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12.E: Cycloalkanes, Cycloalkenes, and Cycloalkynes (Exercises)

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  • Exercise 12-1 Write expanded structures showing the \(\ce{C-C}\) bonds for each of the following condensed formulas. Name each substance by the IUPAC system.

    a. \(\ce{(CH_2)_{10}}\)
    b. \(\ce{(CH_2)_5CHCH_3}\)
    c. \(\ce{(CH_3)_2C(CH_2)_6CHCH_2H_5}\)
    d. the position and configurational isomers of trimethylcyclobutane
    e. \(\ce{(CH_2)_6CHCH_2C(CH_3)_2CH2Cl}\)
    f. \(\ce{[(CH_2)_2CH]_2C(CH_3)C_2H_5}\)

    Exercise 12-2 The energy required to distort \(\ce{C-C-C}\) bond angles from their normal values is approximately \(17.5 \: \text{cal}\) (not \(\text{kcal}\)!) per degree squared per mole. Assuming the normal angle to be \(112.5^\text{o}\), calculate the angle-strain energy of a mole of planar cyclohexane (Figure 12-2). The actual \(\ce{C-C-C}\) bond angles of cyclohexane are \(111.5^\text{o}\); what strain energy corresponds to this angle?

    Exercise 12-3* Figure 5-8 indicates that the difference in energy between the conformation of butane with eclipsed methyls and the gauche form is about \(5 \: \text{kcal mol}^{-1}\). Use this number to estimate the contribution of eclipsing tot he instability of planar cyclohexane. Then calculate the instability of planar cyclohexane by including the angle strain from Exercise 12-2 in your estimate.

    Exercise 12-4 Using the sawhorse convention, draw the possible conformations of chlorocyclohexane with the ring carbons in the planar, in the chair, and in the extreme boat forms. Arrange these in order of expected stability. Show your reasoning.

    Exercise 12-5 Draw the preferred conformation of each of the following:

    a. isopropylcyclohexane
    b. cyclohexylcyclohexane
    c.

    Exercise 12-6*

    a. It commonly is stated that the bulkier the substituent, the more favorable will be the conformation in which it occupies an equatorial position. However, it will be seen from Table 12-2 that the \(-\Delta G^0\) values for the halogens (\(\ce{F}\), \(\ce{Cl}\), \(\ce{Br}\), and \(\ce{I}\)) are not very large and all are about the same, although there is no question that iodine is a much bulkier substituent than fluorine. Use the following data to account qualitatively for the smallness and the commonality of the \(-\Delta G^0\) factors for halogens. In the following table, \(r_{\ce{C-X}}\) is the normal carbon-halogen bond distance, \(r_e\) is the distance calculated from the halogen to the nearest hydrogens when equatorial, \(r_a\) is the same distance when the halogen is axial, and \(r_0\) is the distance corresponding to the minimum on a nonbonded halogen-hydrogen interaction curve, such as shown in Figure 12-9.

    b. How stable would you expect the diaxial conformation of cis-1,3-diiodocyclohexane to be relative to the diequatorial conformation? Give your reasoning.

    Exercise 12-7 Assuming the effects of substituents in the 1- and 4-positions of cyclohexane on the free energies of equatorial-axial equilibria can be assessed by simple addition of the \(\Delta G^0\) values of Table 12-2, calculate the relative free energies of \(1\), \(2\), \(3\), and \(4\). Use these values to calculate equilibrium constants for \(1\) \(\rightleftharpoons\) \(2\), \(3\) \(\rightleftharpoons\) \(4\), and \(1\) \(\rightleftharpoons\) \(3\) at \(25^\text{o}\).\(^4\)

    Exercise 12-8 Explain why simple additivity of \(\Delta G^0\) values as proposed in Exercise 12-7 to predict axial-equatorial equilibria for cis and trans 1,4-disubstituted cyclohexanes would be expected to give poor results with 1,2- and 1,3-disubstituted cyclohexanes.

    Exercise 12-9 Draw the possible chair conformations of trans- and cis-1,3-dimethylcyclohexane. Is the cis or the trans isomer more likely to be the more stable? Explain.

    Exercise 12-10 With cis-2-methyl-5-tert-butyl-1,3-dioxacyclohexane,\(^5\) the conformation with tert-butyl axial is more favorable than the conformation with tert-butyl equatorial.

