Lactic acid in which a methyl group, a hydroxyl group, a carboxylic acid group and a hydrogen atom are attached to a central carbon atom shows optical isomerism due to molecular geometry at the

central carbon atom.

The correct answer is option 3. central carbon atom.

Let us dive into the detailed explanation of why the central carbon atom \((C_2)\) in lactic acid is crucial for optical isomerism and how it relates to the molecule's chirality:

Chirality and Optical Isomerism:

Chiral Centers:

A chiral center in a molecule is a carbon atom that is bonded to four different groups. This asymmetric arrangement leads to the molecule having two non-superimposable mirror image forms called enantiomers. Enantiomers exhibit optical isomerism because they rotate plane-polarized light in opposite directions.

Structure of Lactic Acid (CH₃CHOHCOOH):

Lactic acid consists of a three-carbon backbone with a carboxylic acid group \((-COOH)\) attached to one end and a hydroxyl group \((-OH)\) attached to another carbon. The central carbon atom \((C_2)\) in lactic acid is bonded to four different groups:

Methyl group \((-CH_3)\)

Hydroxyl group \((-OH)\)

Carboxylic acid group \((-COOH)\)

Hydrogen atom \((-H)\)

Chirality at \(C_2\) in Lactic Acid:

The central carbon atom \((C_2)\) in lactic acid has four distinct substituents, satisfying the requirement for chirality:

It is tetrahedrally bonded to four different groups, resulting in a spatial arrangement that lacks a plane of symmetry. Due to this asymmetry, lactic acid exists as a pair of enantiomers that cannot be superimposed on each other.

Importance of \(C_2\) for Optical Isomerism:

The optical activity of lactic acid arises specifically from the chiral center at the central carbon atom \((C_2)\). The two enantiomers of lactic acid rotate plane-polarized light in opposite directions. This property is directly attributable to the different spatial arrangement of the substituents around the chiral center at \(C_2\).

Incorrect Options:

Option (1): The carbon atom of the methyl group \((-CH_3)\) does not have four different substituents and therefore cannot exhibit chirality.

Option (2): The carbon atom of the carboxylic acid group \((-COOH)\) also does not have four different substituents and is not chiral.

Option (4): The oxygen atom of the hydroxyl group \((-OH)\) is not the center of chirality; chirality is determined by the arrangement around the central carbon atom \((C_2)\).

Conclusion:

The correct answer to why lactic acid exhibits optical isomerism lies in the arrangement of substituents around the central carbon atom \((C_2)\). This carbon atom possesses four different groups, making it a chiral center. The presence of this chiral center allows lactic acid to exist as two non-superimposable mirror image forms (enantiomers), which is the basis for its optical activity. Understanding the concept of chirality and the role of specific carbon atoms in determining optical isomerism is fundamental in organic chemistry, especially in the study of stereochemistry and molecular properties.