The first order reaction:
Sucrose `rarr` Glucose + Fructose takes place at `308 K` in `0.5 N HCl`. At time zero the initial total rotation of the mixture is `32.4^(@)`. After `10 min`, the total rotation is `28.8^(@)`. If the rotation of sucrose per mole is `85^(@)`, that of glucose is `7.4^(@)`, and of fructose is `-86.04^(@)`, calculate the half life of the reaction.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Determine the Initial Concentration of Sucrose
We are given the initial total rotation of the mixture as \(32.4^\circ\) and the specific rotation of sucrose as \(85^\circ\). We can calculate the initial concentration of sucrose (\(A\)) using the formula:

\[ A = \frac{\text{Initial Rotation}}{\text{Specific Rotation of Sucrose}} = \frac{32.4}{85} = 0.38 \, \text{moles} \]
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