    Explain why this should be so and predict what should be the favored conformation for trans-2-methyl-4-tert-butyl-1,3-dioxacyclohexane.

    Exercise 12-11 With reference to Figure 12-12, sketch the proton-decoupled \(\ce{^{13}C}\) spectrum you would expect for methylcyclohexane at \(25^\text{o}\). Give your reasoning. (Review Section 9-10C.)

    Exercise 12-12* The \(\ce{^{19}F}\) NMR spectrum of 1,1-difluorocyclohexane at several temperatures and \(56.4 \: \text{MHz}\) is shown in Figure 12-13.

    Figure 12-13: Changes in the \(\ce{^{19}F}\) NMR spectrum of 1,1-difluorocyclohexane with temperature at \(56.4 \: \text{MHz}\) (see Exercise 12-12). Generally, \(\ce{H-C-C-F}\) spin-spin splittings are on the order of \(5\)-\(15 \: \text{Hz}\) and change with rotational angles in much the same way as for \(\ce{H-C-C-H}\) couplings.

    a. Explain why this spectrum changes so drastically with temperature and account for the appearance of four groups of lines observed at \(-100^\text{o}\). (Review Sections 9-10C and 9-10I.)

    b. Sketch the \(\ce{^{19}F}\) spectrum you would expect for 1,1-difluoro-4-tert-butylcyclohexane at \(25^\text{o}\). Give you reasoning.

    Exercise 12-13* Proton NMR spectra often are used to determine whether a substituent is axial or equatorial. Explain what differences one might expect to see in the splitting of the NMR signal from the \(\ce{-CHCl}-\) proton of each of the following two conformations at a temperature low enough so interconversion is very slow. (Review Sections 9-10H and 9-10J.)

    Exercise 12-14 Given the favored nonplanar conformation of cyclobutane (Figure 12-15), predict whether cis-1,2-dibromocyclobutane will be more, or less, stable than the corresponding trans isomer. Do the same for the cis- and trans-1,3-dibromocyclobutanes. Give your reasoning.

    Exercise 12-15 Write structural formulas for all of the possible cis-trans isomers of the following compounds and designate the configuration of each by name (see Section 5-1):

    a. 1,3-dichlorocyclopentane
    b. 1,1,3-trimethylcyclohexane
    c. 1,2,3-trimethylcyclopropane
    d. (3-methylcyclobutyl)-3-methylcyclobutane

    Exercise 12-16 Use the data of Table 12-3 and any needed bond energies to calculate \(\Delta H^0\) for the following reaction in the vapor state at \(25^\text{o}\) with \(n = 3\), \(4\), and \(5\):

    \[\ce{(CH_2)}_n \rightarrow \ce{CH_3(CH_2)}_{n - 3} \ce{CH=CH_2}\]

    What can you conclude about the stability of the cycloalkanes with \(n = 3\), \(4\), and \(5\) with respect to corresponding open-chain compounds with double bonds? Include consideration of the possible entropy effects, Section 4-4B.

    Exercise 12-17 Use the heats of combustion to liquid water given in Table 12-3 and appropriate bond energies to calculate \(\Delta H^0\) (vapor) for ring-opening of the cycloalkanes with bromine in the range \(n = 2\) to \(n = 6\):

    \[\ce{(CH_2)}_n + \ce{Br_2} \rightarrow \ce{(CH_2)}_{n - 2} \ce{(CH_2Br)_2}\]

    Exercise 12-18 Investigate the thermodynamic feasibility of the following propagation steps for opening the rings of cycloalkanes with \(n = 2\) to \(n = 6\) by a radical-chain mechanism:

    \[\ce{(CH_2)}_n + \ce{Br} \cdot \rightarrow \ce{BrCH_2-(CH_2)}_{n-2} \ce{-CH_2} \cdot\]

    \[\ce{BrCH_2-(CH_2)}_{n-2} \ce{-CH_2} \cdot + \ce{Br_2} \rightarrow \ce{(CH_2)}_{n-2} \ce{(CH_2Br)_2} + \ce{Br} \cdot\]

    Use \(83 \: \text{kcal mol}^{-1}\) for the bond-dissociation energy of a normal \(\ce{C-C}\) bond and \(68 \: \text{kcal mol}^{-1}\) for the bond-dissociation energy of a \(\ce{C-Br}\) bond. (An easy way to solve a problem of this type is first to calculate \(\Delta H\) of each step for cyclohexane, for which there is no strain, then to make suitable corrections for the strain that is present for smaller values of \(n\).)

