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Organic Chemistry/Fourth Edition: E-Text CHAPTER 25 CARBOHYDRATES SOLUTIONS TO TEXT PROBLEMS 25.1 (b) Redraw the Fischer projection so as to show the orientation of the groups in three dimensions. H H HOCH2 CHO is equivalent to HOCH2 C CHO OH OH Reorient the three-dimensional representation, putting the aldehyde group at the top and the primary alcohol at the bottom. H CHO turn 90Њ HOCH2 C CHO HOHC OH CH2OH What results is not equivalent to a proper Fischer projection, because the horizontal bonds are directed “back” when they should be “forward.” The opposite is true for the vertical bonds. To make the drawing correspond to a proper Fischer projection, we need to rotate it 180° around a vertical axis. CHO CHO CHO HOHC HOC H is equivalent to HO H CH2OH CH2OH CH2OH rotate 180Њ Now, having the molecule arranged properly, we see that it is L-glyceraldehyde. 701 Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website 702 CARBOHYDRATES (c) Again proceed by converting the Fischer projection into a three-dimensional representation. CHO CHO HOCH2 H is equivalent to HOCH2 C H OH OH Look at the drawing from a perspective that permits you to see the carbon chain oriented ver- tically with the aldehyde at the top and the CH2OH at the bottom. Both groups should point away from you. When examined from this perspective, the hydrogen is to the left and the hydroxyl to the right with both pointing toward you. CHO CHO HOCH2 C H is equivalent to HOHC OH CH2OH The molecule is D-glyceraldehyde. 25.2 Begin by drawing a perspective view of the molecular model shown in the problem. To view the compound as a Fischer projection, redraw it in an eclipsed conformation. O H OH H OH H OH CH HOCH 2 HOCH2 CH O HO H Staggered conformation Same molecule in eclipsed conformation The eclipsed conformation shown, when oriented so that the aldehyde carbon is at the top, vertical bonds back, and horizontal bonds pointing outward from their stereogenic centers, is readily trans- formed into the Fischer projection of L-erythrose. CHO CHO H OH H OH HO C H HO H is equivalent to or HO C H HO H HOCH2 CH O CH OH CH2OH 2 L-Erythrose 25.3 L-Arabinose is the mirror image of D-arabinose, the structure of which is given in text Fig- ure 25.2. The configuration at each stereogenic center of D-arabinose must be reversed to trans- form it into L-arabinose. CHO CHO HO H H OH HOHHO H HOHHO H CH2OH CH2OH d-(Ϫ)-Arabinose l-(ϩ)-Arabinose Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website CARBOHYDRATES 703 25.4 The configuration at C-5 is opposite to that of D-(ϩ)-glyceraldehyde. This particular carbohydrate therefore belongs to the L series. Comparing it with the Fischer projection formulas of the eight D-aldohexoses reveals it to be in the mirror image of D-(ϩ)-talose; it is L-(Ϫ)-talose 25.5 (b) The Fischer projection formula of D-arabinose may be found in text Figure 25.2. The Fischer projection and the eclipsed conformation corresponding to it are CHO 5 5 CH OH HOCH OH HO H H 2 H 2 H HOH 4 C rotate about 4 C H HO 1 O C-3 C-4 bond H HO 1 O HO H HOH 3 2 3 2 CH2OH HO H HO H d-Arabinose Eclipsed conformation Conformation suitable for of d-arabinose furanose ring formation Cyclic hemiacetal formation between the carbonyl group and the C-4 hydroxyl yields the ␣- and ␤-furanose forms of D-arabinose. HOCH O HOCH O 2 OH 2 H H HHOH H HHOOH HO H HO H ␤-d-Arabinofuranose ␣-d-Arabinofuranose (c) The mirror image of D-arabinose [from part (b)] is L-arabinose. CHO CHO 5 HO H H OH CH OH H HO 2 H OH HO H 4 C HO H 1 O H H OH HO H 3 2 CH2OH CH2OH H OH d-Arabinose l-Arabinose Eclipsed conformation of l-arabinose The C-4 atom of the eclipsed conformation of L-arabinose must be rotated 120° in a clock- wise sense so as to bring its hydroxyl group into the proper orientation for furanose ring formation. 