Advanced Organic Chemistry. Part A. Structure and Mechanisms

Francis A. Carey, Richard J. Sundberg

Chapter 3 Structural Effects on Stability and Reactivity - all with Video Answers

Educators

Chapter Questions

Problem 1

Use thermochemical relationships to obtain the requested information.
a. The $\Delta H_{f}$ of cyclohexane, cyclohexene, and benzene are, respectively, $-29.5$, $-1.1$, and $+18.9 \mathrm{kcal} / \mathrm{mol}$. Use this information to estimate the resonance stabilization of benzene.
b. Calculate $\Delta H$ for the air oxidation of benzaldehyde to benzoic acid, given that the $\Delta H_{f}$ of benzaldehyde and benzoic acid are $-8.8$ and $-70.1 \mathrm{kcal} / \mathrm{mol}$, respectively.
c. Using the appropriate heats of formation from Table 3.1, calculate the heat of hydrogenation $\Delta H_{\mathrm{H} 2}$ for 2-methyl-1-pentene.

Muhammad Ahsan

Numerade Educator

02:35

Problem 2

Addition of methylmagnesium bromide to 2 -methylcyclohexanone, followed by iodine-catalyzed dehydration of the resulting alcohol gave three alkenes in the ratio $\mathrm{A}: \mathrm{B}: \mathrm{C}=3: 31: 66$. Each alkene gave a mixture of cis- and trans-1,2dimethylcyclohexane upon catalytic hydrogenation. When the alkene mixture was heated with a small amount of sulfuric acid, the ratio of $\mathrm{A}: \mathrm{B}: \mathrm{C}$ changed to $0.0: 15: 85$. Assign structures to $\mathrm{A}, \mathrm{B}$, and $\mathrm{C}$.

Raghvendra Singh

Numerade Educator

01:29

Problem 3

Measurement of the equilibrium constant for the interconversion of the dithiete 3-A and the dithione $\mathbf{3 - B}$ at several temperatures gave the data below. Calculate $\Delta G, \Delta H$, and $\Delta S$.
a. Calculate the activation parameters $\left(\Delta H^{\ddagger}\right.$ and $\left.\Delta S^{\ddagger}\right)$ at $40^{\circ} \mathrm{C}$ for the acetolysis of 3 -chlorobenzyl tosylate from the data given below:
b. Calculate the activation parameters $\left(E_{a}, \Delta H^{\ddagger}\right.$, and $\left.\Delta S^{\ddagger}\right)$ at $100^{\circ} \mathrm{C}$ from the

Hunza Gilgit

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07:04

Problem 4

a. Calculate the activation parameters $\left(\Delta H^{+}\right.$and $\left.\Delta S^{+}\right)$at $40^{\circ} \mathrm{C}$ for the acetolysis of 3-chlorobenzyl tosylate from the data given below:
(DIAGRAM CAN'T COPY)
$$
\begin{array}{cc}
\hline \text { Temperature }\left({ }^{\circ} \mathrm{C}\right) & k \times 10^5 \mathrm{~s}^{-1} \\
\hline 25.0 & 0.0136 \\
40.0 & 0.085 \\
50.1 & 0.272 \\
58.8 & 0.726 \\
\hline
\end{array}
$$
(DIAGRAM CAN'T COPY)
b. Calculate the activation parameters ( $E_\alpha, \Delta H^1$, and $\Delta S^2$ ) at $100^{\circ} \mathrm{C}$ from the data given for the reaction below.
$$
\begin{array}{cr}
\hline \text { Temperature }\left({ }^{\circ} \mathrm{C}\right) & k \times 10^4 \mathrm{~s}^{-1} \\
\hline 60.0 & 0.30 \\
70.0 & 0.97 \\
75.0 & 1.79 \\
80.0 & 3.09 \\
90.0 & 8.92 \\
95.0 & 15.90 \\
\hline
\end{array}
$$

David Collins

Numerade Educator

02:34

Problem 5

2-Vinylmethylenecyclopropane rearranges thermally to 3-methylenecyclopentene. In the gas phase, the $E_{a}$ is $26.0 \mathrm{kcal} / \mathrm{mol}$, which is close to the estimated energy required for rupture of the $\mathrm{C}(2)-\mathrm{C}(3)$ bond. Two possible mechanisms for this rearrangement are:
a. Sketch qualitative reaction energy profiles for each process, based on the information given.
b. How might an isotopic labeling experiment distinguish between these mechanisms?