    Exercise 12-19 Show how the reactions described in Table 12-4 could be used to determine whether a hydrocarbon of formula \(\ce{C_4H_8}\) is methylcyclopropane, cyclobutane, or 1-butene \(\left( \ce{CH_3CH_2CH=CH_2} \right)\). Write equations for the reactions used.

    Exercise 12-20

    a. Consider that all of the following cyclohexane derivatives have \(\ce{R}\) as a very large group so the conformations shown are the most stable ones. Which member of each pair would you expect to react more rapidly under the given conditions and why? Draw the structure and configuration of the major product. (Review Section 8-8.)

    b. Make sawhorse-type drawings of the possible products of antarafacial addition of bromine to 4-tert-butylmethylcyclohexene. Which isomer would you expect to be formed most rapidly? Give your reasoning.

    Exercise 12-21* Formation of a cycloalkane \(\ce{(CH_2)}_n\) by reactions such as

    \[\ce{Br-(CH_2)}_n \ce{-ZnBr} \rightarrow \ce{(CH_2)}_n + \ce{ZnBr_2}\]

    occurs in competition with other reactions such as

    \[2 \ce{Br-(CH_2)}_n \ce{-ZnBr} \rightarrow \ce{Br-(CH_2)}_{2n} \ce{-ZnBr} + \ce{ZnBr_2}\]

    a. Explain why cyclization reactions of this kind carried out in dilute solutions are likely to give better yields of \(\ce{(CH_2)}_n\) than in concentrated solutions.

    b. Make graphs that show, as a function of \(n\) in the range 3 to 15, how the yield of cycloalkane might be expected to depend on (1) the total strain in the ring formed (see Table 12-3), and (2) the probability that at any given instant the reactive ends will be oriented properly with respect to one another so as to permit cyclization.

    c. Explain how the factors considered in Part b must be balanced relative to one another to account for the reported yields of cyclization products for the following ring sizes: \(\ce{(CH_2)_3} > 80\%\); \(\ce{(CH_2)_4} > 7\%\); \(\ce{(CH_2)_6} \: 45\%\); larger rings \(< 10\%\).

    Exercise 12-22* If the twist-chain conformation \(8\) were rigid rather than flexible, how many different monochlorocycloheptanes would you expect (a) excluding mirror-image isomers and (b) including mirror-image isomers?

    Exercise 12-23* A conformation of cyclooctane called boat-boat can be formed by having two gauche \(\ce{C-C-C-C}\) segments, as shown in Figure 12-19. As drawn, this conformation has all hydrogens staggered and normal \(\ce{C-C-C}\) bond angles. Explain why it is not a favorable conformation. Use of models will be very helpful.

    Figure 12-19: Boat-boat conformation of cyclooctane, based on two gauche forms of butane (see Exercise 12-23).

    Exercise 12-24 Space-filling models (Section 2-2B) indicate that the chiral forms of trans-cyclopentadecene are likely to be readily interconverted at room temperature. How and where might trans-cyclopentadecene be substituted to give stable chiral forms that possess a chiral center but no chiral carbon atoms?

    Exercise 12-25 Name each of the following compounds by an accepted system:

    a.

    b.

    c.

    d.

    e.

    f.

    Exercise 12-26 Use ball-and-stick models to assess the degree of stability to be expected for a decalin with chair-form rings and an axial-axial ring fusion.

    Exercise 12-27 The equatorial form of methylcyclohexane is \(1.5 \: \text{kcal mol}^{-1}\) more stable than the axial form because the axial form has steric hindrance between the methyl and two hydrogens, one in the 3- and the other in the 5-position. Knowing that cis-decalin is about \(2 \: \text{kcal mol}^{-1}\) less stable than trans-decalin, what would you estimate for the relative stabilities of cis- and trans-9-methyldecalin (numbering as in Figure 12-22)?

    Exercise 12-28 Name prismane according to the system described in Section 12-8.

    Exercise 12-29 Draw a sawhorse-style formula for bicyclo[1.1.0]butane and formulas for all of the eight possible dichlorobicyclo[1.1.0]butanes (including chiral forms).

