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20.E: Carbohydrates (Exercises)

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  • Exercise 20-1 The logic necessary to solve this problem essentially is that used by Fischer in his classic work which established the configurations of glucose, arabinose, and mannose.

    a. The projection formulas for all the theoretically possible \(D\)-aldopentoses, \(\ce{HOCH_2(CHOH)_3CHO}\), are shown in Figure 20-1. One of the \(D\)-aldopentoses is the naturally occurring \(D\)-arabinose, which is enantiomeric with the more abundant \(L\)-arabinose. Oxidation of \(D\)-arabinose with nitric acid gives an optically active 2,3,4-dihydroxypentanedioic acid. Which of the \(D\)-aldopentoses could be \(D\)-arabinose?

    b. \(D\)-Arabinose is converted by the Kiliani-Fischer synthesis\(^3\) to \(D\)-glucose and \(D\)-mannose. What do these transformations tell about the relationship between the configurations of mannose and glucose?

    c. Oxidation of \(D\)-glucose and \(D\)-mannose gives the 2,3,4,5-tetrahydroxyhexanedioic acids, glucaric and mannaric acids, respectively, both are optically active. What are the configurations of the \(D\)- and \(L\)-arabinoses?

    d. \(D\)-Glucaric acid can form two different \(\gamma\)-monolactones, whereas \(D\)-mannaric acid can form only one \(\gamma\)-monolactone. What are the configurations of \(D\)-glucose and \(D\)-mannose?

    Exercise 20-2

    a. Deduce possible configurations of natural galactose from the following observations. Give your reasoning. (1) \(D\)-Galactose gives a pentose by one Wohl degradation. On nitric acid oxidation this pentose gives an optically active 2,3,4-trihydroxypentanedioic acid. (2) The pentose by a second Wohl degradation followed by nitric acid oxidation gives \(D\)-tartaric acid.

    b. Write reasonable mechanisms for the reactions involved in the Wohl degradation.

    Exercise 20-3 Determine each of the following sets of structures whether they correspond to the same stereoisomer. The left structure in each example is a Fischer projection formula. Models will be helpful.

    a. and

    b. and

    c. and and

    Exercise 20-4 Draw the chair conformation of \(\beta\)-\(D\)-glucose with all of the substituent groups axial. Explain how hydrogen bonding may complicate the usual considerations of steric hindrance in assessing the stability of this conformation relative to the form with all substituent groups equatorial.

    Exercise 20-5 Make a sawhorse drawing of what you believe to be the favored conformations of \(\alpha\)- and \(\beta\)-\(D\)-ribopyranose and of \(\alpha\)- and \(\beta\)-\(D\)-idopyranose.

    Exercise 20-6 From the following information deduce the ring structures of the sugars. Give your reasoning.

    Exercise 20-7 \(D\)-Arabinose and \(D\)-ribose give the same phenylosazone. \(D\)-Ribose is reduced to the optically inactive 1,2,3,4,5-pentanepentol, ribitol. \(D\)-Arabinose can be degraded by the Ruff method, which involves the following reactions:

    The tetrose, \(D\)-erythrose, so obtained can be oxidized with nitric acid to meso-tartaric acid. Show how this information can be organized to establish the configurations of \(D\)-arabinose, \(D\)-ribose, ribitol, and \(D\)-erythrose.

    Exercise 20-8 Work out a mechanism for the acid-induced hydrolysis of \(\ce{N}\)-glycosides. Pay special attention as to where a proton can be added to be most effective in assisting the reaction. Would you expect that adenosine would hydrolyze more, or less, readily than \(\ce{N}\)-methyl-\(\alpha\)-ribosylamine? Give your reasoning.

    Exercise 20-9

    a. Which of the disaccharides, \(24\) through \(27\), would you expect to be reducing sugars?

    b. Determine the configuration of each of the anomeric carbons in \(24\) through \(27\) as either \(\alpha\) or \(\beta\).

    c. Determine which monosaccharides (neglect the anomeric forms) will be produced on hydrolysis of \(24\) through \(27\). Be sure you specify the configurations as \(D\) or \(L\).

