(a) Using the BDEs in Table 4-2 (p. 143), compute the

Free-radical chlorination of hexane gives very poor yields of 1-chlorohexane, while cyclohexane can be converted to chlorocyclohexane in good yield. (a) How do you account for this difference? (b) What ratio of reactants (cyclohexane and chlorine) would you use for the synthesis of chlorocyclohexane?

Each of the following proposed mechanisms for the free-radical chlorination of methane is wrong. Explain how the experimental evidence disproves each mechanism. 1. \(\mathrm{Cl}_{2}+\mathrm{hv} \rightarrow \mathrm{C} I_{2}^{*} \text { (an "activated" form of } \mathrm{Cl}_{2} \text { ) }\) \(\mathrm{C} I_{2}^{*}+\mathrm{CH}_{4} \rightarrow \mathrm{HCl}+\mathrm{CH}_{3} \mathrm{Cl}\) 2. \(\mathrm{CH}_{4}+\mathrm{hV} \rightarrow \mathrm{CH}_{3}+\mathrm{H}\) \(\mathrm{CH}_{3}+\mathrm{Cl}_{2} \rightarrow \mathrm{CH}_{3} \mathrm{Cl}+\mathrm{Cl}\) \(\mathrm{Cl}+\mathrm{H} \rightarrow \mathrm{HCl}\) Equation Transcription: Text Transcription: Cl2+hvCI2*(an "activated" form of Cl2) CI2*+CH4HCl+CH3Cl CH4+hvCH3+H CH3+Cl2CH3Cl+Cl Cl+HHCl

The following reaction has a value of \(\Delta G^{\circ}=-2.1 \mathrm{~kJ} / \mathrm{mol}(-0.50 \mathrm{kcal} / \mathrm{mol})\) \(\mathrm{CH}_{3} \mathrm{Br}+\mathrm{H}_{2} \mathrm{~S} \rightleftarrows \mathrm{CH}_{3} \mathrm{SH}+\mathrm{HBr}\) 1. Calculate \(\mathrm{K}_{\mathrm{eq}}\) at room temperature \(\left(25^{\circ} \mathrm{C}\right)\) for this reaction as written. 2. Starting with a 1 M solution of \(\mathrm{CH}_{3} \mathrm{Br} \text { and } \mathrm{H}_{2} \mathrm{~S}\) calculate the final concentrations of all four species at equilibrium. Equation Transcription: ? Text Transcription: \Delta G°=-2.1 kJ/mol (-0.50 kcal/mol) CH3Br+H2S? CH3SH+HBr Keq (25°C) CH3Br and H2S

Draw Lewis structures for the following free radicals. 1. The ethyl radical, \(\mathrm{CH}_{3} \mathrm{C}-\mathrm{CH}_{2}\) 2. The tert-butyl radical, \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}\) 3. The isopropyl radical (2-propyl radical) 4. The iodine atom Equation Transcription: Text Transcription: CH_3C-CH_2 (CH_3)_3C

Problem 2P (a) Write the propagation steps leading to the formation of dichloromethane (CH2Cl2)from chloromethane. (b) Explain why free-radical halogenation usually gives mixtures of products. (c) How could an industrial plant control the proportions of methane and chlorine to favor production of CCl4? To favor CH3Cl?

Iodination of alkanes using iodine \(\left(\mathrm{I}_{2}\right)\) is usually an unfavorable reaction. (See Problem 4-17, for example.) Tetraiodomethane \(\left(\mathrm{Cl}_{4}\right)\) can be used as the iodine source for iodination, in the presence of a free-radical initiator such as hydrogen peroxide. Propose a mechanism (involving mildly exothermic propagation steps) for the following proposed reaction. Calculate the value of \(\Delta H\) for each of the steps in your proposed mechanism. Equation Transcription: Text Transcription: (I2) (Cl4) \Delta H CI4 H2O2 HCI3 I3C-I HO-I

1. Propose a mechanism for the free-radical chlorination of ethane, \(\mathrm{CH}_{3}-\mathrm{CH}_{3}+\mathrm{Cl}_{2} \stackrel{h \nu}{\longrightarrow} \mathrm{CH}_{3}-\mathrm{CH}_{2} \mathrm{Cl}+\mathrm{HCl}\) 2. Calculate \(\Delta H^{\circ}\) for each step in this reaction. 3. Calculate the overall value of \(\Delta H^{\circ}\) for this reaction. Equation Transcription: Text Transcription: CH_3-CH_3+Cl_2 \stackrel h \nu\longrightarrow CH}_3-CH_2 Cl+HCl \Delta H^\circ \Delta H^\circ

