Question

The number of stereoisomers possible for the following compound is ....... 

 

Hint:

Stereoisomers occur when substituents can be arranged differently in space around chiral centers, leading to distinct isomers.

Answer 1

Correct Answer: 3

We have the molecule \( \mathrm{Ph-CH(OH)-CH(OH)-Ph} \) (1,2-diphenyl-1,2-ethanediol, “hydrobenzoin”). There are two stereogenic carbon atoms (the two \(\mathrm{CH(OH)}\) centers), so the maximum possible number of stereoisomers is
\[2^n = 2^2 = 4.\]

Label the two stereocenters as $C(_1)$ and $C(_2)$. The four configurational combinations are:
\[(R,R),\quad (S,S),\quad (R,S),\quad (S,R).\]

However, because the two end groups are identical phenyl rings, the molecule with opposite configurations at the two centers (the \((R,S)\) and \((S,R)\) forms) is identical to its mirror image — it has an internal mirror plane and is therefore meso (achiral). Thus \((R,S)\) and \((S,R)\) represent the same single meso isomer, not two different stereoisomers.

The remaining two configurations, \((R,R)\) and \((S,S)\), are nonidentical and are a pair of enantiomers.

So the actual distinct stereoisomers are:

\[\{\text{meso }(R,S)\},\ \{(R,R),\ (S,S)\ \text{(enantiomeric pair)}\}\]
Counting these gives
\[1\ (\text{meso}) + 2\ (\text{enantiomers}) = 3\ \text{stereoisomers}.\]

\[\boxed{3}\]