A sample of Xand Y enantiomers haa a % opl. punihy of uhat is the nlAI % Ma jor enantiome 50. op the

Chemistry
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Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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**Sample Problem on Enantiomeric Purity**

*Problem Statement:*

A sample of X and Y enantiomers has an optical purity of 50%. What is the mass percentage of the major enantiomer? 

*Instructions:*

Show all calculations.

----

**Explanation:**

When dealing with optical purity, it is essential to understand the relationship between optical purity and the excess of one enantiomer over the other. Optical purity is a measure of how much one enantiomer is present in excess of the racemic mixture (an equal mix of both enantiomers). 

1. **Optical Purity Formula:**
   \[
   \text{Optical Purity} = \frac{\text{Observed Rotation}}{\text{Rotation of Pure Enantiomer}} \times 100\%
   \]

2. **Calculation of Major Enantiomer:**
   - Let the percentage of the major enantiomer be \( x \).
   - Then, the percentage of the minor enantiomer is \( 100 - x \).
   - The optical purity equation gives us:
   \[
   x - (100 - x) = \text{Optical Purity}
   \]
   \[
   2x - 100 = 50
   \]
   \[
   2x = 150
   \]
   \[
   x = 75\%
   \]

So, the mass percentage of the major enantiomer is 75%.
Transcribed Image Text:**Sample Problem on Enantiomeric Purity** *Problem Statement:* A sample of X and Y enantiomers has an optical purity of 50%. What is the mass percentage of the major enantiomer? *Instructions:* Show all calculations. ---- **Explanation:** When dealing with optical purity, it is essential to understand the relationship between optical purity and the excess of one enantiomer over the other. Optical purity is a measure of how much one enantiomer is present in excess of the racemic mixture (an equal mix of both enantiomers). 1. **Optical Purity Formula:** \[ \text{Optical Purity} = \frac{\text{Observed Rotation}}{\text{Rotation of Pure Enantiomer}} \times 100\% \] 2. **Calculation of Major Enantiomer:** - Let the percentage of the major enantiomer be \( x \). - Then, the percentage of the minor enantiomer is \( 100 - x \). - The optical purity equation gives us: \[ x - (100 - x) = \text{Optical Purity} \] \[ 2x - 100 = 50 \] \[ 2x = 150 \] \[ x = 75\% \] So, the mass percentage of the major enantiomer is 75%.
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