The specific rotation of a pure enantiomer is `+10^(@)`. The observed rotation, if it is isolated from a reaction with `30%` recemisation and `70%` inversion is

Options

A. `+10^(@)`
B. `-10^(@)`
C. `3^(@)`
D. `-7^(@)`

Answer

To solve the problem, we need to calculate the observed rotation of a mixture that has undergone some degree of racemization and inversion. Here’s a step-by-step solution:

### Step 1: Understand the given data
- Specific rotation of the pure enantiomer, \([α]_{pure} = +10^\circ\)
- Percentage of racemization = 30%
- Percentage of inversion = 70%

### Step 2: Determine the effective percentage of the enantiomer
Since there is 30% racemization, this means that 30% of the original enantiomer has been converted into its opposite enantiomer. Therefore, the effective percentage of the original enantiomer remaining is:
\[ \text{Effective enantiomer} = 100\% - 30\% = 70\% \]

### Step 3: Account for inversion
Inversion means that the rotation due to the original enantiomer is now negative. Since 70% of the mixture is inverted, we consider this in our calculation.

### Step 4: Calculate the observed rotation
Using the formula for observed rotation:
\[ \text{Observed rotation} = \left( \text{Percentage of enantiomer} \times [α]_{pure} \right) / 100 \]
Here, since we have 70% inversion, we will apply the negative sign:
\[ \text{Observed rotation} = -\left( 70 \times 10 \right) / 100 \]
\[ \text{Observed rotation} = -7^\circ \]

### Final Answer
The observed rotation is \(-7^\circ\).

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