Under base-catalyzed conditions, two molecules of acetone can condense to form diacetone alcohol. At room temperature \(\left(25^{\circ} \mathrm{C}\right)\), about \(5 \%\) of the acetone is converted to diacetone alcohol. Determine the value of \(\Delta G^{\circ}\) for this reaction. Equation Transcription: Text Transcription: (25°C) 5% \Delta G^\circ 2 CH3-C-CH3 -OH CH3-C-CH2-C-OH-(CH3)2

When ethene is mixed with hydrogen in the presence of a platinum catalyst, hydrogen adds across the double bond to form ethane. At room temperature, the reaction goes to completion. Predict the signs of \(\Delta H^{\circ} \text { and } \Delta S^{\circ}\) for this reaction. Explain these signs in terms of bonding and freedom of motion. Equation Transcription: Text Transcription: \Delta H^\circ and \Delta S^\circ H_2

1. Using bond-dissociation enthalpies from Table 4-2 (page 143), calculate the heat of reaction for each step in the free-radical bromination of methane. \(\mathrm{Br}_{2}+\mathrm{CH}_{4} \stackrel{\text { heat or light }}{\longrightarrow} \mathrm{CH}_{3} \mathrm{Br}+\mathrm{HBr}\) 2. Calculate the overall heat of reaction. Equation Transcription: Text Transcription: Br_2+CH_4 \stackrel heat or light \longrightarrow CH_3 Br+HBr

For each reaction, estimate whether \(\Delta S^{\circ}\) for the reaction is positive, negative, or impossible to predict. Equation Transcription: Text Transcription: \Delta S^\circ

The reaction of tert-butyl chloride with methanol is found to follow the rate equation \(\text { rate }=\mathrm{k}_{\mathrm{r}}\left[\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}-\mathrm{Cl}\right]\) 1. What is the kinetic order with respect to tert-butyl chloride? 2. What is the kinetic order with respect to methanol? 3. What is the kinetic order overall? Equation Transcription: Text Transcription: (CH_3)_3C-Cl + CH_3-OH (CH_3)_3C-OCH_3+HCl rate=kr[(CH_3)_3C-Cl]

Under certain conditions, the bromination of cyclohexene follows an unusual rate law: 1. What is the kinetic order with respect to cyclohexene? 2. What is the kinetic order with respect to bromine? 3. What is the overall kinetic order? Equation Transcription: Text Transcription: H H +Br_2 H Br Br H rate=k_r[cyclohexene] [ Br_2]^2

When a small piece of platinum is added to a mixture of ethene and hydrogen, the following reaction occurs: Doubling the concentration of hydrogen has no effect on the reaction rate. Doubling the concentration of ethene also has no effect. 1. What is the kinetic order of this reaction with respect to ethene? With respect to hydrogen? What is the overall order? 2. Write the unusual rate equation for this reaction. 3. Explain this strange rate equation, and suggest what one might do to accelerate the reaction.

1. Draw the reaction-energy diagram for the reverse reaction: \(\mathrm{CH}_{3}+\mathrm{HCl} \rightarrow \mathrm{CH}_{4}+\mathrm{Cl}\) 2. What is the activation energy for this reverse reaction? 3. What is the heat of reaction \(\left(\Delta H^{\circ}\right)\) for this reverse reaction? Equation Transcription: Text Transcription: CH3+HClCH4+Cl (\Delta H°)

1. Draw a reaction-energy diagram for the following reaction: \(\mathrm{CH}_{3}+\mathrm{Cl}_{2} \rightarrow \mathrm{CH}_{3} \mathrm{Cl}+\mathrm{Cl}\) The activation energy is \(4 \mathrm{~kJ} \mathrm{~mol}(1 \mathrm{kcal} \mathrm{mol})\), and the overall \(\Delta H^{\circ}\) for the reaction is \(-109 \mathrm{~kJ} / \mathrm{mol}(-26 \mathrm{kcal} / \mathrm{mol})\) 2. Give the equation for the reverse reaction. 3. What is the activation energy for the reverse reaction? Equation Transcription: Text Transcription: CH3+Cl2CH3Cl+Cl 4 kJ mol (1 kcal mol) \Delta H^\circ -109 kJ/mol (-26 kcal/mol)

The bromination of methane proceeds through the following steps: 1. Draw a complete reaction-energy diagram for this reaction. 2. Label the rate-limiting step. 3. Draw the structure of each transition state. 4. Compute the overall value of for the bromination.

