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 determine the specific rotation of an equimolar mixture of α-D(+)-glucose and fructose, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Components**:
- We have an equimolar mixture of α-D(+)-glucose and fructose.
- α-D(+)-glucose is a levorotatory compound with a specific rotation of +52° 5'.
- Fructose is a dextrorotatory compound with a specific rotation of -92° 4'.

2. **Identify the Specific Rotations**:
- Specific rotation of α-D(+)-glucose, [α]D = +52° 5' = +52.083° (converting minutes to degrees).
- Specific rotation of fructose, [α]D = -92° 4' = -92.067° (converting minutes to degrees).

3. **Calculate the Specific Rotation of the Mixture**:
- Since the mixture is equimolar, the specific rotation of the mixture can be calculated using the formula:
\[ [\alpha]_{mix} = \frac{[\alpha]_{glucose} + [\alpha]_{fructose}}{2} \]
- Substituting the values:
\[ [\alpha]_{mix} = \frac{(+52.083) + (-92.067)}{2} \]
\[ [\alpha]_{mix} = \frac{-39.984}{2} = -19.992 \]

4. **Final Result**:
- The specific rotation of the equimolar mixture of α-D(+)-glucose and fructose is approximately -19.992°.