An aqueous solution containing `10 gm` of optically pure fructose was diluted to `500 ml` with water and placed in a polarimeter tube `20 cm` long. The measured roatation was `-5.0^(@)`. To this solution, `500 ml` of a solution containing `10 gm` of racemic fructose is added. What will be the change in specific rotation?

Explanation

To solve the problem, we need to determine the change in specific rotation after adding racemic fructose to an optically pure fructose solution. Here’s a step-by-step breakdown of the solution:

### Step 1: Calculate the Specific Rotation of the Initial Solution
1. **Given Data**:
- Mass of optically pure fructose = 10 g
- Volume of solution = 500 ml
- Length of polarimeter tube = 20 cm = 2 dm
- Observed rotation (α observed) = -5.0°
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