# Identifying a meso compound

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.

• Not all meso compounds have a plane of symmetry. Commented Oct 15, 2020 at 9:12
• @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? Commented Oct 15, 2020 at 9:15
• No. Indeed, many do, but many don't. That's not how chirality is defined. Commented Oct 15, 2020 at 9:18
• This molecule has a center of symmetry. Commented Oct 15, 2020 at 9:31
• 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". Commented Oct 18, 2020 at 15:47

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.