    Exercise 20-10 Draw Haworth and conformational structures for each of the following disaccharides:

    a. 6-\(\ce{O}\)-\(\beta\)-\(D\)-glucopyranosyl-\(\beta\)-\(D\)-glucopyranose
    b. 4-\(\ce{O}\)-\(\beta\)-\(D\)-galactopyranosyl-\(\alpha\)-\(D\)-glucopyranose
    c. 4-\(\ce{O}\)-\(\beta\)-\(D\)-xylopyranosyl-\(\beta\)-\(L\)-arabinopyranose
    d. 6-\(\ce{O}\)-\(\alpha\)-\(D\)-galactopyranosyl-\(\beta\)-\(D\)-fructofuranose

    Exercise 20-11 Show how the structure of maltose can be deduced from the following:

    (1) The sugar is hydrolyzed by yeast \(\alpha\)-\(D\)-glucosidase to \(D\)-glucose.

    (2) Maltose mutarotates and forms a phenylosazone.

    (3) Methylation with dimethyl sulfate in basic solution followed by acid hydrolysis gives 2,3,4,6-tetra-\(\ce{O}\)-methyl-\(D\)-glucopyranose and 2,3,6-tri-\(\ce{O}\)-methyl-\(D\)-glucose.

    (4) Bromine oxidation of maltose followed by methylation and hydrolysis gives 2,3,4,6-tetra-\(\ce{O}\)-methyl-\(D\)-glucopyranose and a tetramethyl-\(D\)-gluconic acid, which readily forms a \(\gamma\)-lactone.

    Exercise 20-12 Cellobiose differs from maltose only in its behavior to enzymatic hydrolysis. It is hydrolyzed by yeast \(\beta\)-\(D\)-glucosidase. What is its structure?

    Exercise 20-13 Show how the structure of lactose may be deduced from the following:

    (1) The sugar is hydrolyzed by \(\beta\)-\(D\)-galactosidase to a mixture of equal parts of \(D\)-glucose and \(D\)-galactose.

    (2) Lactose mutarotates and forms a phenylosazone.

    (3) Bromine oxidation of lactose followed by hydrolysis gives \(D\)-gluconic acid and \(D\)-galactose.

    (4) Methylation and hydrolysis of lactose gives a tetra-\(\ce{O}\)-methyl-\(D\)-galactose and 2,3,6-tri-\(\ce{O}\)-methyl-\(D\)-glucose. The same galactose derivative can be obtained from the methylation and hydrolysis of \(D\)-galactopyranose.

    (5) Bromine oxidation of lactose followed by methylation and hydrolysis yields tetra-\(\ce{O}\)-methyl-1,4-gluconolactone and the same galactose derivative as in (4).

    Exercise 20-14 Explain how the \(\beta\)-\(D\)-glucoside units of cellulose produce a polymer with a stronger, more compact physical structure than the \(\alpha\)-\(D\)-glucose units of starch. Models will be helpful.

    Exercise 20-15 Write Fischer projections, Haworth projections, and sawhorse conformational drawings for the following:

    a. \(\alpha\)-\(D\)-glucuronic acid
    b. \(\beta\)-\(D\)-iduronic acid
    c. \(\alpha\)-\(D\)-guluronic acid

    Exercise 20-16 Explain how you could account for the fact that ascorbic acid is most stable in the enediol form rather than having its \(\ce{C_3}\) and \(\ce{C_2}\) carbons arranged either as \(\ce{-C(=O)-CH(OH)}-\) or as \(\ce{-CH(OH)-C(=O)}-\).

    Exercise 20-17* Write mechanisms, supported by analogy insofar as possible, for the carboxylation and cleavage reactions of Equation 20-4 as you would expect them to occur in the absence of an enzyme. Both reactions can be reasonably expected to be induced by \(\ce{OH}^\ominus\), and it may be helpful to review the properties of enols described in Section 17-1.

    Exercise 20-18* From the discussion in Section 15-5F, it should be clear that the reaction of an alcohol phosphate with ADP to give ATP, \(\ce{ROPO_3^{2-}} + \text{ADP} \rightarrow \text{ATP} + \ce{ROH}\), is not likely to have a favorable equilibrium constant. Explain why one might expect the following reaction to be more energetically favorable.

    Exercise 20-19* The heat of combustion of glucose(s) to \(\ce{CO_2} \left( g \right)\) and \(\ce{H_2O} \left( l \right)\) is \(670 \: \text{kcal mol}^{-1}\), whereas that of 2-oxopropanoic acid \(\left( l \right)\) is \(280 \: \text{kcal mol}^{-1}\). Neglecting the heats of solution of the compounds in water, estimate the energy of glucose \(\left( aq \right) + \ce{O_2} \rightarrow 2 \ce{CH_3COCO_2H} \left( aq \right) + 2 \ce{H_2O} \left( l \right)\).

