# 4.E: Alkanes (Exercises)

Exercise 4-1 Use the data of Tables 4-1 and 4-2 to estimate the boiling points of tetradecane, heptadecane, 2-methylhexane, and 2,2-dimethylpentane.

Exercise 4-2 Write detailed structures and predict which compound in each pair would have (1) the lower boiling point and (2) the higher water solubility.

a. $$\ce{H_2NCH_2CH_2NH_2}$$, $$\ce{H_3CCH_2CH_2CH_3}$$
b. $$\ce{CH_3OCH_3}$$, $$\ce{CH_3CH_2OH}$$
c. $$\ce{CH_3CH_2CH_2CH_2OH}$$, $$\ce{(CH_3)_2COH}$$
d. $$\ce{CH_3CO_2H}$$, $$\ce{HCO_2CH_3}$$
e. $$\ce{CH_3(CH_2)_6CO_2H}$$, $$\ce{CH_3(CH_2)_7CO_2H}$$

Exercise 4-3 The heat of combustion of 1 mole of liquid decane to give carbon dioxide and liquid water is $$1620.1 \: \text{kcal}$$. The heat of vaporization of decane at $$25^\text{o}$$ is $$11.7 \: \text{kcal mol}^{-1}$$. Calculate the heat of combustion that would be observed for all the participants in the vapor phase.

Exercise 4-4 Kilogram for kilogram, would the combustion of gaseous methane or of liquid decane (to $$\ce{CO_2}$$ and liquid water) give more heat?

Exercise 4-5 Use the bond-energy table (4-3) to calculate $$\Delta H^0$$ for the following reactions in the vapor phase at $$25^\text{o}$$:

a. $$\ce{CH_3CH_2CH_3} + 5 \ce{O_2} \rightarrow 3 \ce{CO_2} + 4 \ce{H_2O}$$
b. $$\ce{CH_4} + \frac{3}{2} \ce{O_2} \rightarrow \ce{CO} + 2 \ce{H_2O}$$
c. $$\ce{CO} + 3 \ce{H_2} \rightarrow \ce{CH_4} + \ce{H_2O}$$

Exercise 4-6 Calculate $$\Delta H^0$$ for $$\ce{C} \left( s \right) \rightarrow \ce{C} \left( g \right)$$ from the heat of combustion of 1 gram-atom of carbon to $$\ce{CO_2}$$ as $$94.05 \: \text{kcal}$$, and the bond energies in Table 4-3.

Exercise 4-7 The dissociation $$\ce{HO-H} \rightarrow \ce{HO} \cdot + \ce{H} \cdot$$ for gaseous water at $$25^\text{o}$$ has $$\Delta H^0$$ equal to $$+119.9 \: \text{kcal}$$. What is $$\Delta H^0$$ for dissociation of the $$\ce{O-H}$$ bond of $$\ce{HO} \cdot$$?

Exercise 4-8 Methane reacts slowly with bromine atoms and it has been established that $$\Delta H^0$$ for the following reaction is $$17 \: \text{kcal mol}^{-1}$$ of $$\ce{CH_4}$$:

$\ce{CH_4} + \ce{Br} \cdot \rightarrow \ce{CH_3} \cdot + \ce{HBr} \: \: \: \: \: \Delta H^0 = +17 \: \text{kcal}$

a. Calculate the $$\ce{C-H}$$ bond strength of $$\ce{CH_4}$$ from this result and any other required bond energies you choose to employ.

b. The heat of the following reaction in the vapor state is $$192 \: \text{kcal mol}^{-1}$$ of $$\ce{CH_4}$$:

$\ce{CH_4} + 2 \ce{O_2} \rightarrow \ce{CO_2} + 2 \ce{H_2O} \left( g \right) \: \: \: \: \: \Delta H^0 = -192 \: \text{kcal}$

From $$\Delta H^0$$ and any other required bond energies in Table 4-3, compute a second $$\ce{C-H}$$ bond-energy value for methane.

c. Consider whether the two $$\ce{C-H}$$ bond-energy values obtained in Parts a and b should be the same in theory and experiment, provided that the experimental error is small.

