Which compound is optically inactive out of following

(I) n-propyl chloride

(II) secondary butyl chloride

(III) tert butyl chloride, (IV) isopropyl chloride.

The correct option is Only I, III, IV.

Understanding Optical Activity and Chirality:

A organic molecule is optically active if it contains at least one chiral carbon atom (a stereocenter) and lacks a plane or center of symmetry. A chiral carbon is defined as a tetrahedral carbon atom bonded to four completely different groups or atoms.

If a molecule does not have any chiral carbon atom (or is superimposable on its mirror image), it is achiral and therefore optically inactive.

Analyzing Each Compound:

(I) n-propyl chloride:

Chemical structure: CH₃-CH₂-CH₂-Cl

- C-1 is attached to 2 hydrogen atoms, 1 chlorine atom, and 1 ethyl group.
- C-2 is attached to 2 hydrogen atoms, 1 methyl group, and 1 chloromethyl group.
- C-3 is attached to 3 hydrogen atoms.

None of the carbon atoms are attached to four different groups. Therefore, n-propyl chloride has no chiral center and is optically inactive.

(II) secondary butyl chloride (sec-butyl chloride):

Chemical structure: CH₃-CH(Cl)-CH₂-CH₃

- C-2 is attached to four distinct groups: a hydrogen atom (-H), a chlorine atom (-Cl), a methyl group (-CH₃), and an ethyl group (-CH₂CH₃).

Because C-2 is a chiral carbon, secondary butyl chloride is chiral and is optically active.

(III) tert-butyl chloride:

Chemical structure: (CH₃)₃C-Cl

- The central carbon atom is bonded to three identical methyl groups (-CH₃) and one chlorine atom (-Cl).

Since three of the four groups are identical, there is no chiral center. Thus, tert-butyl chloride is optically inactive.

(IV) isopropyl chloride:

Chemical structure: (CH₃)₂CH-Cl

- The central carbon atom is attached to two identical methyl groups (-CH₃), one hydrogen atom (-H), and one chlorine atom (-Cl).

Since it has two identical groups attached to the central carbon, it lacks a chiral carbon and is optically inactive.

Conclusion:

Compounds I (n-propyl chloride), III (tert-butyl chloride), and IV (isopropyl chloride) do not possess any chiral carbon atoms and are optically inactive.

Hence, the optically inactive compounds are Only I, III, IV.