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21.E: Resonance and Molecular Orbital Methods (Exercises)

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    84559
  • Exercise 21-1 Determine which of the following structures can be represented by one or more specific electron-pairing schemes similar to the Kekulé structures of benzene:

    Exercise 21-2 Calculate the heat of formation of 1,3-butadiene in the gas phase at \(25^\text{o}\) from the bond energies in Table 4-3 and the knowledge that \(\Delta H^0\) for \(\ce{C} \left( s \right) \rightarrow \ce{C} \left( g \right)\) is \(171.3 \: \text{kcal}\). The heat of formation is defined as \(\Delta H^0\) for \(4 \ce{C} \left( s \right) + 3 \ce{H_2} \left( g \right) \rightarrow \ce{C_4H_6} \left( g \right)\). The experimental value of the heat of formation is \(26.3 \: \text{kcal}\). Calculate the stabilization energy of 1,3-butadiene.

    Exercise 21-3 The heat of formation of propenal by \(3 \ce{C} \left( s \right) + 2 \ce{H_2} \left( g \right) + \frac{1}{2} \ce{O_2} \left( g \right) \rightarrow \ce{C_3H_4O} \left( g \right)\) is \(-25.1 \: \text{kcal}\). Using the bond energies of Table 4-3 and \(\Delta H^0 = +171.3 \: \text{kcal}\) for \(\ce{C} \left( s \right) \rightarrow \ce{C} \left( g \right)\), calculate a stabilization energy for propenal.

    Exercise 21-4 Use the qualitative VB and MO methods to predict whether addition of \(\ce{HCl}\) to 1,3-cyclohexadiene would be favored to give 3-chlorocyclohexene or 4-chlorocyclohexene.

    Exercise 21-5 Set up an atomic-orbital model for the enolate anion, \(\ce{CH_2=CH-O}^\ominus\) and consider how it should be formulated by the VB and MO methods. Write a hybrid structure of the general type of \(18e\) and \(21c\) for the enolate anion and predict the most likely positions of the atoms for the anion in its most stable configuration.

    Exercise 21-6 Use Figure 21-9 to predict the \(\pi\)-electron distribution in the 2-propenyl radical \(\left( \ce{CH_2=CH-CH_2} \cdot \right)\) and the 2-propenyl anion \(\left( \ce{CH_2=CH-CH_2^-} \colon \right)\). Show your reasoning.

    Exercise 21-7 1,3-Butadiene has a substantial stabilization energy, whereas ethene has none, yet attack of \(\ce{Br}^\oplus\) on 1,3-butadiene occurs more readily than on ethene. Explain how 1,3-butadiene can have a stabilization energy greater than ethene but still be more reactive toward reagents that donate \(\ce{Br}^\oplus\).

    Exercise 21-8 The experimental \(-\Delta H^0\) \(\left( 25^\text{o} \right)\) is \(707.7 \: \text{kcal}\) for combustion of one mole of gaseous 1,3-cyclopentadiene to liquid water and carbon dioxide. From this value compute a stabilization energy for cyclopentadiene with the aid of the heat of vaporization of water \(\left( 10 \: \text{kcal mol}^{-1} \right)\) and any required bond energies. Show your method. Discuss briefly any uncertainties that may arise in estimating a resonance energy for cyclopentadiene that would not be similarly important for 1,3-butadiene.

    Exercise 21-9 The heat of combustion of one mole of benzene to carbon dioxide and liquid water is \(789 \: \text{kcal}\). Calculate values for the stabilization energy of benzene that correspond to (a) the bond energies of Table 4-3 and (b) the ethene \(\ce{C-H}\) bond energy of Section 12-4B, combined with the assumption that the bond energy \(\left( 90.6 \: \text{kcal} \right)\) of a carbon single bond between two carbon double bonds, \(\ce{=C-C=}\), is \(8 \: \text{kcal}\) stronger than a normal \(\ce{C-C}\) bond. The point of this exercise is to show how the stabilization energy of benzene is affected when bond energies are taken to depend on the hybridization assumed for carbon, instead of being chosen to give the best possible fit to the heats of combustion of aliphatic compounds.

