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Michael C Grasso

Are molecules chiral if a rotation leads back to the same compound?

Ashish Virmani  Follow

The property that you are describing for D-idaric acid is called C2 symmetry. This means that when you rotate a molecule (or any object) by 180 degrees, it appears identically to the original orientation. In D-idaric acid, the C2 symmetry axis is halfway along the bond between C3 and C4.

Having a C2 symmetry axis doesn't tell us if the compound is chiral or not. Achiral compounds have an (internal) plane of symmetry or a point of symmetry. D-Idaric acid does not meet either of these requirements and is a chiral molecule.

Galactaric acid does not have a C2 symmetry axis but does have a plane of symmetry. Galactaric acid is achiral. Since galactaric acid has stereocenters but is not chiral, we describe it as meso.

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Edobhiye Sunday  Follow
@user4779 Sorry, that wasnt correct. Galactaric acid is not C2 symmetric.More
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Forex  Follow
Ill add a couple of examples of the chemical utility of C2 compounds when I get a chance later.More
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Douglas Porter  Follow
Just the answer Im looking for thank you. When you mention both D-Idaric acid and Galactaric acid having C2 symmetry, I notice Galactaric acid isnt the same when rotated 180 degrees?More
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Anussukee Wijegunarathna  Follow

You can have "symmetric" chiral molecules like you describe.

This is a subtle point and your particular choice isn't chiral.

In typical organic chemistry, instructors mention about mirror images, but leave some of the subtle details to later courses.

There are many types of chiral molecules and some of them look quite symmetric. Consider a pinwheel or propeller. You can rotate along the axis of the propeller and it will be symmetric, but there's a tilt/twist to the blades:

enter image description here

So these two images are mirror, but there's a chiral axis and the direction of rotation is reversed. They are enantiomers. This case has three-way symmetry, but it's possible to have a "two leaf" pinwheel that's still chiral. Proper rotations don't make mirror images.

Your case, D-idaric acid, is C2 symmetric.

enter image description here

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