The number of different stereoisomers that exist for the compound shown below is:

Question

Quizplus · Accepted Answer

11ecba2d_128e_4103_a3bf_238a65aab51f_MD0008_00 Stereoisomers are compounds that contain the same molecular formula and same connectivity but differ in spatial arrangement. The number of stereoisomers for a molecule is related to the number of stereocenters in the compound. The maximum number of stereoisomers possible for a compound is determined by the expression 2ⁿ, where n is the number of stereocenters. The actual number of stereoisomers for a particular compound could be less than 2ⁿ if two of the stereoisomers have an internal mirror plane of symmetry (a meso compound), such that the symmetry causes the stereoisomers to be conformations of the same compound. This compound has two stereocenters (on carbons 1 and 3) because each carbon has four different substituents. Using the expression 2ⁿ, the maximum number of stereoisomers is 2² = 4. The (1S, 3S) and (1R, 3R) stereoisomers are nonsuperimposable mirror images, as are the (1S, 3R) and (1R, 3S) stereoisomers, indicating that each of these compound pairs are enantiomers. None of the four stereoisomers has an internal plane of symmetry. Therefore, the compound in this question has four different stereoisomers. (Choice A) The number of stereocenters in this compound is two, but this value does not provide the number of different stereoisomers. (Choice B) The maximum possible number of stereoisomers is four, but the actual number of stereoisomers could be three only if one of the stereocenter configuration combinations for this compound were a meso compound (with an internal plane of symmetry). In such a case, two of the possible four stereochemical configurations would be the same compound, which would decrease the number of different stereoisomers by one. (Choice D) There would be eight maximum possible stereoisomers if this compound had three stereocenters (2³ = 8). However, the central carbon is not chiral, so there are only two stereocenters. Educational objective: The maximum number of stereoisomers possible for a compound is determined by the expression 2ⁿ, where n is the number of stereocenters. However, the actual number of stereoisomers for a particular compound could be less than 2ⁿ if two of the possible stereochemical configurations have an internal mirror plane of symmetry (meso compound), making them conformations of the same compound.

The Number of Different Stereoisomers That Exist for the Compound