    Exercise 21-10 Suggest reasons why (a) the stabilization energy of biphenylene is less than twice that of benzene, and (b) the heat of combustion of naphthalene is less than that of azulene.

    Exercise 21-11 Graphite crystals consist of a network of planar hexagonal rings of carbon atoms arranged in parallel layers. The distance between the layer planes is \(3.35 \: \text{Å}\) and all the \(\ce{C-C}\) bonds within the hexagonal network are equal to \(1.421 \: \text{Å}\).

    a. Sketch the carbon framework in graphite.
    b. What is likely to be the state of hybridization of carbon?
    c. Use the VB method to estimate the percentage of double-bond character for the \(\ce{C-C}\) bonds in graphite.
    d. Make a plot of double-bond character versus bond length for ethene, benzene, and graphite.
    e. From your plot estimate the length of a single bond between \(sp^2\)-hybridized carbons. How does this value compare with the \(sp^2\)-\(sp^2\) distances listed in Table 21-3? What conclusion might be drawn from this as to the importance of resonance in 1,3-butadiene?

    Exercise 21-12 Draw the possible Kekulé-type structures for biphenylene (five) and naphthalene (three). Assuming the structures may be weighted equally, estimate the double-bond character and bond lengths for both compounds. Indicate which bonds of these hydrocarbons should be attacked preferentially by ozone.

    Exercise 21-13 For a regular polygon inscribed in a circle with a corner down, use trigonometry to calculate the molecular-orbital energies as in Figure 21-13.

    Exercise 21-14* Consider the appropriateness and results from application of the \(\left( 4n + 2 \right)\) \(\pi\)-electron rule to predict the stability of the following compounds:

    Exercise 21-15 The \(\pi\)-molecular orbitals of tricyclo[5.3.0.0\(^{2, 6}\)]-1,3,5,7,9-decapentaene have the following energies: \(\alpha + 2.562 \beta\), \(\alpha + 1.732 \beta\), \(\alpha + \beta\), \(\alpha + \beta\), \(\alpha + 0.414 \beta\), \(\alpha\), \(\alpha - \beta\), \(\alpha - 1.562 \beta\), \(\alpha - 1.732 \beta\), \(\alpha - 2.414 \beta\). Make an energy diagram of these orbitals, as in Figure 21-13, and calculate the total \(\pi\)-electron energy and the delocalization energy for this hydrocarbon.

    Exercise 21-16 Cyclooctatetraene can add two electrons and form a rather stable planar dianion, \(\ce{C_8H_8^{2-}}\). Use the data of Figure 21-13 to help you write an electronic configuration for this anion and calculate its total \(\pi\)-electron energy. Suppose you had planar cyclooctatetraene with four localized \(\pi\) bonds of the ethene type. What is the \(\pi\)-electron energy of such a system? Now add two more \(\pi\) electrons to this localized cyclooctatetraene; what will the localized total \(\pi\)-electron energy be? What do you calculate for the delocalization energy of the cyclooctatetraene dianion? Is is the same as the delocalization energy of cyclooctatetraene itself? Show your reasoning.

    Exercise 21-17 One of the problems with the qualitative MO method is that it does not give a good simple answer to whether a four-electron \(\pi\) system, such as \(32\), is just as stable as the butadiene \(\pi\) system, \(33\), which we treated in detail in Section 21-4:

    What does the qualitative VB method predict about the entity formed when four \(\pi\) electrons are added to the orbitals of \(32\)? Calculation yields the following MO energies for \(32\): \(\alpha \pm 1.73 \beta\), \(\alpha\), and \(\alpha\). Arrange the molecular orbitals in order of increasing energy and compare the predicted electronic configuration with that obtained by the VB method. Show your reasoning. (An entity corresponding to \(32\) with a triplet ground state has been identified as a reaction intermediate.)

