How many optically active isomers are possibl | vedclass

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(A) The structure of $2,3-$dibromobutane-$1,4-$dioic acid is $HOOC-CH(Br)-CH(Br)-COOH$. This molecule contains two chiral centers at $C2$ and $C3$. Si

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$2$

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(A) The structure of $2,3-$dibromobutane-$1,4-$dioic acid is $HOOC-CH(Br)-CH(Br)-COOH$. This molecule contains two chiral centers at $C2$ and $C3$. Since the molecule is symmetric (the two ends are identical),we can determine the number of stereoisomers using the formula for symmetric molecules. For a symmetric molecule with an even number of chiral centers $(n=2)$,the number of optically active isomers (enantiomers) is $2^{(n-1)} = 2^{(2-1)} = 2^1 = 2$. The two optically active isomers are the $(2R, 3R)$ and $(2S, 3S)$ forms. The other isomer is the meso form $(2R, 3S)$,which is optically inactive due to an internal plane of symmetry. Therefore,there are $2$ optically active isomers.

How many optically active isomers are possible for $2,3-$dibromobutane-$1,4-$dioic acid?

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