question_answer

Trans-3, 6-dimethyloct-4-ene (A) exists in two diastereomers (I) and (II) Which of the following statements is CORRECT?

A) Total number of stereoisomer for (A) is 6.

B)  Both I and II are optically active.

C) If the stereochemistry about the double bond in (A) is cis, the total number of stereoisomers possible for (A) is 3.

D) If the stereochemistry about the double bond in (A) is trans, (II) is optically inactive due to presence of plane of symmetry.

Correct Answer: C

Solution :

[c] Two asymmetric C atoms with the same terminal group (n = number of asymmetric C atom and is even) Number of O.A \[={{2}^{n-1}}=2\] Number of meso form \[={{2}^{(n-2)/\,2}}=1\] Total optical isomers = 3                           One double bond = 2 diasteromers                  Total stereoisomers \[=3+2=5\] If compound [a] is cis, we get two diastereomers. (III) (IV). (Ill) is meso (O.I.A) due to plane of symmetry is O.A. (two enantiomers). Total stereoisomers when [a] is cis = 3             (II) is O.I.A (meso) due to centre of symmetry.             (1) 5     (2). I is optically active (4) Centre of symmetry