    Exercise 20-20* The following interconversion is catalyzed by the enzyme triose phosphate isomerase:

    Explain how you might use bond energies to estimate whether the equilibrium constant, \(K\), for this reaction would be greater, or less, than unity.

    Exercise 20-21* Assuming that one molecule of glucose is oxidized to two molecules of 2-oxopropanoic acid (pyruvic acid), how many moles of ATP are formed from ADP in the overall reaction by the sequence of steps given in Figure 20-9?

    Exercise 20-22* The reaction \(\text{ADP} + \ce{RCO-SR'} + \ce{PO_4^{3-}} \rightarrow \text{ATP} + \ce{RCO_2H} + \ce{HSR'}\) is substantially more favorable than the corresponding reaction with \(\ce{RCO_2R}\). On the basis of the valence-bond treatment, explain why this should be so.

    Exercise 20-23* Citric acid is prochiral. Nonetheless, if one were to introduce acetyl CoA labeled with \(\ce{^{14}C}\) (radioactive carbon) at the carboxyl group, \(\ce{CH_3-^{14}COS} \textbf{CoA}\), into the citric acid cycle, the 2-oxopentanedioate acid (2-ketoglutarate) formed in the fourth step of the cycle would have all of the \(\ce{^{14}C}\) in the carboxylate group farthest away from the ketone carbonyl group. For some years, this result was used to argue that citric acid itself could not be an intermediate in the formation of 2-oxopentanedioate. Review Section 19-8 and explain how, in stereospecific enzyme-induced reactions, citric acid could be an intermediate in the formation of 2-oxopentanedioate even if the \(\ce{^{14}C}\) would not appear equally in both carboxylic carbons of the product.

    Exercise 20-24* What analogy can you draw from reactions studied in previous chapters to the cleavage \(\ce{RCOCH_2COS} \textbf{CoA} + \ce{HS} \textbf{CoA} \rightarrow \ce{RCOS} \textbf{CoA} + \ce{CH_3COS} \textbf{CoA}\)? What reagents would you expect to cause this reaction to occur in water solution?

    Exercise 20-25* A first step in unraveling the mechanism of the metabolism of fatty acids was made in 1904 by F. Knoop, who found that dogs metabolized 4-phenylbutanoic acid to phenylethanoic acid and 3-phenylpropionic acid to benzoic acid. What does this pattern of results indicate about the mechanism of degradation of fatty acids? Give your reasoning.

    Exercise 20-26* A very strong man can lift \(225 \: \text{kg}\) \(\left( 500 \: \text{lb} \right)\) 2 meters \(\left( 6.5 \: \text{ft} \right)\). Muscle action gets its energy from the reaction \(\text{ATP} + \ce{H_2O} \rightarrow \text{ADP} + \ce{H_2PO_4^-}\), a process with a \(\Delta G^0\) of \(-7 \: \text{kcal}\).

    a. Assuming \(50\%\) efficiency in the use of the hydrolysis free energy, how many grams of ATP (MW 507) would have to be hydrolyzed to achieve this lifting of the weight? (One \(\text{kg}\) raised one meter requires \(2.3 \: \text{cal}\) of energy.)

    b. How many grams of glucose would have to be oxidized to \(\ce{CO_2}\) and water to replenish the ATP used in Part a on the basis of a \(40\%\) conversion of the energy of combustion to ATP? (\(\Delta G^0\) for combustion of glucose is \(-686 \: \text{kcal}\).)

    Exercise 20-27 A naturally occurring optically active pentose \(\left( \ce{C_5H_{10}O_5} \right)\) reduces Tollen's reagent and forms a tetraethanoate with ethanoic anhydride. It gives an optically inactive phenylosazone. Write all the possible structures for this pentose that are in accord with each of the experimental observations.

    Exercise 20-28 A hexose, \(\ce{C_6H_{12}O_6}\), which we shall call X-ose, on reduction with sodium amalgam gives pure \(D\)-sorbitol, and upon treatment with phenylhydrazine gives an osazone different from that of \(D\)-glucose. Write a projection formula for X-ose and equations for its reactions.