    Exercise 21-18 Use the orbital energies of Figures 21-9, 21-13, and 21-14 to calculate the delocalization energies of the following ions:

    a. and

    b. and

    c. and

    d. \(\ce{CH_2=CH}- \overset{\oplus}{\ce{C}} \ce{H_2}\) and \(\ce{CH_2=CH}- \overset{\overset{\ominus}{\cdot \cdot}}{\ce{C}} \ce{H_2}\)

    e. \(\ce{CH_2=CH-CH=CH}- \overset{\oplus}{\ce{C}} \ce{H_2}\) and \(\ce{CH_2=CH-CH=CH}- \overset{\overset{\ominus}{\cdot \cdot}}{\ce{C}} \ce{H_2}\)

    Figure 21-14: Energies and schematic representations of the \(\pi\) molecular orbitals of the \(\ce{CH_2=CH-CH=CH-CH_2^+}\) cation (see Exercise 21-18).

    Exercise 21-19* Tetrafluoroethene undergoes a slow [2 + 2] addition to ethene by what appears to be a stepwise biradical mechanism. What would you expect the stereochemistry of the deuteriums in the product to be if one started with cis-1,2-dideuterioethene, , and the reaction proceeded by

    a. a stepwise biradical mechanism?
    b. a concerted mechanism with a transition state such as \(37\)?
    c. a concerted mechanism with a transition state such as \(38\)?

    Exercise 21-20* Use Figures 21-13 and 21-16 to estimate the difference in \(\pi\)-electron energy for the two following transition states (\(39\) and \(40\)) for [4 + 4] cycloaddition of 1,3-butadiene. Show your method.

    Exercise 21-21 The Cope rearrangement is a type of sigmatropic rearrangement that occurs with 1,5-dienes. An example is the rearrangement of 3-methyl-1,5-hexadiene to 1,5-heptadiene:

    On the basis of this result and the \(4n + 2\) rule, work out a mechanism for the reaction and then use this mechanism to predict what product will be formed from the Cope rearrangement of 3,4-dimethyl-1,5-hexadiene. Show your reasoning.

    Exercise 21-22 Unlike the conversion of bicyclo[2.1.0]-2-pentene to 1,3-cyclopentadiene, bicyclo[4.1.0]-2,4-heptadiene is transformed to 1,3,5-cycloheptatriene very rapidly at low temperatures by what appears to be a wholly concerted mechanism. Account for this difference.

    Exercise 21-23* Show how one can predict the stereochemistry of the electrocyclic rearrangement of trans,cis,trans-2,4,6-octatriene to 5,6-dimethyl-1,3-cyclohexadiene by a favorable concerted thermal mechanism.

    Exercise 21-24*

    a. Sulfur dioxide is an angular molecule that can be represented as having a nonbonding electron pair in an \(sp^2\) hybrid orbital and one "vacant" \(p\) orbital on sulfur. Use this formulation to derive a thermally allowed transition state for the reversible 1,4-cycloaddition of \(\ce{SO_2}\) to 1,3-butadiene (Section 13-3C).

    b. The three-membered ring sulfone, shown below, is very unstable and rapidly dissociations to \(\ce{SO_2}\) and ethene. This process is used for the synthesis of alkenes by the dissociation of cyclic sulfones (Ramberg-Bäcklund reaction). Determine whether the transition state for the thermally favorable reaction is conrotatory or disrotatory.

    Exercise 21-25* Indicate whether the following reactions are likely to occur thermally by favorable concerted mechanisms:

    a.

    b.

    c.

    Exercise 21-26* Show how tetracyclo[2.1.1.0\(^{5,6}\)]-2-hexene may be formed by irradiation of benzene. Would you expect this substance to revert to benzene by a concerted electrocyclic ring opening?

