructose (which is the other component after hydrolysis) is -92.4°.

3. **Calculate the Specific Rotation of the Mixture**:
- For an equimolar mixture, the specific rotation can be calculated using the formula:
\[ [\alpha]_{D, \text{mixture}} = \frac{[\alpha]_{D, \text{glucose}} + [\alpha]_{D, \text{fructose}}}{2} \]
- Plugging in the values:
\[ [\alpha]_{D, \text{mixture}} = \frac{52.5 + (-92.4)}{2} \]
\[ = \frac{52.5 - 92.4}{2} \]
\[ = \frac{-39.9}{2} = -19.95° \]

4. **Conclusion**:
- The specific rotation of the equimolar mixture of α-D(+)-glucose and fructose is approximately -19.95°.

### Final Answer:
The specific rotation \([α]_{D}\) of the equimolar mixture of α-D(+)-glucose is approximately -19.95°.