4.15: Additional Problems
- Page ID
- 482269
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Conformations
PROBLEM3-42 Consider 2-methylbutane (isopentane). Sighting along the C2–C3 bond:
(a) Draw a Newman projection of the most stable conformation.
(b) Draw a Newman projection of the least stable conformation.
(c) If a CH3 ⟷ CH3 eclipsing interaction costs 11 kJ/mol (2.5 kcal/mol) and a CH3 ⟷ CH3 gauche interaction costs 3.8 kJ/mol (0.9 kcal/mol), make a quantitative plot of energy versus rotation about the C2–C3 bond.
PROBLEM3-43 What are the relative energies of the three possible staggered conformations around the C2–C3 bond in 2,3-dimethylbutane? (See Problem 3-42.)
PROBLEM3-44 Construct a qualitative potential-energy diagram for rotation about the C–C bond of 1,2-dibromoethane. Which conformation would you expect to be most stable? Label the anti and gauche conformations of 1,2-dibromoethane.
PROBLEM3-45Which conformation of 1,2-dibromoethane (Problem 3-44) would you expect to have the largest dipole moment? The observed dipole moment of 1,2-dibromoethane is μ = 1.0 D. What does this tell you about the actual conformation of the molecule?
PROBLEM3-46 Draw the most stable conformation of pentane, using wedges and dashes to represent bonds coming out of the paper and going behind the paper, respectively.
PROBLEM3-47 Draw the most stable conformation of 1,4-dichlorobutane, using wedges and dashes to represent bonds coming out of the paper and going behind the paper, respectively.
PROBLEM3-51 The barrier to rotation about the C–C bond in bromoethane is 15 kJ/mol (3.6 kcal/mol).
(a) What energy value can you assign to an H ↔ Br eclipsing interaction?
(b) Construct a quantitative diagram of potential energy versus bond rotation for bromoethane.
PROBLEM3-52 Increased substitution around a bond leads to increased strain. Take the four substituted butanes listed below, for example. For each compound, sight along the C2–C3 bond and draw Newman projections of the most stable and least stable conformations. Use the data in Table 3.5 to assign strain-energy values to each conformation. Which of the eight conformations is most strained? Which is least strained?
(a) 2-Methylbutane (b) 2,2-Dimethylbutane (c) 2,3-Dimethylbutane (d) 2,2,3-Trimethylbutane
Visualizing Chemistry
PROBLEM 4-22 Draw a Newman projection along the C2–C3 bond of the following conformation of 2-butanol.
PROBLEM4-23 Name the following compound, identify each substituent as axial or equatorial, and tell whether the conformation shown is the more stable or less stable chair form (green = Cl):
PROBLEM4-24 A trisubstituted cyclohexane with three substituents—red, green, and blue—undergoes a ring-flip to its alternate chair conformation. Identify each substituent as axial or equatorial, and show the positions occupied by the three substituents in the ring-flipped form.
PROBLEM4-25 The following cyclohexane derivative has three substituents—red, green, and blue. Identify each substituent as axial or equatorial, and identify each pair of relationships (red–blue, red–green, and blue–green) as cis or trans.
PROBLEM4-26 Glucose exists in two forms having a 36:64 ratio at equilibrium. Draw a skeletal structure of each, describe the difference between them, and tell which of the two you think is more stable (red = O).
Cycloalkane Isomers
PROBLEM4-27 Draw the five cycloalkanes with the formula C5H10.
PROBLEM4-28 Give IUPAC names for the following compounds.
(a) (b)
(c)
(d)
(e)
PROBLEM4-29 Draw a stereoisomer of trans-1,3-dimethylcyclobutane.
PROBLEM4-30 Tell whether the following pairs of compounds are identical, constitutional isomers, stereoisomers, or unrelated.
(a) cis-1,3-Dibromocyclohexane and trans-1,4-dibromocyclohexane
(b) 2,3-Dimethylhexane and 2,3,3-trimethylpentane
(c)
PROBLEM4-31 Draw three isomers of trans-1,2-dichlorocyclobutane, and label them as either constitutional isomers or stereoisomers.
PROBLEM4-32 Identify each pair of relationships among the –OH groups in glucose (red–blue, red–green, red–black, blue–green, blue–black, green–black) as cis or trans.
PROBLEM4-33 Draw 1,3,5-trimethylcyclohexane using a hexagon to represent the ring. How many cis–trans stereoisomers are possible?
Cycloalkane Conformation and Stability
PROBLEM4-34 Hydrocortisone, a naturally occurring hormone produced in the adrenal glands, is often used to treat inflammation, severe allergies, and numerous other conditions. Is the indicated −OH group axial or equatorial?
PROBLEM4-35 A 1,2-cis disubstituted cyclohexane, such as cis-1,2-dichlorocyclohexane, must have one group axial and one group equatorial. Explain.
PROBLEM4-36 A 1,2-trans disubstituted cyclohexane must have either both groups axial or both groups equatorial. Explain.
PROBLEM4-37 Why is a 1,3-cis disubstituted cyclohexane more stable than its trans isomer?
PROBLEM4-38 Which is more stable, a 1,4-trans disubstituted cyclohexane or its cis isomer?
PROBLEM4-39 cis-1,2-Dimethylcyclobutane is less stable than its trans isomer, but cis-1,3-dimethylcyclobutane is more stable than its trans isomer. Draw the most stable conformations of both, and explain.
PROBLEM4-40 From the data in Figure 4.13 and Table 4.1, estimate the percentages of molecules that have their substituents in an axial orientation for the following compounds:
(a) Isopropylcyclohexane
(b) Fluorocyclohexane
(c) Cyclohexanecarbonitrile, C6H11CN
PROBLEM4-41 Assume that you have a variety of cyclohexanes substituted in the positions indicated. Identify the substituents as either axial or equatorial. For example, a 1,2-cis relationship means that one substituent must be axial and one equatorial, whereas a 1,2-trans relationship means that both substituents are axial or both are equatorial.