Umut Ozuguzel

Texas Tech University

01:56

Problem 6

The Baeyer-Villiger oxidation of ketones to esters (or lactones) occurs by the following mechanism:
For endo-substituted bicyclo[2.2.1]heptan-7-ones, the product ratios shown below are observed. Account for the effect of the substituents.

Mary Shields

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05:09

Problem 7

a. Create Hammett plots versus $\sigma$ and $\sigma^{-}$for the reaction shown below from the data given. Determine the value of $\rho$ and compare the correlation with the two sets of substituent constants.
b. The pseudo-first order rate constants for acid-catalyzed hydration of substituted styrenes in $3.5 \mathrm{M} \mathrm{HClO}_{4}$ at $25^{\circ} \mathrm{C}$ are given. Plot the data against $\sigma$ and $\sigma^{+}$and determine $\rho$ and $\rho^{+}$. Interpret the significance of the results.
c. The acidity of a series of substituted benzyldimethylammonium ions has been measured. Determine whether these data are correlated by the Hammett equation using $\sigma$ and $\sigma^{+}$. What is the value of $\rho$ ? What interpretation do you put on its sign and magnitude?

Raymond Matshanda

Numerade Educator

02:12

Problem 8

Write the rate law that would apply to the rate of product formation for each of the following reaction mechanisms.

Nima Gharibi

Numerade Educator

01:24

Problem 9

One method of estimating "aromatic stabilization" is to compare the heats of hydrogenation of cyclic conjugated systems with an acyclic molecule having the same number of conjugated bonds and $\pi$ electrons. The table below gives the AM1 calculated heat of hydrogenation for various cyclic conjugated systems and for the corresponding polyene $\left[\Delta H_{\mathrm{H} 2}\right.$ (ref.) $]$ For example, for benzene the comparison would be with $1,3,5$-hexatriene. Calculate the aromatic stabilization or antiaromatic destabilization for each system. What conclusions do you draw? Relate your conclusions to HMO theory in Chapter 1 . How does this computation deal with "strain?"

Emily Himsel

Numerade Educator

05:17

Problem 10

A number of experimentally inaccessible $\Delta H$ values have been computed at the G2(MP2) level and are given below in kcal/mol. Taking for comparison $\Delta H_{\mathrm{H} 2}$ of ethene as $-32.4 \mathrm{kcal} / \mathrm{mol}$, of l-butene as $-30.3 \mathrm{kcal} / \mathrm{mol}$, and of cyclopropane to propane as $-38.6 \mathrm{kcal} / \mathrm{mol}$, indicate what factors lead to the observed differences in each step of the sequences shown.

Mukesh Devi

Numerade Educator

00:40

Problem 11

The Cannizzaro reaction is a disproportionation that takes place in strongly basic solution and converts aromatic aldehydes to the corresponding benzyl alcohol and sodium benzoate.
$$
2 \mathrm{ArCH}=\mathrm{O}+\mathrm{NaOH} \longrightarrow \mathrm{ArCH}_{2} \mathrm{OH}+\mathrm{ArCO}_{2} \mathrm{Na}
$$
Several mechanisms, all of which involve a hydride transfer as a key step, have been postulated. On the basis of the following information, formulate one or more mechanisms that would be consistent with all the data provided. Indicate the significance of each observation with respect to the mechanism(s) you postulate.
1. When the reaction is carried out in $\mathrm{D}_{2} \mathrm{O}$, the benzyl alcohol contains no deuterium in the methylene group.
2. When the reaction is carried out in $\mathrm{H}_{2}{ }^{18} \mathrm{O}$, both the benzyl alcohol and sodium benzoate contain ${ }^{18} \mathrm{O}$.
3. The overall reaction rate is given by the expression
$$
\text { Rate }=k_{\mathrm{obs}}[\mathrm{Ph} \mathrm{CH}=\mathrm{O}]^{2}\left[{ }^{-} \mathrm{OH}\right]
$$
4. The rates of substituted benzaldehydes are correlated by a Hammet LFER with $\rho=+3.76$
5. The solvent isotope effect $k_{\mathrm{D} 2 \mathrm{O}} / k_{\mathrm{H} 2 O}=1.90$

Nikhil Choudhary

Numerade Educator

05:36

Problem 12

A mechanism for alkene arylation catalyzed by Pd(II) is outlined below. The isotope effect $k_{\mathrm{H}} / k_{\mathrm{D}}$ was found to be 5 when benzene- $d_{6}$ was used. There was no isotope effect when styrene- $\beta-d_{2}$ was used. Which steps in the reaction mechanism could be rate determining, given this information on isotope effects?