Exercise 4-9 Calculate the pressures of each of the participants at equilibrium in the reaction $$\ce{CH_4} + \ce{Cl_2} \rightarrow \ce{CH_3Cl} + \ce{HCl}$$ when $$\ce{CH_4}$$ and $$\ce{Cl_2}$$ are mixed, each at one atmosphere pressure. Assume that $$K_\text{eq} = 10^{18}$$.

Exercise 4-10

a. Calculate $$\Delta H^0$$ from bond energies for the conversion of 1-hexene to cyclohexane at $$25^\text{o}$$ and from this, with $$\Delta S^0$$ as $$-20.7 \: \text{e.u. mol}^{-1}$$, calculate the equilibrium constant $$K_\text{eq}$$ from Equation 4-2. For comparison, calculate the equilibrium constant that would be expected if the degrees of disorder of the reactants and the products were equal (i.e., $$\Delta S^0 = 0$$).

b. How large can $$\Delta S^0$$ be at $$25^\text{o}$$ for a reaction before our $$\pm 15 \: \text{kcal}$$ rule starts to give incorrect answers?

Exercise 4-11 Knowing that the equilibrium constant $$K_\text{eq}$$ for formation of nonane from solid carbon and hydrogen gas is $$4.7 \times 10^{-5}$$, explain why liquid nonane does not forthwith decompose into its elements.

Exercise 4-12 A possible mechanism for the reaction of chlorine with methane would be to have collisions by which a chlorine molecule removes a hydrogen according to the following scheme:

Use appropriate bond energies to assess the likelihood of this reaction mechanism. What about the possibility of a similar mechanism with elemental fluorine and methane?

Exercise 4-13 Calculate $$\Delta H^0$$ for each of the propagation steps of methane chlorination by a mechanism of the type

Compare the relative energetic feasibilities of these chain-propagation steps with those of other possible mechanisms.

Exercise 4-14 Show how the data in Table 4-6 might be extrapolated to predict the principal product to be expected from the vapor-phase, light-induced monochlorination of 1,1-dimethylcyclopropane.

Exercise 4-15* Use the data given in Section 4-5A for the percentages of the monochlorides formed in the vapor-phase chlorination of 2-methylbutane at $$300^\text{o}$$ and take into account the statistical factors for the different numbers and kinds of hydrogens in answering the following:

a. From the ratio of 1-chloro-2-methylbutane to 1-chloro-3-methylbutane formed, what can you say about the $$\ce{C-H}$$ bond strengths at the $$\ce{CH_3}$$ carbons?

b. Calculate the ratio of rates of attack of $$\ce{Cl} \cdot$$ on the individual hydrogens attached to primary ($$\ce{C_1}$$ and $$\ce{C_4}$$), secondary $$\left( \ce{C_3} \right)$$, and tertiary $$\left( \ce{C_2} \right)$$ carbons of 2-methylbutane. Check these ratios by showing they are consistent with the composition of the overall chlorination product.

c. Use your relative rate ratios from Part b to calculate the ratios of isomers to be expected in the thermal $$\left( 300^\text{o} \right)$$ monochlorination of (a) propane, (b) 2-methylpropane, and (c) 2,2-dimethylbutane. Show your method in detail.

Exercise 4-16

a. Write equations to show reasonable radical-chain initiation, propagation, and termination steps in the monobromination of 2-methylbutane shown in Section 4-5A. Explain clearly why the products of chain termination are obtained in trace amounts only.

b. Use bond energies of Tables 4-3 and 4-6 and bond-dissociation energies of $$63 \: \text{kcal}$$ for tertiary $$\ce{C-Br}$$ and $$68 \: \text{kcal}$$ for secondary $$\ce{C-Br}$$ bonds to estimate $$\Delta H^0$$ for each of the propagation steps leading to the two observed products. Which propagation step in the formation of 2-bromo-2-methylbutane is expected to be the slow step?

c. Calculate the relative rates of attack of bromine atoms at the tertiary $$\ce{C-H}$$ versus the secondary $$\ce{C-H}$$ bonds from the product composition in the bromination of 2-methylbutane. Are the relative rates qualitatively consistent with what you would expect based on the $$\Delta H^0$$ data?