    Exercise 21-27* There are three possible biradicals that could be formed by simple combination of two molecules of 1,2-propadiene, \(50\), \(51\), and \(52\):

    a. Show how each one of these could be formed, and what cyclic product(s) you would expect each to give.

    b. Evaluate the degree of electron delocalization expected for \(50\), \(51\), and \(52\) in terms of specific VB structures, and predict qualitatively which biradical you would expect to be formed most easily. Give your reasoning. (As part of your answer you will need to evaluate the importance of electron-pairing schemes for ethenyl-type radicals, such as \(\ce{R}- \overset{\cdot}{\ce{C}} \ce{=CH_2} \longleftrightarrow \ce{R}- \overset{\cdot \cdot}{\ce{C}} - \overset{\cdot}{\ce{C}} \ce{H_2}\). It is easy to be confused about this; check the rules in Section 6-5B.)

    c. By combining the following \(\Delta H^0\) values, estimate \(\Delta H^0\) for the formation of each of the biradicals \(50\), \(51\), and \(52\). Correlate the results with your predictions in Part b.

    Exercise 21-28 Use the VB method in accord with the rules of Section 6-5B to evaluate the contributions of the electron-pairing schemes shown below. (In some cases it will be helpful to use ball-and-stick models to evaluate the relative energies of the VB structure.)

    a.

    b.

    c.

    d. \(\ce{CH_2=CH-O}^\ominus \longleftrightarrow \: ^\ominus \ce{CH_2-CH=O}\)

    e. \(\ce{CH_2=CH}- \overset{\oplus}{\ce{N}} \ce{H_3} \longleftrightarrow \overset{\oplus}{\ce{C}} \ce{H_2-CH=NH_3}\)

    f.

    g.

    h.

    i.

    Exercise 21-29 Write three isomeric structures for \(\ce{C_4H_2}\) with tetravalent carbon and univalent hydrogen. Describe which isomer has the most favorable geometrical configuration and estimate the resonance energy for this isomer.

    Exercise 21-30 Write the five Kekulé-type resonance structures of phenanthrene and show how these structures can account for the fact that phenanthrene, unlike benzene, adds bromine, but only across the 9,10-positions.

    Use the data in Tables 4-3 and 21-1 to estimate \(\Delta H^0\) for the addition of 1 mole of bromine to phenanthrene. (Don't forget to include the SE of the addition product.)

    Exercise 21-31 Which compound in each of the following pairs would lose chloride ion more readily and form a carbonium ion? Explain.

    \[\ce{CH_2=CH-CH_2-CH_2Cl} \: \text{and} \: \ce{CH_2=CH-CH_2Cl}\]

    \[\ce{CH_2=CH-CHCl-CH=CH_2} \: \text{and} \: \ce{CH_2=CH-CH=CH-CH_2Cl}\]

    Exercise 21-32 Devise an atomic-orbital model for cyclooctatetraene in accord with the geometry expressed by formula \(25a\) (Section 21-9A) and explain why electron delocalization is not likely to be important for a structure with this geometry.

    Exercise 21-33 The conjugated 1,3,5,7,9-cyclodecapentaene with the double-bond configuration as in \(53\) is far less stable than either azulene, \(54\), or bicyclo[4.4.1]-1,3,5,7,9-undecapentaene, \(55\). Explain why this is so on the basis of the VB method (molecular models will be helpful).

    Exercise 21-34 1,3-Diazole (imidazole) is a planar molecule with substantial delocalization (resonance) energy.

    a. Devise an atomic orbital model of imidazole and sketch out the \(\pi\) molecular orbitals you would expect for the molecule on the basis of those in Figure 21-13.

    b. 1,3-Diazole is relatively acidic and forms the anion \(\ce{C_3N_2H_3^-}\). Which is the acidic hydrogen? Draw valence-bond structures for the anion and indicate which ones should be expected to contribute most to the hybrid structure.

    Exercise 21-35 Predict which of the following molecules would have some degree of resonance stability by applying the Hückel \(\left( 4n + 2 \right)\) \(\pi\)-electron rule.

    a.

    b.

    c.

    d.

    e.*

    f.*

    Exercise 21-36 Account for the following experimental observations:

    a. 3,4-Dimethylenecyclobutene does not give a Diels-Alder adduct with even the most reactive dienophiles.

    b. Compound \(56\) is an exceptionally strong dibasic organic acid.

    c. 2,4-Cyclopentadienone is not a stable compound and readily polymerizes.

