(1) 2n + 2 stereoisomers

(2) n⁻² stereoisomers

(3) 2^{n − 2} stereoisomers

(4) 2ⁿ stereoisomers

A carbohydrate molecule with n chiral centers can have a maximum of 2ⁿ stereoisomers. This fundamental principle from stereochemistry applies generally, including to carbohydrates like glucose (n=4, 16 stereoisomers).

Question Breakdown

The query tests the standard formula for stereoisomers in molecules with chiral centers, specifically for carbohydrates, which are aldoses or ketoses with multiple chiral carbons.

Option Analysis

• (1) 2ⁿ + 2: Incorrect; adds an arbitrary +2 with no stereochemical basis—real examples like glyceraldehyde (n=1) yield exactly 2, not 4.

• (2) n−2: Incorrect; yields negative or nonsensical values (e.g., n=1 gives -1), ignoring exponential stereoisomer growth.

• (3) 2ⁿ − 2: Incorrect; subtracts 2 arbitrarily, undercounting maximums (e.g., glucose n=4 should be 16, not 14). Applies only if meso forms exist, but question says “can have” (maximum).

• (4) 2ⁿ: Correct; each chiral center doubles possibilities (R/S configurations), so maximum stereoisomers = 2ⁿ. Valid for carbohydrates without meso symmetry.

A carbohydrate molecule n chiral centre stereoisomers count reaches a maximum of 2ⁿ, essential knowledge for GATE Life Sciences aspirants studying biochemistry stereochemistry. Each chiral carbon (with four different substituents) creates two configuration options, exponentially multiplying total stereoisomers in sugars like glucose or fructose.

Stereoisomer Basics

Stereoisomers are molecules with identical connectivity but different spatial arrangements around chiral centers. For carbohydrates (aldoses/ketoses), the formula 2ⁿ holds without meso compounds unless specified.

• Applies to open-chain forms (e.g., D-glucose: 4 chiral centers → 16 stereoisomers).

• Cyclic forms add anomeric (α/β) variants but question focuses on chiral centers.

Formula Derivation

With n chiral carbons, each independently R or S: total = 2×2×…×2 (n times) = 2ⁿ.

Exam Strategy

In MCQs, select 2ⁿ (“can have” implies maximum). Exceptions like meso tartaric acid (2ⁿ-2=2 instead of 4) are rare in general carbohydrate questions. Master for GATE: D/L, epimers, enantiomers follow this rule.