1. Using the BDEs in Table 4-2 (p. 143), compute the value of \(\Delta H^{\circ}\) for each step in the iodination of methane. 2. Compute the overall value of \(\Delta H^{\circ}\) for iodination. 3. Suggest two reasons why iodine does not react well with methane. Equation Transcription: Text Transcription: \Delta H^\circ \Delta H^\circ

Problem 18P What would be the product ratio in the chlorination of propane if all the hydrogens were abstracted at equal rates?

Problem 19P Classify each hydrogen atom in the following compounds as primary (1°), secondary (2°), or tertiary (3°). (a) butane (b) isobutane (c) 2-methylbutane (d) cyclohexane (e) norbornane (bicyclo[2.2.1]heptane)

Use the bond-dissociation enthalpies in Table 4-2 (page 143) to calculate the heats of reaction for the two possible first propagation steps in the chlorination of isobutane. Use this informa- tion to draw a reaction-energy diagram like Figure 4-8, comparing the activation energies for formation of the two radicals.

Problem 21P Predict the ratios of products that result from chlorination of isopentane (2-methylbutane).

1. When n-heptane burns in a gasoline engine, the combustion process takes place too quickly. The explosive detonation makes a noise called knocking. When 2,2,4-trimethylpentane (isooctane) is burned, combustion takes place in a slower, more controlled manner. Combustion is a free-radical chain reaction, and its rate depends on the reactivity of the free-radical intermediates. Explain why isooctane has less tendency to knock than does n-heptane. 2. Alkoxy radicals are generally more stable than alkyl radicals. Write an equation showing an alkyl free radical (from burning gasoline) abstracting a hydrogen atom from tert-butyl alcohol, \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{COH}\). Explain why tert-butyl alcohol works as an antiknock additive for gasoline. 3. Use the information in Table 4-2 (page 143) to explain why toluene \(\left(\mathrm{PhCH}_{3}\right)\) has a very high octane rating of 111. Write an equation to show how toluene reacts with an alkyl free radical to give a relatively stable radical. Equation Transcription: Text Transcription: (CH_3)_3COH (PhCH_3)

1. Compute the heats of reaction for abstraction of a primary hydrogen and a secondary hydrogen from propane by a fluorine radical. \(\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{CH}_{3}+\mathrm{F} \cdot \quad \longrightarrow \quad \mathrm{CH}_{3}-\mathrm{CH}_{2}-\dot{\mathrm{C}} \mathrm{H}_{2}+\mathrm{HF}\) \(\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{CH}_{3}+\mathrm{F} \cdot \longrightarrow \mathrm{CH}_{3}-\dot{\mathrm{C}} \mathrm{H}-\mathrm{CH}_{3}+\mathrm{HF}\) 2. How selective do you expect free-radical fluorination to be? 3. What product distribution would you expect to obtain from the free-radical fluorination of propane? Equation Transcription: Text Transcription: CH_3-CH_2-CH_3+F dot longrightarrow CH_3-CH_2-CH_2+HF CH_3-CH_2-CH_3+F dot longrightarrow CH_3-CH-CH_3+HF

Problem 24P 2,3-Dimethylbutane reacts with bromine in the presence of light to give a monobrominated product. Further reaction gives a good yield of a dibrominated product. Predict the structures of these products, and propose a mechanism for the formation of the monobrominated product.

In the presence of a small amount of bromine, cyclohexene undergoes the following light- promoted reaction: 1. Propose a mechanism for this reaction. 2. Draw the structure of the rate-limiting transition state. 3. Use the Hammond postulate to predict which intermediate most closely resembles this transition state. 4. Explain why cyclohexene reacts with bromine much faster than cyclohexane, which must be heated to react. Equation Transcription: Text Transcription: Br_2 hv Br HBr

Problem 26P Draw resonance forms to show how the BHA radical is stabilized by delocalization of the radical electron over other atoms in the molecule.