(a) 1,3-Trans disubstituted (b) 1,4-Cis disubstituted (c) 1,3-Cis disubstituted
(d) 1,5-Trans disubstituted (e) 1,5-Cis disubstituted (f) 1,6-Trans disubstituted
Cyclohexane Conformational Analysis
PROBLEM4-42 Draw the two chair conformations of cis-1-chloro-2-methylcyclohexane. Which is more stable, and by how much?
PROBLEM4-43 Draw the two chair conformations of trans-1-chloro-2-methylcyclohexane. Which is more stable?
PROBLEM4-44 Galactose, a sugar related to glucose, contains a six-membered ring in which all the substituents except the –OH group, indicated below in red, are equatorial. Draw galactose in its more stable chair conformation.
PROBLEM4-45 Draw the two chair conformations of menthol, and tell which is more stable.
PROBLEM4-46 There are four cis–trans isomers of menthol (Problem 4-45), including the one shown. Draw the other three.
PROBLEM4-47 The diaxial conformation of cis-1,3-dimethylcyclohexane is approximately 23 kJ/mol (5.4 kcal/mol) less stable than the diequatorial conformation. Draw the two possible chair conformations, and suggest a reason for the large energy difference.
PROBLEM4-48 Approximately how much steric strain does the 1,3-diaxial interaction between the two methyl groups introduce into the diaxial conformation of cis-1,3-dimethylcyclohexane? (See Problem 4-47.)
PROBLEM4-49 In light of your answer to Problem 4-48, draw the two chair conformations of 1,1,3-trimethylcyclohexane and estimate the amount of strain energy in each. Which conformation is favored?
PROBLEM4-50 One of the two chair structures of cis-1-chloro-3-methylcyclohexane is more stable than the other by 15.5 kJ/mol (3.7 kcal/mol). Which is it? What is the energy cost of a 1,3-diaxial interaction between a chlorine and a methyl group?
General Problems
PROBLEM4-51 We saw in Problem 4-20 that cis-decalin is less stable than trans-decalin. Assume that the 1,3-diaxial interactions in cis-decalin are similar to those in axial methylcyclohexane [that is, one CH2↔H interaction costs 3.8 kJ/mol (0.9 kcal/mol)], and calculate the magnitude of the energy difference between cis- and trans-decalin.
PROBLEM4-52 Using molecular models as well as structural drawings, explain why trans-decalin is rigid and cannot ring-flip whereas cis-decalin can easily ring-flip.
PROBLEM4-53 trans-Decalin is more stable than its cis isomer, but cis-bicyclo[4.1.0]heptane is more stable than its trans isomer. Explain.
PROBLEM4-54 As mentioned in Problem 3-53, the statin drugs, such as simvastatin (Zocor), pravastatin (Pravachol), and atorvastatin (Lipitor) are the most widely prescribed drugs in the world.
(a) Are the two indicated bonds on simvastatin cis or trans?
(b) What are the cis/trans relationships among the three indicated bonds on pravastatin?
(c) Why can’t the three indicated bonds on atorvastatin be identified as cis or trans?
PROBLEM4-55 myo-Inositol, one of the isomers of 1,2,3,4,5,6-hexahydroxycyclohexane, acts as a growth factor in both animals and microorganisms. Draw the most stable chair conformation of myo-inositol.
PROBLEM4-56 How many cis–trans stereoisomers of myo-inositol (Problem 4-55) are there? Draw the structure of the most stable isomer.
PROBLEM4-57 Julius Bredt, discoverer of the structure of camphor, proposed in 1935 that bicycloalkenes such as 1-norbornene, which have a double bond to a bridgehead carbon, are too strained to exist. Explain. (Making a molecular model will be helpful.
PROBLEM4-58 Tell whether each of the following substituents on a steroid is axial or equatorial. (A substituent that is “up” is on the top side of the molecule as drawn, and a substituent that is “down” is on the bottom side.
(a) Substituent up at C3 (b) Substituent down at C7 (c) Substituent down at C11
PROBLEM4-59 Amantadine is an antiviral agent that is active against influenza type A infection. Draw a three-dimensional representation of amantadine, showing the chair cyclohexane rings.
PROBLEM4-60 There are two different isomers named trans-1,2-dimethylcyclopentane. Similarly, you have two different appendages called hands. What is the relationship between them? (We’ll explore this kind of isomerism in the next chapter.)
PROBLEM4-61 Ketones react with alcohols to yield products called ketals. Why does the all-cis isomer of 4-tert-butyl-1,3-cyclohexanediol react readily with acetone and an acid catalyst to form a ketal, but other stereoisomers do not react? In formulating your answer, draw the more stable chair conformations of all four stereoisomers and the product ketal for each one.
PROBLEM4-62 Alcohols undergo an oxidation reaction to yield carbonyl compounds when treatment with CrO3. For example, 2-tert-butylcyclohexanol gives 2-tert-butylcyclohexanone. If axial −OH groups are generally more reactive than their equatorial isomers, which do you think reacts faster, the cis isomer of 2-tert-butylcyclohexanol or the trans isomer? Explain.
PROBLEM4-63 In the next chapter we’ll look at cycloalkanes—saturated cyclic hydrocarbons—and we’ll see that the molecules generally adopt puckered, nonplanar conformations. Cyclohexane, for instance, has a puckered shape like a lounge chair rather than a flat shape. Why?
PROBLEM4-63 We’ll see in the next chapter that there are two isomeric substances, both named 1,2-dimethylcyclohexane. Explain.