JEE Chemistry 2024 Question with Solution

Given: 2-chlorobutane reacts with $\text{Cl}_2/h\nu$ and dichloro products of formula $\text{C}_4\text{H}_8\text{Cl}_2$ are to be considered for optical activity.

Find: The total number of optically active isomers formed.

The solution analyzes the dichloro products obtained from chlorination of 2-chlorobutane:

$$\text{CH}_3-\text{CH}(\text{Cl})-\text{CH}_2-\text{CH}_3$$

Possible relevant structural isomers listed are 1,2-dichlorobutane, 1,3-dichlorobutane, 2,2-dichlorobutane, and 2,3-dichlorobutane.

For 1,2-dichlorobutane:

$$\text{CH}_2\text{Cl}-\text{CH}(\text{Cl})-\text{CH}_2-\text{CH}_3$$

There is one chiral center, so it gives 2 enantiomers.

For 1,3-dichlorobutane:

$$\text{CH}_2\text{Cl}-\text{CH}_2-\text{CH}(\text{Cl})-\text{CH}_3$$

There is one chiral center, so it gives 2 enantiomers.

For 2,2-dichlorobutane:

$$\text{CH}_3-\text{C}(\text{Cl})_2-\text{CH}_2-\text{CH}_3$$

This is achiral, so it gives 0 optically active isomers.

For 2,3-dichlorobutane:

$$\text{CH}_3-\text{CH}(\text{Cl})-\text{CH}(\text{Cl})-\text{CH}_3$$

According to the solution, this contributes 2 optically active enantiomers, while the meso form is optically inactive.

Hence, total optically active isomers:

$$2 + 2 + 2 = 6$$

Therefore, the total number of optically active isomers is $6$. The correct option is C.

Note: The question text shows $\text{C}_4\text{H}_7\text{Cl}_3$, but the solution consistently works with $\text{C}_4\text{H}_8\text{Cl}_2$ dichloro products. The answer has been derived from the solution, which is treated as authoritative.

Given: Chlorination of 2-chlorobutane produces positional isomers, and we must count only the optically active ones.

Find: Total number of optically active stereoisomers.

The solution uses a casewise check:

1. 1,2-dichlorobutane has one chiral carbon.

$$\Rightarrow 2 \text{ optically active isomers}$$

2. 1,3-dichlorobutane has one chiral carbon.

$$\Rightarrow 2 \text{ optically active isomers}$$

3. 2,2-dichlorobutane has no chiral center.

$$\Rightarrow 0 \text{ optically active isomers}$$

4. 2,3-dichlorobutane has two stereocenters. From the solution, one meso form is inactive and one enantiomeric pair is active.

$$\Rightarrow 2 \text{ optically active isomers}$$

Adding the active isomers:

$$6 = 2 + 2 + 0 + 2$$

Thus, the total number of optically active isomers is $6$.