    Exercise 21-37* 1,2-Propadiene is represented in Figure 13-4 as if it were two isolated Hückel ring systems. This molecule also may be represented as a stable Möbius system of \(4 \pi\) electrons. Draw an orbital diagram of 1,2-propadiene to indicate this relationship. If 1,2-propadiene twisted so that the hydrogens on the ends all were in the same plane, \(57\), would it be a Hückel or a Möbius polyene, or neither?

    Exercise 21-38 Bicyclo[2.2.0]-1(4)-hexene is highly strained and quite unstable. When it decomposes at room temperature, tetracyclo[6.2.2.0\(^{1,8}\).0\(^{3,6}\)]-3(6)-dodecene is formed.\(^{10}\)

    a. Write a structure formula for the product.

    b. Show a reasonable sequence by which it might be formed, with the knowledge that bicyclo[2.2.0]-1(4)-hexene is an extraordinarily reactive dienophile in [4 + 2] cycloadditions.

    Exercise 21-39 Bicyclo[2.2.0]-2,5-hexadiene is much less stable than its isomer, benzene, yet it does not rearrange to benzene except at elevated temperatures. Give a reason for this observation.

    Exercise 21-40 Show the expected stereochemistry of the product of each of the following thermally concerted reactions:

    a. 2-trans,4-cis,6-cis,8-trans-decatetraene \(\rightarrow\) 7,8-dimethyl-1,3,5-cyclooctatriene

    b.

    c. \(\overset{124^\text{o}}{\rightleftharpoons}\) only one stereoisomer is formed

    d.

    Exercise 21-41* Use the procedure of Section 21-10F to set up transition-state orbitals and determine whether these lead to a favored Hückel or a favored Möbius transition state for the following processes:

    a. (remember that hydrogen uses \(1s\) orbitals for bonding)

    b. (investigate the orbital systems )

    c. (a 1,3 hydrogen shift)

    Exercise 21-42

    a. Consider each of the following transformations and determine the number of participating orbitals and electrons in each reactant. (Review Section 21-10F if you have trouble.)

    1.

    2.

    3.

    4.

    5.

    b. Determine whether the reactions in Part a are thermally allowed.

    Exercise 21-43* Tetracyanoethene undergoes [2 + 2] cycloaddition with cis- and trans-1-methoxypropene. The following facts are known about these reactions.

    1. Addition is several thousand times faster in \(\ce{CH_3CN}\) (a quite polar solvent) than in cyclohexane.

    2. The [2 + 2] addition product becomes less stereospecific as the solvent is changed from nonpolar to polar.

    3. The cis- and trans-1-methoxypropene are interconverted by tetracyanoethene at a rate comparable to the [2 + 2] addition rate with tetracyanoethene.

    4. In methanol, only a small amount of [2 + 2] cycloadduct is formed and the principal product is \(\ce{HC(CN)_2C(CN)_2CH(CH_3)CH(OCH_3)_2}\).

    a. Write the structures for the [2 + 2] addition.

    b. What do Facts 1 and 2 indicate about the mechanism? Write the possible steps involved.

    c. Draw an energy diagram for the reaction in a polar solvent as a function of a reaction coordinate in the style of Figure 13-1. This diagram should agree with Fact 3. (Be sure you study the legend of Figure 13-1 before drawing your diagram.)

    d. Account for the formation of \(\ce{HC(CN)_2C(CN)_2CH(CH_3)CH(OCH_3)_2}\) along with a [2 + 2] cycloadduct in methanol (a polar solvent). Would you expect any \(\ce{CH_3OC(CN)_2CH(CH_3)CH_2OCH_3}\) to be formed? Explain.

    \(^{10}\)Numbering such as 1(4) means that the double bond comes between carbons 1 and 4 and is used only where necessary to avoid ambiguity.

    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."