calculate the number of optical isomers in glucose
Answers
Explanation:
If a molecule contains a single chiral carbon, two enantiomers exist. Carbohydrates, and many other synthetic and naturally occurring organic molecules, contain more than a single chiral carbon; sucrose we have said contains nine. Before considering further the reactions of carbohydrates, we must examine the complications introduced into the structures of sugars by this multitude of chiral centers.
First consider sugars with two chiral centers, the aldotetroses. Each chiral carbon (C-2 and C-3) can exist in either the R or S configuration. Four stereoisomers are therefore possible, R,R; S,S; S,R; and R,S. These four isomers are shown in Fig. 10-4. Note that the isomers fall into pairs of enantiomers, 2R,3R being the mirror image of 2S,3S and 2R,3S the mirror image of 2S,3R. Because they are now mirror images, these pairs obviously have identical physical properties and rotate the plane of polarized light by equal amounts in opposite directions. But the 2R,3R-isomer is not a mirror image of either the 2R,3S- or 2S,3R-isomer, and will differ from them in physical and chemical properties. Stereoisomers that are not mirror images are called diastereomers. So each erythrose is a diastereomer of both threose isomers. The aldotetroses then fall into two pairs of sugars, erythrose and threose, with different physical properties. Each of these sugars exists as enantiomers (+)-erythrose and (-)-erythrose, (+)-threose and (-)-threose.


Figure 10-4. The aldotetroses contain two chiral carbon atoms, each of which may exist in an R- or S- form, giving rise to four stereoisomers. The two erythrose isomers are mirror images (enantiomers), as are the two threose isomers. Each erythrose is a diastereomer of the threoses, and vice versa.
To draw these stereoisomers quickly and conveniently, we use Fischer projection formulas (Fig. 10-5). In this convention the carbon backbone is drawn vertically and the hydroxyl and hydrogen substituents are placed horizontally to the right or left. These horizontal bonds by definition project outward, toward the viewer, while the vertical bonds are behind the plane of the paper, away from the viewer. The carbon atoms making up the backbone lie at the intersections of the vertical and horizontal lines. The Fischer convention is illustrated in Fig. 10-5 for (2R,3R)-erythro
Figure 10-5. In the Fischer convention the molecule is viewed from above with horizontal groups projecting out of the page, vertical groups behind the page.
Each time we add a chiral center to a molecule, we double the possible number of stereoisomers. With 1 chiral center, there are 2 isomers, 2 chiral centers, 4 possible isomers, 3 centers, 8 isomers and 4 centers, 16 possible stereoisomers. For an arbitrary number (n) of chiral centers in a molecule there are as many as 2n possible stereoisomers. Sucrose, with nine chiral carbons, has 29 stereoisomers, or 512. Glucose has four chiral carbons in its aldehyde form, and so there are 24, or 16 possible stereoisomers of this formula, only one of which is dextrose [(+)-glucose]. These 16 isomers are shown in Fig. 10-6. We could, of course, designate the stereochemistry at each chiral carbon as R or S; in this way carbons 2 through 5 in dextrose could be labeled 2R,3S,4R,5R. More commonly, the sugars are divided into two classes, D- or L-, depending upon whether the hydroxyl on the bottom chiral carbon is on the right (Dextro) or left (Levo) in the Fischer formulas. This has been done in Fig. 10-6. The symbols "D" and "C" are vestiges of the system used to designate configuration before the invention of R and S. None of these has anything to do with the sign of rotation of the plane of the plane-polarized light, represented by d-, l-, (+)-, or (-)-.