Ian Kaigh

Numerade Educator

04:08

Problem 13

Comparison of the gas phase acidity of substituted benzoic acids with $\mathrm{p} K_{a}$ values in aqueous solutions reveals some interesting comparisons.
1. The trend in acidity as a function of substituent is the same for both gas phase and aqueous solution, but the substituent effects are much stronger in the gas phase. (The $\Delta \Delta G$ for any give substituent is about 10 times larger in the gas phase.)
2. Whereas acetic and benzoic acid are of comparable acidity in water, benzoic acid is considerably more acidic in the gas phase. $\left(\mathrm{p} K_{a}\right.$ values are $4.75$ and $4.19$, respectively; and $\Delta G$ of ionization is $8.6 \mathrm{kcal} / \mathrm{mol}$ more positive for acetic acid.)
3. While the substituent effect in the gas phase is nearly entirely an enthalpy effect, it is found that in solution, the substituent effect is largely due to changes in $\Delta S$.

Aadit Sharma

Numerade Educator

00:59

Problem 14

Discuss how difference between the gas phase and solution can cause these effects. It has been found that the ${ }^{13} \mathrm{C}$ chemical shift of aromatic ring carbons are a good indicator of the intrinsic electron-releasing or electron-withdrawing capacity of substituents, without any perturbation from approaching reagents. Such perturbation is always present when substituent effects are measured on the basis ofreactivity. The changes in chemical shifts of $\mathrm{C}(4)$ in some substituted benzenes are given below. Plot these against $\sigma, \sigma^{+}$, and $\sigma^{-}$. What conclusions do you draw from these plots in regard to the mix of resonance and polar components

Lottie Adams

Numerade Educator

00:44

Problem 15

The ionization constants ( $\mathrm{p} K_{a}$ ) of 4-substituted pyridines have been measured, as have the $\Delta H$ of ionization at $25^{\circ} \mathrm{C}$. Calculate $\Delta S$ for each ionization. Compare the contribution of $\Delta H$ and $\Delta S$ to the free energy of ionization. Test the data for linear free-energy correlations. Are the LFER dominated by the $\Delta H$ or $\Delta S$ term?

Nidhi Singhi

Numerade Educator

12:39

Problem 16

a. Norbornene, norbornadiene, nortricyclane, and quadricyclane can all be hydrogenated to norbornane. The heats of hydrogenation are given in the chart. These data allow calculation of $\Delta H_{f}$ for the other derivatives and the results are given as Exp. in the table. The table also gives $\Delta H_{f}$ values calculated for each compound by $\mathrm{MM}$ and three semiemirical $\mathrm{MO}$ methods. Compare the accuracy of the semiempirical methods in predicting the experimental heats of formation.
Subsequently, the same compounds were computed by ab initio and DFT methods. Isodesmic reactions were used to compare the $\Delta H_{f}$ of the compounds (except for G3(MP2), where atomization energies were used). Compare the ab initio and DFT results with the semiempirical results from Part (a).
c. Heats of hydrogenation have also been calculated from the semiempirical data. Since the heats of hydrogenation include the $\Delta H_{f}$ of $\mathrm{H}_{2}$, which is zero, they can be calculated as follows:
$$
\Delta H_{\mathrm{H} 2}=\Delta H_{f \text { product }}-\Delta H_{f \text { reactant }}
$$
This leads to the calculated $\Delta H_{\mathrm{H} 2}$ shown below. The $\Delta H_{\mathrm{H} 2}$ can also be calculated on a strain compensation basis:
$$
\Delta H_{\mathrm{H} 2}=\Delta H_{f \text { product }}-\Delta H_{f \text { reactant }}+\text { strain relief }
$$
The calculated values are included in the table. Compare the calculated and experimental results.

Chareen Guzman

Numerade Educator

05:51

Problem 17

The second-order rate constants for the reaction of a number of amines with benzyl chloride are tabulated below. Calculate $\Delta H^{\ddagger}$ and $\Delta S^{\ddagger}$ from the data.Compare the reactivity of the various amines. What trends and correlations between reactivity and $\Delta H^{\ddagger}$ do you note?

