Stereoisomers maximum number

Many naturally occurring compounds contain several chirality centers By an analysis similar to that described for the case of two chirality centers it can be shown that the maximum number of stereoisomers for a particular constitution is 2" where n is equal to the number of chirality centers... 

When two or more of a molecule s chirality centers are equivalently substituted meso forms are possible and the number of stereoisomers is then less than 2" Thus 2" represents the maximum number of stereoisomers for a molecule containing n chirality centers... 

Section 7 12 For a particular constitution the maximum number of stereoisomers is 2" where n is the number of structural units capable of stereochemical variation—usually this is the number of chirality centers but can include E and Z double bonds as well The number of stereoisomers is reduced to less than 2" when there are meso forms... 

The monosaccharide glucose contains four asymmetric carbons carbons 2, 3, 4 and 5. A general formula for calculating the maximum number of stereoisomers is given by 2n, where n is the number of asymmetric carbons. For this compound, since n = 4, the maximum number of stereoisomers is 24 = 16. 

In general, the maximum number of optically active isomers is given by 2n where n represents the number of asymmetric carbon atoms. Thus for a compound where n = 1, as in lactic acid, there would be two stereoisomers, one the dextro and the other the laevo. For a compound with two asymmetric carbon atoms, there would be 22 = 4 stereoisomers. But if the two asymmetric carbon atoms carry exactly identical groups, as in tartaric acid, the number would be fewer than four and we know that it exists in three forms, the d the 1 and the meso. 

Stereoisomers with more than one chiral center and which are not mirror images of each other hence, stereoisomers that are not enantiomers of each other. For example, L-threonine and D-threonine are an enantiomeric pair whereas L-threonine and D-allothreonine are a diastereomeric pair (as is L-threonine and L-allothreo-nine). Diastereomers will have similar physical, chemical, and spectral properties but those properties will not be identical. If n is the number of chiral centers, then the maximum number of stereoisomers will be equal to 2. However, the actual number for a given set of isomers may be less than 2 due to the presence of meso forms. See Enantiomer Epimer Meso Form... 

The maximum number of stereoisomers is 2" where n is the number of nonidentical chiral centers. Figure 1-2 shows the four stereoisomers present in a molecule with two chiral centers. Non-superimposable mirror images are enantiomers, while the other species in the figure are diastereomers. Unlike enantiomers, diastereomers have different physical properties. 

Stereoisomerism in compounds with two stereo centres diastereomers and meso structure In compounds whose stereoisomerism is due to tetrahedral stereocentres, the total number of stereoisomers will not exceed 2", where n is the number of tetrahedral stereocentres. For example, in 2,3,4-trihydroxybutanal, there are two chiral carbons. The chiral centres are at C-2 and C-3. Therefore, the maximum number of possible isomers will be 2 = 4. All four stereoisomers of 2,3,4-trihydroxybutanal (A-D) are optically active, and among them there are two enantiomeric pairs, A and B, and C and D, as shown in the structures below. 

Label each chirality center in these compounds with an asterisk and calculate the maximum number of stereoisomers for each ... 

Stereoisomers are classified by symmetry as either enantiomers or diaste-reomers. Enantiomers have identical physical properties except for the direction of optical rotation. Diastereomers are basically stereoisomers that are not enantiomers of each other. A pair of enantiomers exists for all molecules containing a single chiral center and have the opposite configuration at each of the stereo centers. The maximum number of stereoisomers for a compound with n stereo centers is T. Diastereomers, on the other hand, have the same configuration at one of the two centers and have the opposite configuration at the other. 

When n = 2, 2 = 4. With two stereogenic centers, the maximum number of stereoisomers is four, although sometimes there are fewer than four. 

ProblGtn 5.16 What is the maximum number of stereoisomers possible for a compound with (a) three stereogenic centers (b) eight stereogenic centers ... 

Switching the positions of H and Br (or any two groups) on one stereogenic center of either A or B forms a new stereoisomer (labeled C in this example), which is different from both A and B. Then draw the mirror image of C, labeled D. C and D are nonsuperimposable mirror images—enantiomers. We have now drawn four stereoisomers for 2,3-dibromopentane, the maximum number possible. 

Whereas 2,3-dibromopentane has two stereogenic centers and the maximum of four stereoisomers, 2 -dibromobutane has two stereogenic centers but fewer than the maximum number of stereoisomers. 

With two stereogenic centers, the maximum number of stereoisomers = 4. 

It is important to note that the 2" rule predicts only the maximum number of stereoisomers possible in compounds with more than one center of chirality. For example, some compounds with two asymmetrically substituted carbon atoms may have only three stereoisomeric forms. This occurs when three of the substituents on one asymmetric carbon are the same as those on the other asymmetric carbon, as shown... 

Thus the presence of two chiral centers can lead to the existence of as many as four stereoisomers. For compounds containing three chiral centers, there could be as many as eight stereoisomers for compounds containing four chiral centers, there could be as many as sixteen stereoisomers, and so on. The maximum number of stereoisomers that can exist is equal to 2 , where n is the number of chiral centers. (In any case where mesa compounds exist, as discussed in the following section, there will be fewer than this maximum number.)... 

If there is more than one chiral centre in a molecule, then the maximum number of possible d,l pairs of stereoisomers increases, and is given by the formula 2 1, where n is the number of chiral centres. So, if there are two chiral centres there are four possible stereoisomers, comprising two d,l pairs. Stereoisomers are called diastereomers if their relationship to one another is not enantiomeric. Where two diastereomers differ only in the stereochemistry at one chiral centre, then they are called epimers. If the two c groups in the prochiral example given above were in such positions that if they were replaced diastereomers would be formed, then the c groups would be called diastereotopic. 

Stereoisomers with one chiral carbon can only exist as a pair of enantiomers. More possibilities exist if there are two or more chiral carbons. Drawing stereoisomers of a formula should be done in a systematic fashion and in pairs of mirror images. These mirror images can be tested for superimposability. The maximum number of enantiomers possible for a compound is 2n where n is the number of chiral carbons this is known as the van t Hoff rule. 

As mentioned previously, the maximum number of configurations for a molecule with two chiral carbons is 2, or 4. However, if each of the two chiral carbons is bonded to the same four nonidentical groups, fewer than four stereoisomers exist. The example of tartaric acid, studied by Pasteur, helps to explain this phenomenon. 

Many organic compounds have more than one asymmetric carbon. The more asymmetric carbons a compound has, the more stereoisomers are possible for the compound. If we know how many asymmetric carbons a compound has, we can calculate the maximum number of stereoisomers for that compound a compound can have a maximum of 2 stereoisomers (provided it doesn t have any other stereocenters), where n equals the number of asymmetric carbons. For example, 3-chloro-2-butanol has two asymmetric carbons. Therefore, it can have as many as four (2 = 4) stereoisomers. The four stereoisomers are shown both as perspective formulas and as Fischer projections. 

In the examples we have just seen, each compound with two asymmetric carbons has four stereoisomers. However, some compounds with two asymmetric carbons have only three stereoisomers. This is why we emphasized in Section 5.9 that the maximum number of stereoisomers a compound with n asymmetric carbons can have (provided it doesn t have any other stereocenters) is 2 , instead of stating that a compound with n asymmetric carbons has 2 stereoisomers. 

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