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I have a couple of basic questions on stereochemistry that confused me. Please help me understand them.

1) Why does a molecule become achiral if it has a plane of symmetry even though it has steriocentes?

2) When working with Fischer Projections, they say you can rotate a Fischer projection 180 degrees, but not by 90 degrees. I don't understand why.

Moreover, can you please suggest me a good resource wherein I can learn stereochemistry (not to very advanced level)?

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1) Why does a molecule become achiral if it has a plane of symmetry even though it has stereocenters?

If a plane of symmetry bisects a molecule such that one half of the bisected molecule is the mirror image of the other half of the bisected molecule, then the entire molecule must be superimposable on its mirror image, it must be achiral. Said differently, if mirror symmetry exists within a molecule, then the mirror image of the entire molecule will be superimposable upon the original drawing of the entire molecule.

Here's an example of a molecule ($\ce{A}$) with 2 chiral groups ($\ce{G_{R}}$ and ($\ce{G_{S}}$). There is a plane of symmetry that bisects $\ce{A}$, it is perpendicular to the plane of the screen and contains the central carbon atom and the 2 methyl groups. Now, when we draw the mirror image of $\ce{A}$ (let's call it ($\ce{\bar{A}}$), we find that it is superimposable upon the original drawing of $\ce{A}$ by a simple 180-degree rotation. Even though $\ce{A}$ contains 2 chiral substituents, the molecule as a whole is achiral.

Illustration depicting a molecule, A, as superimposable on its mirror image

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If you rotate the substituents on a Fischer projection by 90 degrees you change the stereochemistry of each substituent.

The up/down positions on a Fischer projection indicate substituents projected away from you. The left and right positions indicate substituents projected toward you.

Here's a rotated tetrahedral molecule to help you see what I mean by the substituents are projected away/toward you.

enter image description here

We can represent toward using a solid wedge and away using a hatched wedge:

enter image description here

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