David Collins

Numerade Educator

04:07

Problem 18

Some data are given below for both gas phase $(\Delta G)$ and DMSO $(\mathrm{p} K)$ acidity of substituted toluenes, phenylacetonitriles, and phenylmalononitriles that illustrate the strongly acidifying effect of the cyano substituent. For each series, plot $\Delta G$ versus $\mathrm{p} K$. Do the plots show any evidence of a solvent attenuation effect; that is, do the substituent effects appear to be weaker in DMSO than in the gas phase?

Caroline Basil

Numerade Educator

03:28

Problem 19

The rate of thermal rearrangement of 3-aryl-2,2-dimethylmethylenecyclopropanes has been studied as a function of aryl substituents. Some of the data are given below. Examine the rate data for correlation with the Hammett $\sigma$-substituent constants. What conclusion do you draw about the mechanism?

Uma Kumari

Numerade Educator

15:47

Problem 20

The series of isodesmic reactions shown below has been calculated at the MP2/aug-cc-PVDZ level. The results are in good agreement with experimental gas phase proton affinity data.
Data are also available for the $\mathrm{p} K_{a}$ of mono-, di-, and tri-cyanomethane. These data suggest substantially less cumulative drop-off as compared to an acetyl substituent. The first acetyl group causes a substantially larger increase in acidity, whereas the second acetyl has a smaller effect.$\begin{array}{ccccccc} & & & & & 0 & 0 \\ & \mathrm{CH}_{4} & \mathrm{CH}_{3} \mathrm{CN} & \mathrm{CH}_{2}(\mathrm{CN})_{2} & \mathrm{CH}(\mathrm{CN})_{3} & \mathrm{CH}_{3} \mathrm{CCH}_{3} & \mathrm{CH}_{3} \mathrm{CCH}_{2} \mathrm{CCH}_{3} \\ \mathrm{pK} & 49.6 & 29.4 & 11.7 & -5.1 & 19.3 & 8.9\end{array}$ $\beta$-Cyano substituents also have a quite strong acidifying effect. A value of $29 \pm 6 \mathrm{kcal} / \mathrm{mol}$ has been estimated, as compared to $42 \mathrm{kcal} / \mathrm{mol}$ for $\alpha$-cyano. Structural computations find a shortening of the $\mathrm{C}(\alpha)$ - $\mathrm{CN}$ bond in $\alpha$-cyanoethyl anion but a lengthening of the $C(\beta)-C N$ bond in the $\beta$-cyanoethyl anion. What structural features of the CN might contribute to its anion stabilizing capacity, as compared with other EWG substituents such as acetyl.

Umut Ozuguzel

Texas Tech University

02:50

Problem 21

The diastereoselectivity of alkyl radical addition to substituted alkylidene malononitriles is a function of the size of the attacking radical when there is a bulky substituent at the $\gamma$-carbon. Conformational analysis of the reactant indicates that it prefers conformation a over b by $3.0 \mathrm{kcal} / \mathrm{mol}$. Suggest a TS structure, showing reactant conformation and reagent trajectory that is in accord with these results. Use the Curtin-Hammet principle (p. 296) to construct a reaction energy diagram that illustrates the product composition in terms of TS energy.

Madeline Currie

Numerade Educator

03:25

Problem 22

In the interpretation of substituent effects, consideration must be given as to whether the effect is primarily on the reactant or the product. Some data pertaining to the changes in some substituted benzoic acids, derived from PM3 computations, are given below. The calculated $\delta \Delta H$ for ionization in the gas phase is given, as are the charges of the $\mathrm{H}, \mathrm{CO}_{2} \mathrm{H}$, and $\mathrm{CO}_{2}^{-}$groups and the energy of the anion HOMO. Construct correlation plots of $\delta \Delta H$ with each of the structural properties and also against the values of $\sigma_{m}$ and $\sigma_{p}$ from Table $3.26 .$ What conclusions do you draw about the effects of substituents on $\mathrm{H}, \mathrm{CO}_{2} \mathrm{H}$, and $\mathrm{CO}_{2}^{-}$, and how would these results be reflected in relative acidity?

Lottie Adams

Numerade Educator

01:36

Problem 23

From the kinetic data below, calculate $\Delta H^{*}$ and $\Delta S^{*}$ for each nucleophilic substitution reaction with $n$-butyl tosylate in methanol and DMSO. What trends do you note in $\Delta H^{*}$ and how would you explain them? What trends do you note in $\Delta S^{*}$ and how would you explain them?

Amanda Hyde

Numerade Educator

01:36

Problem 24

Amanda Hyde

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