Q.27 The achiral molecules among the following (I, II, III and IV) are
(A) I and III (B) II and IV (C) III and IV (D) I and IV
The achiral molecules in this question are I and IV, because each possesses an internal plane of symmetry and is therefore meso (I) or overall symmetric (IV) and optically inactive. Molecules II and III are chiral as they lack such a symmetry element and exist as enantiomeric pairs. Thus, the correct option is (D) I and IV.
Introduction: achiral molecules among I, II, III and IV
In stereochemistry, identifying achiral molecules among closely related structures requires checking for internal symmetry elements such as a plane or center of symmetry. The problem “achiral molecules among I, II, III and IV” features dihydroxy dicarboxylic acids, a substituted epoxide and a substituted cyclohexane, making it a compact test of meso compounds and conformational symmetry.
Concept recap: chirality, achirality and meso compounds
-
A molecule is chiral if it is not superimposable on its mirror image, usually because at least one tetrahedral atom is attached to four different groups.
-
Achiral molecules either lack stereogenic centers or possess internal symmetry (plane, center, or improper axis) that makes the molecule superimposable on its mirror image.
-
A meso compound is an achiral molecule that nevertheless contains two or more stereocenters but has an internal plane of symmetry that renders it optically inactive.
These principles are the basis for evaluating each of the four structures.
Option I: why structure I is achiral (meso)
Structure I is a HOOC–CH(OH)–CH(OH)–COOH system in which both chiral carbons bear identical substituents (each attached to H, OH, COOH and the adjacent CH(OH) group), and the stereochemistry is such that one center is R and the other is S (opposite configuration).
-
When drawn in the usual zig‑zag form, the molecule displays an internal mirror plane passing vertically through the central C–C bond, reflecting one half into the other while interchanging R and S centers; this plane makes the molecule superimposable on its mirror image, so it is achiral.
-
Because it has two stereocenters but is optically inactive due to that internal plane of symmetry, structure I is a meso compound and therefore achiral.
Hence, molecule I belongs to the set of achiral molecules required in the question.
Option II: why structure II is chiral
Structure II is also a dihydroxy dicarboxylic acid, but the relative stereochemistry of the two chiral centers is different from I (both wedges or both dashes in the drawing), corresponding to a (R,R) or (S,S) pair rather than an R,S pair.
-
This configuration means there is no internal mirror plane: reflecting one chiral center into the other does not map the substituents correctly, so the two halves are not mirror images within the same molecule.
-
As a result, the molecule exists as a pair of non‑superimposable mirror images (enantiomers); each enantiomer is chiral and would rotate plane‑polarized light in opposite directions, so structure II is chiral, not achiral.
Therefore, structure II is not among the achiral molecules.
Option III: substituted epoxide and its chirality
Structure III is a three‑membered epoxide ring bearing a phenyl substituent on one carbon and a methoxycarbonyl (CO₂Me) substituent on the adjacent carbon, with the two substituents shown on opposite faces of the ring (one wedge, one dash).
-
Each substituted epoxide carbon is attached to four different groups when the ring is considered, so at least one stereocenter is present, and the relative cis/trans arrangement removes any internal mirror plane.
-
The molecule lacks any symmetry element that could relate the two faces of the epoxide or make the entire structure superimposable on its mirror image, so it forms a pair of enantiomers and is therefore chiral.
Hence, structure III is not achiral and should not be selected.
Option IV: cyclohexane with OH and tert‑butyl – achiral
Structure IV is a substituted cyclohexane ring bearing an OH group at one carbon (drawn axial up) and a tert‑butyl group at another carbon (drawn axial down), with the tert‑butyl appearing as a symmetric “T” because all three methyl groups are identical.
-
Even though the ring is substituted, neither substituted carbon is a true stereocenter: each ring carbon is attached to two identical ring paths (the two directions around the symmetric cyclohexane ring), and the tert‑butyl carbon is attached to three identical methyl groups, so no tetrahedral center in the molecule has four different substituents.
-
The overall molecule has a plane of symmetry passing through the OH‑bearing carbon and the center of the tert‑butyl group, dividing the ring into two equivalent halves; the presence of this symmetry and the absence of stereocenters make the molecule achiral.
Thus, structure IV is achiral and belongs with structure I as required.
Final answer and option analysis
Putting these analyses together:
-
I: meso dihydroxy dicarboxylic acid with an internal plane of symmetry → achiral.
-
II: dihydroxy dicarboxylic acid without internal symmetry (R,R / S,S) → chiral.
-
III: asymmetrically substituted epoxide lacking any symmetry plane → chiral.
-
IV: substituted cyclohexane with no stereocenters and a plane of symmetry → achiral.
Therefore, the achiral molecules among I, II, III and IV are I and IV, corresponding to option (D) I and IV.