    Exercise 20-29 Compound A, \(\ce{C_5H_{10}O_4}\), is optically active, forms a diethanoate ester with ethanoic anhydride, but does not give a silver mirror with \(\ce{Ag}^\oplus \ce{(NH_3)_2}\). When treated with dilute acid, A yields methanol and B, \(\ce{C_4H_8O_4}\). B is optically active, reduces \(\ce{Ag}^\oplus \ce{(NH_3)_2}\), and forms a triethanoate ester with ethanoic anhydride. On reduction, B gives optically inactive C, \(\ce{C_4H_{10}O_4}\). Mild oxidation of B gives D, a carboxylic acid, \(\ce{C_4H_8O_5}\). Treatment of the amide of D with dilute sodium hypochlorite solution gives \(\left( + \right)\)-glyceraldehyde \(\left( \ce{C_3H_6O_3} \right)\). (For a description of this reaction see Section 23-12E.) Use these facts to derive structures and stereochemical configurations for A, B, C, and D. Write equations for all the reactions involved.

    Exercise 20-30 Draw Haworth- and conformation-type formulas for each of the following:

    a. methyl 2,3,4,6-\(\ce{O}\)-tetramethyl-\(\alpha\)-\(D\)-glucopyranoside
    b. \(\beta\)-\(D\)-arabinofuranosyl-\(\alpha\)-\(L\)-arabinofuranoside
    c. \(L\)-sucrose

    Exercise 20-31 Sugars condense with anhydrous 2-propanone in the presence of an acid catalyst to form cyclic ketals known as isopropylidene derivatives:

    The reaction of \(D\)-glucose with 2-propanone and an acid catalyst produces a mono- and a diisopropylidene derivative. Acid hydrolysis of the diisopropylidene derivative gives the monoisopropylidene compound. \(\ce{O}\)-Methylation of the diketal derivative (Section 20-4A) followed by hydrolysis of the ketal groups forms 3-\(\ce{O}\)-methyl-\(D\)-glucose. \(\ce{O}\)-Methylation of the monoketal derivative followed by hydrolysis of the ketal function forms a tri-\(\ce{O}\)-methyl-\(D\)-glucose. This tri-\(\ce{O}\)-methyl-\(D\)-glucose when \(\ce{O}\)-methylated forms an isomer of penta-\(\ce{O}\)-methyl-\(D\)-glucopyranose. This isomer when subjected to hydrolysis in dilute acid yields an isomer of 2,3,4,6-tetra-\(\ce{O}\)-methyl-\(D\)-glucopyranose (\(20\), Figure 20-4). Write structures for these cyclic ketals which agree with the experimental evidence. Give your reasoning. (Review Sections 20-2C and 20-4A.)

    Figure 20-32 Complete the following sequence of reactions, writing structures for all the products, A-I.

    a. \(\alpha\)-\(D\)-glucofuranose \(\underset{\ce{HCl}}{\overset{1 \: \text{mol 2-propanone}}{\longrightarrow}} A\) (see Exercise 20-31)

    b. \(A \overset{\ce{NaIO_4}}{\longrightarrow} B\)

    c. \(B \overset{\ce{Na^{14}CN}}{\longrightarrow} C + D\)

    d. \(C + D \underset{2. \: \ce{H}^oplus, \: \ce{H_2O}}{\overset{1. \: \ce{H_2O}, \: \ce{OH}^\ominus}{\longrightarrow}} E + F +\) 2-propanone

    e. \(E + F \underset{\ce{-H_2O}}{\overset{\text{heat}}{\longrightarrow}} G + H\)

    f. \(G + H \underset{\ce{H_2O}}{\overset{\ce{NaBH_4}}{\longrightarrow}} i +\) \(D\)-glucose-6-\(\ce{^{14}C}\)

    Exercise 20-33 Write a mechanism for the interconversion of an aldohexose and a ketohexose that is catalyzed by hydroxide ion. What products would you expect starting with \(D\)-glucose?

    Exercise 20-34 The glycoside amygdalin \(\left( \ce{C_{20}H_{27}O_{11}N} \right)\) is hydrolyzed with the aid of the enzyme emulsin (but not with the enzyme maltase) to give \(D\)-glucose, \(\ce{HCN}\), and benzenecarbaldehyde. \(\ce{O}\)-Methylation of amygdalin, followed by acid hydrolysis, gives 2,3,4,6-tetra-\(\ce{O}\)-methyl-\(D\)-glucose and 2,3,4-tri-\(\ce{O}\)-methyl-\(D\)-glucose. Write a structure for amygdalin that fits with these observations.

    \(^3\)The steps of the Kiliani-Fischer synthesis are:

    Contributors

    • John D. Robert and Marjorie C. Caserio (1977) Basic Principles of Organic Chemistry, second edition. W. A. Benjamin, Inc. , Menlo Park, CA. ISBN 0-8053-8329-8. This content is copyrighted under the following conditions, "You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format."