number of stereoisomers for a meso compound

[OneManShow]

I know that the formula is 2^n for an asymmetric molecule. But what about a meso compound?
In one of the TBR question explanations this is what it says:
The 2^n formula represents the max # of stereoisomers. For every meso structure, you must subtract one from the total.
Can someone explain what this last sentence means?

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[malpractician]

that's a good question, easy.

look at tartaric acid with 2n, you'd get 4 stereoisomers. wrong. It is 3, because the meso compound should only be counted once.

 

[BerkReviewTeach]

I know that the formula is 2^n for an asymmetric molecule. But what about a meso compound?
In one of the TBR question explanations this is what it says:
The 2^n formula represents the max # of stereoisomers. For every meso structure, you must subtract one from the total.
Can someone explain what this last sentence means?

A meso compound is superimposible on its mirror image, so if you use the 2^n rule, you'll end up counting it twice. Like malpractician (great moniker BTW) said, you can see this most easily with a molecule with two stereogenic carbons like tartaric acid (HO2C-CH(OH)-CH(OH)-CO2H). It has two chiral centers, one at carbon-2 and the other at carbon-3. You would think from the formula that there are four stereoisomers possible, (1) 2R,3R, (2) 2R,3S, (3) 2S,3R, and (4) 2S,3S. However, 2R,3S is the same structure as 2S,3R (a meso compound), so there are only three stereoisomers possible.

That's why the formula is #stereoisomers = 2^n - #meso structures. Hope this explains it.

 

[Rosalindbungs]

A meso compound is superimposible on its mirror image, so if you use the 2^n rule, you'll end up counting it twice. Like malpractician (great moniker BTW) said, you can see this most easily with a molecule with two stereogenic carbons like tartaric acid (HO2C-CH(OH)-CH(OH)-CO2H). It has two chiral centers, one at carbon-2 and the other at carbon-3. You would think from the formula that there are four stereoisomers possible, (1) 2R,3R, (2) 2R,3S, (3) 2S,3R, and (4) 2S,3S. However, 2R,3S is the same structure as 2S,3R (a meso compound), so there are only three stereoisomers possible.

That's why the formula is #stereoisomers = 2^n - #meso structures. Hope this explains it.

Is "n" the number of chiral centers?

 

[BerkReviewTeach]

Is "n" the number of chiral centers?

yes.

So it becomes a probability question. Consider three centers on a molecule. Each has the option of being R or S. Three events with two possible alignments leads to a total of 2exp3 outcomes.

• They are:
  RRR
  RRS
  RSR
  RSS
  SRR
  SRS
  SSR
  SSS

It's like flipping a coin three times.

Hope that helps.