Write an equation for the reaction of vitamin E with an oxidizing radical \(\text { (RO.) }\) to give \(\mathrm{ROH}\) and a less reactive free radical. Equation Transcription: Text Transcription: (RO.) ROH

The triphenylmethyl cation is so stable that some of its salts can be stored for months. Explain why this cation is so stable. Equation Transcription: Text Transcription: C+

Rank the following carbocations in decreasing order of stability. Classify each as primary, secondary, or tertiary. Equation Transcription: Text Transcription: (CH3)2CHCH2-CH2 CH3-CH-CH(CH3)2 CH3-C(CH3)CH2CH3

Rank the following radicals in decreasing order of stability. Classify each as primary, secondary, or tertiary. Equation Transcription: Text Transcription: (CH3)2CHCH2-CH2 CH3-CH-CH(CH3)2 CH3-C(CH3)CH2CH3

Acetylacetone (pentane-2,4-dione) reacts with sodium hydroxide to give water and the sodium salt of a carbanion. Write a complete structural formula for the carbanion, and use resonance forms to show the stabilization of the carbanion. Equation Transcription: Text Transcription: H_3C-C-O-CH_2-C-O-CH_3

Acetonitrile \(\left(C H_{3} C \equiv N\right)\) is deprotonated by very strong bases. Write resonance forms to show the stabilization of the carbanion that results. Equation Transcription: Text Transcription: (CH_3CN)

When it is strongly heated, ethyl diazoacetate decomposes to give nitrogen gas and a carbene. Draw a Lewis structure of the carbene. Equation Transcription: Text Transcription: : N \equiv N^{+}-C H-C-O-O-C H_{2} C H_{3}

The following reaction is a common synthesis used in the organic chemistry laboratory course. When we double the concentration of methoxide ion (CH3O-), we find that the reaction rate doubles. When we triple the concentration of 1-bromobutane, we find that the reaction rate triples. 1. What is the order of this reaction with respect to 1-bromobutane? What is the order with respect to methoxide ion? Write the rate equation for this reaction. What is the overall order? 2. One lab textbook recommends forming the sodium methoxide in methanol solvent, but before adding 1-bromobutane, they first distill off enough methanol to reduce the mixture to half of its original volume. What difference in rate will we see when we run the reaction (using the same amounts of reagents) in half the volume of solvent? Equation Transcription: Text Transcription: CH_3CH_2CH_2CH_2Br+CH_3O- \rightarrow CH_3OH CH_3CH_2CH_2CH_2OCH_3+Br-

Consider the following reaction-energy diagram. 1. Label the reactants and the products. Label the activation energy for the first step and the second step. 2. Is the overall reaction endothermic or exothermic? What is the sign of \(\Delta H^{\circ}\)? 3. Which points in the curve correspond to intermediates? Which correspond to transition states? 4. Label the transition state of the rate-limiting step. Does its structure resemble the reactants, the products, or an intermediate? Equation Transcription: Text Transcription: \Delta H^{\circ}

Problem 36SP Draw a reaction-energy diagram for a one-step exothermic reaction. Label the parts that represent the reactants, products, transition state, activation energy, and heat of reaction.

Problem 37SP Draw a reaction-energy diagram for a two-step endothermic reaction with a rate-limiting second step.

Treatment of tert-butyl alcohol with concentrated \(H C I \) gives tert-butyl chloride. When the concentration of \(H^{+}\) is doubled, the reaction rate doubles. When the concentration of tert-butyl alcohol is tripled, the reaction rate triples. When the chloride ion concentration is quadrupled, however, the reaction rate is unchanged. Write the rate equation for this reaction. Equation Transcription: Text Transcription: HCI H^+

Label each hydrogen atom in the following compounds as primary \(\left(1^{\circ}\right)\), secondary \(\left(2^{\circ}\right)\), or tertiary \(\left(3^{\circ}\right)\). Equation Transcription: Text Transcription: (1°) (2°) (3°) CH_3CH_2CH(CH_3)_2 (CH_3)_3CCH_2CH_3 (CH_3)_2CHCH(CH_3)CH_2CH_3 CH_3 H CH_3

