Question

How many optical isomers are possible for lactic acid:

• A. 4
• B. 0
• C. 6
• D. 2

Hint:

Optical isomers exist when a molecule has at least one chiral center. Use \( 2^n \) to determine the number of isomers, where \( n \) is the number of chiral centers.

Answer 1

The Correct Option is D

Step 1: Understanding optical isomerism. Optical isomerism arises when a compound has a chiral center (an atom, usually carbon, attached to four different groups). Lactic acid (\( \text{CH}_3\text{CH}(\text{OH})\text{COOH} \)) contains one chiral carbon atom, making it capable of existing as two enantiomers (non-superimposable mirror images). 

Step 2: Calculation of optical isomers. The number of optical isomers for a compound is given by \( 2^n \), where \( n \) is the number of chiral centers. For lactic acid, \( n = 1 \): \[ \text{Number of optical isomers} = 2^1 = 2 \] 

Step 3: Why other options are incorrect. - (A) 4: This would require two chiral centers. 
- (B) 0: Incorrect, as lactic acid has a chiral center. 
- (C) 6: This is not possible with one chiral center.

Answer 2

The question asks how many optical isomers are possible for lactic acid. Let's work out the number of stereocenters in the molecule and check it against each option.

1. 4: Four optical isomers would require the molecule to have two separate chiral centers, since the count of optical isomers follows \( 2^n \) for \( n \) chiral centers. Lactic acid does not have two such centers, so this option overstates the number.
2. 0: Zero optical isomers would mean the molecule has no chiral center at all. Lactic acid's structure, \( \text{CH}_3\text{CH}(\text{OH})\text{COOH} \), has a carbon bonded to four different groups, methyl, hydroxyl, hydrogen, and carboxyl, so it is chiral, ruling this option out.
3. 6: Six is not a value the \( 2^n \) formula produces for any whole number of chiral centers, so it does not correspond to any realistic count for this molecule.
4. 2: The central carbon of lactic acid is attached to four different substituents, methyl, hydroxyl, hydrogen, and the carboxyl group, making it a single chiral center. A molecule with exactly one chiral center has \( 2^1 = 2 \) optical isomers, its two non-superimposable mirror images, commonly labeled D(+)-lactic acid and L(-)-lactic acid.

Since lactic acid has exactly one chiral carbon, the number of optical isomers it can form works out to 2 by the standard \( 2^n \) rule.

So the correct answer is 2.