Exercise 4-17* The peroxide-induced bromination of methylbenzene with bromotrichloromethane gives bromomethylbenzene and trichloromethane:

Write initiation, propagation, and termination steps for this radical-chain reaction. Estimate a $$\Delta H^0$$ for the overall reaction using the bond-dissociation energies of Table 4-6. Would you expect bromotrichloromethane to be a selective or nonselective brominating agent? Explain.

Exercise 4-18* tert-Butyl hypochlorite is a useful chlorinating agent. On irradiation, or with chemical initiators, this reagent with methylbenzene gives chloromethylbenzene:

Write a possible mechanism for the reaction, showing the propagation steps with $$\ce{(CH_3)_3CO} \cdot$$ as the chain-propagating radical. Use the bond-dissociation energies of Table 4-6 to determine whether your mechanism is energetically and kinetically feasible. Assume the $$\ce{O-Cl}$$ bond-dissociation energy of tert-butyl hypochlorite is $$61 \: \text{kcal mol}^{-1}$$.

Exercise 4-19*

a. $$\ce{N}$$-Bromosuccinimide (NBS) is an excellent brominating reagent and is used widely to prepare bromoalkenes from alkenes (Wohl-Ziegler reaction):

The reaction is initiated with chemical initiators (peroxides) and is as selective as bromination with molecular bromine. Write plausible propagation steps (three of them) for this reaction, given the fact that the actual brominating agent appears to be molecular bromine that is generated from NBS by $$\ce{HBr}$$.

b. What products would you expect to be formed on bromination of 2-methylbutane with $$\ce{N}$$-bromosuccinimide?

Exercise 4-20 Calculate $$\Delta H^0$$ for the following reactions in the vapor state at $$25^\text{o}$$, using the bond energies of Table 4-3:

a. $$2 \ce{CH_4} + 7 \ce{Cl_2} \rightarrow \ce{CCl_3-CCl_3} + 8 \ce{HCl}$$
b. $$\ce{CH_3CH_3} + \frac{7}{2} \ce{O_2} \rightarrow 2 \ce{CO_2} + 3 \ce{H_2O}$$
c. $$\ce{CH_3CH_3} + \ce{H_2} \rightarrow 2 \ce{CH_4}$$
d. $$\ce{CH_3CH_3} + \ce{Br_2} \rightarrow 2 \ce{CH_3Br}$$
e. $$\ce{CH_4} + 2 \ce{Cl_2} \rightarrow \ce{C} \left( g \right) + 4 \ce{HCl}$$

Exercise 4-21

a. Would $$\Delta H^0$$ for Exercise 4-20e be greater, or less if $$\ce{C}$$ (solid) were the reaction product? Explain.

b. What are the implications of the heats of reaction determined in Exercise 4-20c and d with regard to the "saturated" character of ethane?

Exercise 4-22 A $$\ce{C-F}$$ bond energy can be computed from thermochemical studies of the vapor-phase reaction

$\ce{CH_4} + 4 \ce{F_2} \rightarrow \ce{CF_4} + 4 \ce{HF} \: \: \: \: \: \Delta H^0 = -460 \: \text{kcal}$

Show how the $$\Delta H^0$$ value for this reaction may be used to calculate the energy of the $$\ce{C-F}$$ bond if all the other bond energies are known.