    Exercise 12-30* How could you phrase Bredt's rule so it could distinguish between the lack of stability of \(16\) and the stability of bicyclo[5.5.0]-1,2-decene, both compounds having a double-bonded carbon at a ring junction?

    Exercise 12-31* Using the system described in Section 12-8, name the following compound:

    To what degree do you think this compound violates Bredt's rule? (Use of ball-and-stick models will be helpful here.) By what kind of mechanism would you expect bromine to add to the double bond? (Review Sections 12-3A, 12-5, 10-6, and 10-7.)

    Exercise 12-32 Write structural formulas for substances (one for each part) that fit the following descriptions. Make sawhorse drawings of the substances for which conformational problems are involved.

    a. a compound of formula \(\ce{C_4H_8}\) that reacts slowly with sulfuric acid and also with bromine (light induced)
    b. the most highly strained isomer of \(\ce{C_5H_{10}}\)
    c. the possible products from treatment of 1-ethyl-2-methylcyclopropane with bromine (light-induced)
    d. the least-stable chair and the least-stable boat conformations of cis-1,4-dichlorocyclohexane
    e. the most stable geometrical isomer of 1,3-di-tert-butylcyclobutane
    f. a compound with a six-membered ring that is most stable with the ring in a boat form
    g. trans-bicyclo[7.1.0]decane
    h. the most stable conformation of trans-1,3-di-tert-butylcyclohexane
    i. the most stable conformation of cis-2-tert-butyl-cis-decalin
    j. a boat-boat conformation of cis-decalin
    k. trans,trans,trans-tricyclo[8.4.0.0\(^{2,7}\)]tetradecane

    Exercise 12-33 The \(\Delta H^0\) value for hydrogenation of cyclopropane to propane at \(25^\text{o}\) in the vapor state is \(-37.5 \: \text{kcal mol}^{-1}\). Use this value and any other bond energies to calculate the bond energies of the \(\ce{C-C}\) bonds in cyclopropane on the assumption that all of its \(\ce{C-C}\) bonds are equally strong and the \(\ce{C-H}\) bonds are \(6 \: \text{kcal mol}^{-1}\) stronger than normal. Notice than, by definition, the bond energies must give the proper value of \(\Delta H^0\) for the following reaction:

    \[\ce{(CH_2)_3} \left( g \right) \rightarrow 3 \ce{C} \left( g \right) + 6 \ce{H} \left( g \right)\]

    Use your cyclopropane bond energies to calculate \(\Delta H^0\) values for the following reactions:

    a. \(\ce{(H_2)_3} \rightarrow \cdot \ce{CH_2-CH_2-CH_2} \cdot\) (normal \(\ce{C-C}\) bonds)
    b. \(2 \ce{(CH_2)_3} \rightarrow \ce{(CH_2)_6}\)

    Exercise 12-34 Draw structural formulas in reasonable perspective for each of the following substances:

    a. the cis and trans isomers of bicyclo[3.3.0]octane
    b. trans-tricyclo[3.1.0.0\(^{2,6}\)]hexane
    c. tricyclo[3.1.0\(^{2,6}\)]hexane
    d. trans-2,6-dichlorobicyclo[2.2.2]octane
    e. quinquecyclo[4.4.0.0\(^{2,5}\).0\(^{3,9}\).0\(^{4,8}\)]decane

    Exercise 12-35 Draw each of the following compounds in perspective to show the preferred conformation. Construct models if in doubt.

    a. 2-tert-butyl-trans-decalin
    b. bicyclo[2.2.2]octane
    c. spiro[5.4]decane
    d. trans-3-phenyl-1-methylcyclohexane

    Exercise 12-36 When bromine adds to 4-tert-butyl-1-methylcyclohexane in \(\ce{CH_3OH}\) solution, which of the following structures, A-F, would be the major product? Give your reasoning in detail.

    Exercise 12-37 Which conformational or position isomer in each of the following pairs would you expect to be the most stable (of lowest energy)? (Models will be helpful.)

    a.

    b.

    c.

    d.

    \(^4\)It is important to notice that, in some cases, simple additivity of \(\Delta G^0\) values can give quite erroneous results when the groups involved are polar. Thus trans-1,4-dichlorocyclohexane appears to be more stable in the diaxial conformation than in the diequatorial conformation.

    \(^5\)The oxa prefix to the name of a hydrocarbon means that a carbon in the chain has been replaced by oxygen (see Section 15-11A).

    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."