5 CH OH H OH H HO 2 H 1 4 C C OH H O rotate about OH H O H C-3 C-4 bond HOCH2 3 2 H OH H OH Original eclipsed conformation Conformation suitable for of l-arabinose furanose ring formation Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website 704 CARBOHYDRATES Cyclization gives the ␣- and ␤-furanose forms of L-arabinose. O O H OH H H OH H H OH H OH HOCH2 HOCH2 HOH HOH ␣-l-Arabinofuranose ␤-l-Arabinofuranose In the L series the anomeric hydroxyl is up in the ␣ isomer and down in the ␤ isomer. (d) The Fischer projection formula for D-threose is given in the text Figure 25.2. Reorientation of that projection into a form that illustrates its potential for cyclization is shown. H H O 1 O C H 2 1 HO H is equivalent to 4 C H OH O H 3 OH 2 4 3 CH2OH HO H d-Threose Cyclization yields the two stereoisomeric furanose forms. H O H O O OH H 4 C ϩ H OH 1 O HHOH HHOOH 3 2 HO H HO H HO H ␤-d-Threofuranose ␣-d-Threofuranose 25.6 (b) The Fischer projection and Haworth formula for D-mannose are CHO H HOCH HO H 2 CH OH H O H 2 H OH HO H OH H C H OH HO HO O HO HO HO HO H H OH H H H H CH2OH d-Mannose ␤-d-Mannopyranose (Haworth formula) The Haworth formula is more realistically drawn as the following chair conformation: H OH HOCH2 HO O HO OH H H H H ␤-d-Mannopyranose Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website CARBOHYDRATES 705 Mannose differs from glucose in configuration at C-2. All hydroxyl groups are equatorial in ␤-D-glucopyranose; the hydroxyl at C-2 is axial in ␤-D-mannopyranose. (c) The conformational depiction of ␤-L-mannopyranose begins in the same way as that of ␤-D-mannopyranose. L-Mannose is the mirror image of D-mannose. CHO CHO HO H HOH HO CH OH H HO 2 HO H H OH H C H OH HO H H H O H H OH HO H HO OH CH2OH CH2OH d-Mannosel-Mannose Eclipsed conformation of l-mannose To rewrite the eclipsed conformation of L-mannose in a way that permits hemiacetal forma- tion between the carbonyl group and the C-5 hydroxyl, C-5 is rotated 120° in the clockwise sense. HO H H 6 55CH OH H OH H O HO 2 HO HO H H rotate about CH2OH CH2OH 4 C - - 4 C H H 1 O C 4 C 5 bond H H 1 O H H H H H OH 3 2 3 2 HO OH HO OH HO OH ␤-l-Mannopyranose (remember, the anomeric hydroxyl is down in the l series) Translating the Haworth formula into a proper conformational depiction requires that a choice be made between the two chair conformations shown. H O OH H H HO H H H H O HOCH CH2OH H 2 O OH H H H H HO H H OH OH OH HO OH H OH HO OH CH2OH Haworth formula of Less stable chair conformation; More stable chair conformation; ␤ -l-mannopyranose CH2OH is axial CH2OH is equatorial (d) The Fischer projection formula for L-ribose is the mirror image of that for D-ribose. CHO CHO HOHHO H CH2OH H O HO HO H H OH HO H C HO HO O HO HO H OH HO H H H OH CH2OH CH2OH H H H H d-Ribose l-Ribose Eclipsed conformation of l-ribose is Haworth formula of oriented properly for ring closure. ␤-l-ribopyranose Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website 706 CARBOHYDRATES Of the two chair conformations of ␤-L-ribose, the one with the greater number of equatorial substituents is more stable. OH O OH HO HO H O O OH HO HO HO HO OH H OH OH H H Less stable chair More stable chair conformation of conformation of ␤-l-ribopyranose ␤-l-ribopyranose 25.7 The equation describing the equilibrium is OH OH OH HOCH2 HOCH2 HOCH2 HO O HO OH HO O OH HO HO CH O HO OH ␣-D-Mannopyranose Open-chain form of D-mannose ␤-D-Mannopyranose ␣ 20 Њ ␣ 20 Њ [ ]D 29.3 [ ]D 17.0 Let A ϭ percent ␣ isomer; 100 Ϫ A ϭ percent ␤ isomer. Then A(ϩ29.3°) ϩ (100 Ϫ A)(Ϫ17.0°) ϭ 100(ϩ14.2°) 46.3A ϭ 3120 Percent ␣ isomer ϭ 67% Percent ␤ isomer ϭ (100 Ϫ A) ϭ 33% 25.8 Review carbohydrate terminology by referring to text Table 25.1. A ketotetrose is a four-carbon ke- tose. Writing a Fischer projection for a four-carbon ketose reveals that only one stereogenic center is present, and thus there are only two ketotetroses. They are enantiomers of each other and are known as D- and L-erythrulose. CH2OH CH2OH CO CO H OH HO H CH2OH CH2OH d-Erythrulose l-Erythrulose 25.9 (b) Because L-fucose is 6-deoxy-L-galactose, first write the Fischer projection formula of D-galactose, and then transform it to its mirror image, L-galactose.
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