2-chlorobutane +Cl2→C4H8Cl2 (isomers)Total number of optically active isomers shown by C4H8Cl2, obtained in the above reaction is _______

The total number of optically active isomers of C4H8Cl2 obtained in the above reaction is 3.

Here's the step-by-step explanation:

1. The given compound is 2-chlorobutane (C4H9Cl). When it reacts with Cl2, one hydrogen atom is replaced by a Cl atom, resulting in the formation of C4H8Cl2.

2. The possible isomers of C4H8Cl2 are 1,1-dichlorobutane, 1,2-dichlorobutane, 1,3-dichlorobutane, 1,4-dichlorobutane, and 2,2-dichlorobutane.

3. Out of these, 1,2-dichlorobutane and 1,3-dichlorobutane are chiral and hence optically active. Each of these has two enantiomers (non-superimposable mirror images), so that's 4 optically active isomers.

4. However, the reaction of 2-chlorobutane with Cl2 can't produce 1,3-dichlorobutane, because the Cl2 molecule can't reach the 3rd carbon atom to replace a hydrogen atom there.

5. So, the reaction can only produce the two enantiomers of 1,2-dichlorobutane and one enantiomer of 1,1-dichlorobutane, for a total of 3 optically active isomers.