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Question

Which of the following are pairs of enantiomers?


A
D-Lactic acid and (+)-Lactic acid
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B
D-Lactic acid and (-)-Lactic acid
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C
2R-2-bromobutane and 2S-2-bromobutane
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D
2R,3S-2,3-dihydroxybutanedioic acid and 2S,3R-2,3dihydroxybutanedioic acid
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Solution

The correct options are
B D-Lactic acid and (-)-Lactic acid
C 2R-2-bromobutane and 2S-2-bromobutane

This is how Lactic acid looks like:

Do note that in the above 2-d form, we have discarded the stereochemical information.

L-Lactic acid or (-)-Lactic acid looks like:

D-Lactic acid or (+)-Lactic acid looks like:



At the chiral center, there is an inversion when we compare D-Lactic acid and L-Lactic acid isn’t it? Also, in either of these compounds, there are no elements of symmetry. So clearly, both compounds are chiral. At the chiral center, since there is an inversion, we can conclude that both are non-superimposable mirror images of each other. I want you to try superimposing each compound and its mirror image.

Can you try and deduce the structures of 2R-2-bromobutane and 2S-2-bromobutane?

Like in the case of D-Lactic acid and L-Lactic, here also we have an inversion at the 2nd carbon (where Br atom is a substituent). So definitely, these are a pair of enantiomers.
Let us first try and draw the 2R,3S configuration of Tartaric acid:

Now try and draw the 2S,3R configuration of Tartaric acid:

Now take the 2R,3S configuration of Tartaric acid and rotate it as shown:

Clearly, both are identical. In fact, they are both meso tartaric acid! It is pretty obvious if you try and draw a plane that bisects the C2 – C3 bond (orthogonally) into two equal, symmetrical halves!
Hence, 2R,3S-2,3-dihydroxybutanedioic acid and 2S,3R-2,3dihydroxybutanedioic acid are one and the same. By definition, they both are “the same” meso tartaric acid. It will not show optical activity. Hence 2R,3S-2,3-dihydroxybutanedioic acid and 2S,3R-2,3dihydroxybutanedioic are not enantiomers.


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