How do you calculate how many stereoisomers a compound has?

Answer 1

Since for every atom that can exist in more than one configuration, you have R or S (#sp^3#), or E or Z (#sp^2#), you have two configurations for each of those atoms.

  • If you had #2# of those atoms, then you have #4# configuration combinations: (R,R), (R,S), (S,R), (S,S).
  • For #3# of those atoms, you have: (R,R,R), (R,R,S), (R,S,R), (S,R,R), (R,S,S), (S,R,S), (S,S,R), (S,S,S), which is #8#.

    Let us call an atom or group of atoms that can exist in more than one configuration a stereounit.

    That means for #n# stereounits, you have #2^n# stereoisomers possible.

    However, note that if there are any meso compounds (i.e. if the molecule has a chance of having a plane of symmetry dividing two identical halves that each contain asymmetric centers), then we must account for them because the symmetry reduces the number of different compounds.

    An example of a meso compound vs. a regular chiral compound...

    Thus, we revise the formula to give:

    #\mathbf("Total Stereoisomers" = 2^n - "meso structures")#

    where #n = "number of stereounits"#.

    Note that if we had used the traditional definition of a stereocenter instead of a stereounit (i.e. #sp^3# carbons only), this compound screws things up:

    ...it has two stereocenters, but three atoms which can be in more than one configuration.

    Hence, by the stereocenter definition, it has 4 structures, when in fact it DOESN'T.

    Two configurations for the left carbon, two configurations for the right carbon, and two configurations for the middle carbon, meaning #2^3 = 8# stereoisomers. Try drawing them out in your spare time!

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Answer 2

To calculate the number of stereoisomers for a compound, use the formula (2^n), where (n) represents the number of chiral centers or the total number of stereocenters in the molecule. This formula assumes the compound does not have any meso isomers or internal planes of symmetry.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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