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I am still a first year student; I was asked in the exam to identify the meso comound out of some choices. The answer key said that the compound below is meso. But I see no plane of symmetry here. Am I wrong or the question? I hope someone clarifies please. Sorry if the question was super silly.

supposed meso compund

user208973
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    Not all meso compounds have a plane of symmetry. – Ivan Neretin Oct 15 '20 at 09:12
  • @Ivan Neretin Don't all achiral molecules have a plane of symmetry? Sometimes the plane is not obvious, but after some changes in conformations it is revealed. But i think this isn't the case here, right? – user208973 Oct 15 '20 at 09:15
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    No. Indeed, many do, but many don't. That's not how chirality is defined. – Ivan Neretin Oct 15 '20 at 09:18
  • So how is it defined? – user208973 Oct 15 '20 at 09:21
  • @user716591 the Wikipedia entry is as good a place to start as any https://en.wikipedia.org/wiki/Meso_compound – Waylander Oct 15 '20 at 09:24
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    This molecule has a center of symmetry. – Maurice Oct 15 '20 at 09:31
  • You might want to look at this: https://chemistry.stackexchange.com/questions/48995/is-2r-3s-butane-2-3-diol-chiral/87415#87415 – user55119 Oct 15 '20 at 14:59
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    Place your hands palms down with thumb-to-thumb and index fingers touching. Plane of symmetry! Turn over one hand, place thumbs to index fingers. Center of symmetry! You have brought a "racemate of hands" together to form meso "compounds". – user55119 Oct 18 '20 at 15:47

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As the comments imply, having a center of symmetry makes a molecule achiral. This is because, geometrically, inverting through the center equals a mirror reflection plus a 180° rotation. If you start with an atom at point $(x,y,z)$ and you reflect it through the $xy$ plane, the atom is now at $(x,y,-z)$. Now rotate 180° around the $z$ axis and you're at $(-x,-y,-z)$ just like inverting through the center.

Your molecule has no symmetry with respect to just a mirror reflection or just a 180° rotation. (It might look like you could rotate 180° within the plane of the paper, but the stereochemistry is different.) But it does have a symmetry with respect to the combination of the two, which is that center of inversion, so you can match the mirror image to the original by allowing the rotation. That makes the molecule meso.

Oscar Lanzi
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