Exercise 4-23 The heat of combustion of liquid benzene to give carbon dioxide and liquid water is $$780.96 \: \text{kcal mol}^{-1}$$. The heat required to vaporize one mole of benzene is $$8.2 \: \text{kcal}$$ and one mole of water $$10.5 \: \text{kcal}$$. Calculate the heat of combustion of benzene from the bond energies given in Table 4-3 and determine the extent to which benzene is more, or less, stable than expected from bond energies shown.

Exercise 4-24 Suppose we assume the following bond energies $$\left( \text{kcal} \right)$$:

$\begin{array}{crcr} \ce{\equiv C-H} & 120 & \ce{C \equiv C} & 230 \\ \ce{=C-H} & 104 & \ce{C=C} & 167 \\ \ce{-C-H} & 98 & \ce{C-C} & 88 \end{array}$

What corresponding values would we have to assign to $$\ce{C-Br}$$ bonds if the $$\Delta H^0$$ values calculated for the reactions $$\ce{HC \equiv CH} + \ce{Br_2} \rightarrow \ce{BrHC=CHBr}$$ and $$\ce{BrHC=CHBr} + \ce{Br_2} \rightarrow \ce{CHBr_2CHBr_2}$$ are to be exactly the same as those calculated using only the bond energies from Table 4-3? Show your reasoning.

Exercise 4-25 Explain why there is an increasingly poor correlation between $$\Delta H^0$$ and the equilibrium constant $$K_\text{eq}$$ for the formation of methane, propane, hexane, and nonane from solid carbon and hydrogen gas (Table 4-5).

Exercise 4-26 The $$\Delta H^0$$ values for formation of cyclohexane from 1-hexene and of hydrogen chloride from hydrogen and chlorine differ by less than $$3 \: \text{kcal mol}^{-1}$$ but the respective equilibrium constants are different by a factor of $$10^7$$. Explain.

Exercise 4-27* The entropy change $$\Delta S^0$$ for the formation of chloroethane by chlorination of ethane is $$+0.5 \: \text{e.u.}$$, and for the formation of chloroethane by combination of hydrogen chloride with ethene $$\Delta S^0$$ is $$-31 \: \text{e.u.}$$ Explain.

$\begin{array}{ll} \ce{CH_3-CH_3} + \ce{Cl_2} \rightarrow \ce{CH_3CH_2Cl} + \ce{HCl} & \Delta S^0 = +0.5 \: \text{e.u.} \\ \ce{CH_2=CH_2} + \ce{HCl} \rightarrow \ce{CH_3CH_2Cl} & \Delta S^0 = -31 \: \text{e.u.} \end{array}$

Exercise 4-28 Investigate the energies $$\left( \Delta H^0 \right)$$ of possible chain mechanisms for the light-induced monobromination of methane and compare with those for chlorination. What are the prospects for iodination of methane?

Exercise 4-29 The heat of combustion of cyclopropane, $$\ce{(CH_2)_3}$$, to give carbon dioxide and liquid water is $$499.8 \: \text{kcal mol}^{-1}$$. Show how this value, assuming normal $$\ce{C-H}$$ bond strengths, can be used to calculate the average $$\ce{C-C}$$ bond energy of cyclopropane.

Exercise 4-30 Write a mechanism analogous to that usually written for methane chlorination that would lead to production of hexachloroethane as in Exercise 4-20a. (This reaction is used for commercial production of hexachloroethane.)

Exercise 4-31 With reference to the data in Table 4-6, draw the structure(s) of the major organic product(s) to be expected from hydrogen abstraction in the following reactions:

a. $$\ce{(CH_3)_3CH} + \ce{Br_2} \overset{\text{light}}{\longrightarrow}$$

b.

c.

