11. How many chiral carbons does the following structure have when n is even?
a. all its carbons are chiral
b. n
c. n+1
d. n+2

The correct answer is option C: the molecule has $n+1$ chiral carbons when $n$ is even.

Introduction

In stereochemistry, exam questions often ask “how many chiral carbons does the following structure have when $n$ is even?” using a Fischer projection of a polymer-like chain with repeating –CHOH– units between two terminal –COOH groups. Understanding how to count chiral centers in such symmetric chains is essential for CSIR NET, GATE and other competitive exams.

Understanding Chiral Carbons in Fischer Projection

Structure Description

The structure shown is a vertical Fischer projection with a –COOH group at the top, a –COOH group at the bottom, and in between a linear chain of carbons each carrying –H and –OH on the horizontal bonds. The middle part is represented as (H–C–OH)_n(H–C–OH)_n, meaning there are n identical –CHOH– repeating units between the two terminal –CHOH– carbons next to the –COOH groups.

Chirality Analysis

Each internal –CHOH– carbon is tetrahedral and attached to four different groups (H, OH, upper carbon segment, lower carbon segment), so it is potentially chiral.

However, when n is even, the whole chain acquires an internal plane of symmetry passing horizontally through the center, which can make one central carbon achiral (a meso situation).

Step-by-Step Counting

1. Count total potentially chiral carbons in the chain.
   There are n repeating –CHOH– units plus 2 terminal –CHOH– carbons directly attached to each –COOH.
   Total tetrahedral –CHOH– carbons = n+2.
2. Analyze symmetry when n is even.
   An even number of repeating units means the chain can be divided into two equal halves by a plane passing through one of the carbons.
   The carbon exactly at the center then has two identical substituent paths above and below, so it no longer has four different groups and becomes achiral.
3. Subtract the achiral (symmetric) carbon.
   Total stereocenters = (n+2)−1 = n+1.

Detailed Option Analysis

Option A: “all its carbons are chiral”

NOT CORRECT. Not all carbons in the structure are chiral because the two terminal carboxyl carbons (COOH) are trigonal planar and attached to only three substituents, so they cannot be chiral centers. Additionally, due to the internal plane of symmetry when n is even, one central –CHOH– carbon becomes achiral.

Option B: “n”

TOO LOW. This option suggests that only the repeating –CHOH– units contribute to chirality, ignoring the two extra –CHOH– carbons adjacent to the terminal –COOH groups. Since these terminal –CHOH– carbons are also chiral, the total exceeds n.

Option C: “n+1” (CORRECT)

There are n+2 tetrahedral –CHOH– carbons in total, but one of them becomes achiral due to the internal plane of symmetry when n is even. Thus, the correct number of chiral carbons is n+1.

Option D: “n+2”

OVERESTIMATES. This option corresponds to simply counting every –CHOH– carbon as chiral and ignoring symmetry. With an even n and identical –COOH termini, the central carbon loses chirality, so n+2 is one too many.