A molecule is chiral when it is different from its mirror image, and achiral if it is identical to its mirror image. To check if the mirror image is identical to the original object, we have to check if the two are super-imposable. Sometimes no rotation is necessary to show the molecule and mirror image are idential, and sometimes we need to rotate the mirror image, for example by 180°. This is so confusing. Can someone explain exactly what is to be done in simple words?
Answer
Whether you need to rotate a molecule to show that it superimposes with its mirror image depends on how you position your mirror.
Take human bodies, for example. They have approximate mirror symmetry (bilateral symmetry), with the left side looking similar to the right side. If you stand in front of a mirror with one of your shoulders touching it, an observer will be able to see the symmetry without rotating the mirror image in their mind. If you face the mirror, you have to imagine turning the mirror image by 180 degrees along the long axis (head to toe, like a pirouette). If you are standing on a mirror placed on the floor (careful not to break it...), you have to imagine turning the mirror image 180 degrees around a front-back axis (like a cart wheel) to see that you and mirrored you are super-imposable.
If the plane of the mirror is not aligned with two of your body axes (top-bottom, front-back, right-left), the necessary rotations will be different from 180 degrees.
This reminds me of the question why a mirror switches left and right, and not top and bottom (see this article). Once you understand why this is a silly question, you can return to checking molecules for chirality by placing them in front of a mirror.
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