Exercise 4-32 Use the data in Table 4-6 to predict the products of the following reactions. Indicate any ambiguities that you encounter as the result of insufficient data.

a. $$\ce{CH_2=CHCH_3} + \ce{Cl} \cdot \rightarrow$$

b. $$\ce{CCl_3Br} + \ce{CH_3CH_2} \cdot \rightarrow$$

c. $$\ce{CH_3SH} + \ce{CH_3CH_2} \cdot \rightarrow$$

d. $$\ce{H_2O_2} \overset{\text{heat}}{\longrightarrow}$$

Exercise 4-33* The oxidation of hydrocarbons by atmospheric oxygen to give hydroperoxides is called autoxidation:

$\ce{RH} + \ce{O_2} \rightarrow \ce{ROOH}$

It is a detrimental reaction because it leads to the deterioration of organic compounds exposed to air (e.g., rubber cracking). Furthermore, the product, $$\ce{ROOH}$$, in common with virtually all organic compounds with $$\ce{-O-O}-$$ bonds, has the potential of undergoing rapid decomposition on heating, which in fact may occur with explosive violence.

The mechanism of autoxidation is a radical-chain process that is initiated by formation of a hydrocarbon radical, $$\ce{R} \cdot$$.

a. Write the propagation steps for this reaction, using $$\ce{R} \cdot$$ or $$\ce{ROO} \cdot$$ as the chain-propagating radical. How do you expect that antioxidants added to materials such as rubber act to help protect them from autoxidation (see Section 4-4D).

b. Use the data of Table 4-6 to determine the most favorable products of autoxidation of cyclohexene and methylbenzene $$\left( \ce{C_6H_5CH_3} \right)$$.

c. It is extremely hazardous to store some organic chemicals for long periods of time in unsealed containers exposed to air and light. Aldehydes and ethers are particularly dangerous chemicals to store in this way. Explain why this should be so.

Exercise 4-34* The first step in preparing the very useful elastomer Hypalon involves treating a mixture of long-chain alkanes, $$\ce{H(CH_2)}_n \ce{H}$$, where $$n = 50$$-$$200$$, with sulfuryl chloride $$\left( \ce{SO_2Cl_2} \right)$$ in the presence of substances that can initiate radical-chain chlorination, as described in Section 4-5B. The product molecules contain many $$\ce{C-Cl}$$ bonds and a few $$\ce{C-SO_2-Cl}$$ bonds, the latter of which are subsequently used in a curing step to improve the physical properties. How can the chain mechanism for chlorination with $$\ce{SO_2Cl_2}$$ be modified to account for the formation of $$\ce{C-SO_2-Cl}$$ bonds?

Exercise 4-35* Explain why the product distribution in the chlorination of propane by sulfuryl chloride is expected to differ according to whether the hydrogen-abstraction step is accomplished by $$\ce{Cl} \cdot$$ or $$\cdot \ce{SO_2Cl}$$.

Exercise 4-36* tert-Butyl hypobromite is a radical brominating agent that is similar to tert-butyl hypochlorite (Exercise 4-18*), but is less easily prepared than the hypochlorite. A good substitute, provided radical bromination is possible, is a mixture of $$\ce{BrCCl_3}$$ and $$ce{(CH_3)_3COCl}$$. Thus, bromination of cyclohexene results if a high ratio of bromotrichloromethane to hypochlorite is used.

Suggest how this reaction is initiated and propagated, and explain why it is necessary to have an excess of bromotrichloromethane.

Exercise 4-37* Use the data of Table 4-6 and tin-hydrogen and tin-chlorine bond energies of $$80 \: \text{kcal}$$ and $$120 \: \text{kcal}$$, respectively, to determine the overall feasibility of the following reaction:

a. Assume the reaction proceeds by a radical-chain mechanism and work out energetically feasible initiation and propagation steps.

b. Draw energy diagrams like those shown in Figure 4-4 that correspond to each of the propagation steps. Indicate clearly on your diagrams which step would be expected to have the highest activation energy (that is, be the slower step), which point on your curves corresponds to the transition state, and which energy differences correspond to the energy change $$\left( \Delta G^0 \right)$$ in that step of the reaction (assume $$T \Delta S^0 = 0$$).

## 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."