Cholesterol, when isolated from natural sources, is obtained as a single enantiomer. The observed rotation `alpha` of a 0.3 g sample of cholesterol in 5mL of chloroform solution contained in a 10 cm polarimeter tube is `-0.78^(@)`. Calculate the specific rotation of cholesterol. A sample of synthetic cholesterol was prepared consisting entirely of (+)-cholesterol. This synthetic (+)-cholesterol was mixed with some natural (-)-cholesterol. The mixture had a specific rotation `[alpha]_(D)^(20) " of " -13^(@).` What fraction of the mixture was (+)-cholesterol ?

Explanation

To solve the problem step by step, we will first calculate the specific rotation of cholesterol and then determine the fraction of the mixture that was (+)-cholesterol.

### Step 1: Calculate the Specific Rotation of Cholesterol

The formula for specific rotation \([α]\) is given by:

\[
[α] = \frac{α}{l \cdot c}
...