Use bond-dissociation enthalpies (Table 4-2, p. 143) to calculate values of \(\Delta H^{\circ}\) for the following reactions. 1. \(C H_{3}-C H_{3}+I_{2} \rightarrow C H_{3} C H_{2} I+H I\) 2. \(C H_{3} C H_{2} C l+H I \rightarrow C H_{3} C H_{2} I+H C l\) 3. \(\left(C H_{3}\right)_{3} C-O H+H C l \rightarrow\left(C H_{3}\right)_{3} C-C l+H_{2} O\) 4. \(C H_{3} C H_{2} C H_{3}+H_{2} \rightarrow C H_{3} C H_{3}+C H_{4}\) 5. \(C H_{3} C H_{2} O H+H B r \rightarrow C H_{3} C H_{2}-B r+H_{2} O\) Equation Transcription: Text Transcription: \Delta H^{\circ} CH_3-CH_3+I_2 \rightarrow CH_3CH_2I+HI CH_3CH_2Cl +HI \rightarrow CH_3CH_2I+HCl (CH_3)_3C-OH+HCl \rightarrow (CH_3)_3C-Cl+H_2O CH_3CH_2CH_3+H_2 \rightarrow CH_3CH_3+CH_4 CH_3CH_2OH+HBr \rightarrow CH_3CH_2-Br+H2O

Use the information in Table 4-2 (p. 143) to rank the following radicals in decreasing order of stability. Equation Transcription: Text Transcription: \dot CH_3 CH_3CH_3 CH_2 (CH_3)_3C (CH_3)_2CH CH_2=CH-CH_2 ________________

Problem 42SP For each alkane, 1. Draw all the possible monochlorinated derivatives. 2. Determine whether free-radical chlorination would be a good way to make any of these monochlorinated derivatives. (Will the reaction give mostly one major product?) 3. Which monobrominated derivatives could you form in good yield by free-radical bromination? (a) cyclopentane (b) methylcyclopentane (c) 2-methylpentane (d) 2,2,3,3-tetramethylbutane

Write a mechanism for the light-initiated reaction of cyclohexane with chlorine to give chlorocyclohexane. Label the initi- ation and propagation steps. Equation Transcription: Text Transcription: Cl_2 hv \rightarrow Cl + CHCl

Draw the important resonance forms of the following free radicals. Equation Transcription: Text Transcription: CH2=CH-CH2 CH2 CH3-C-O-O \dot O \dot

In the presence of a small amount of bromine, the following light-promoted reaction has been observed. 1. Write a mechanism for this reaction. Your mechanism should explain how both products are formed. (Hint: Notice which H atom has been lost in both products.) 2. Explain why only this one type of hydrogen atom has been replaced, in preference to any of the other hydrogen atoms in the starting material. Equation Transcription: Text Transcription: H_3C CH_3+Br_2 \rightarrow hv H_3C CH_3 Br+H_3C CH_3 H Br

For each compound, predict the major product of free-radical bromination. Remember that bromination is highly selective, and only the most stable radical will be formed. Equation Transcription: Text Transcription: CH_2CH_3

Problem 47SP When exactly 1 mole of methane is mixed with exactly 1 mole of chlorine and light is shone on the mixture, a chlorination reaction occurs. The products are found to contain substantial amounts of di-, tri-, and tetrachloromethane, as well as unreacted methane. (a) Explain how a mixture is formed from this stoichiometric mixture of reactants, and propose mechanisms for the formation of these compounds from chloromethane. (b) How would you run this reaction to get a good conversion of methane to CH3Cl? Of methane to CCl4?

Problem 48SP The chlorination of pentane gives a mixture of three monochlorinated products. (a) Draw their structures. (b) Predict the ratios in which these monochlorination products will be formed, remembering that a chlorine atom abstracts a secondary hydrogen about 4.5 times as fast as it abstracts a primary hydrogen.

1. Draw the structure of the transition state for the second propagation step in the chlorination of methane. \(\mathrm{CH}_{3}+\mathrm{Cl}_{2} \rightarrow \mathrm{CH}_{3} \mathrm{Cl}+\mathrm{Cl}\) Show whether the transition state is product-like or reactant-like, and which of the two partial bonds is stronger. 2. Repeat for the second propagation step in the bromination of methane. Equation Transcription: Text Transcription: CH_3+Cl_2 \rightarrow CH_3Cl+Cl

When ethene is treated in a calorimeter with H2 and a Pt catalyst, the heat of reaction is found to be \(-137 \mathrm{~kJ} / \mathrm{mol}(+32.7 \mathrm{kcal} / \mathrm{mol})\), and the reaction goes to completion. When the reaction takes place at \(1400^{\circ} \mathrm{K}\), the equilibrium is found to be evenly balanced, with \(\mathrm{K}_{e q}=1\) Compute the value \(\Delta \mathrm{S}\) for this reaction. Equation Transcription: Text Transcription: -137 kJ/mol (+32.7 kcal/mol) 1400°K Keq=1 \Delta S CH2=CH2+H2Pt catalyst CH3-CH3 H=-137 kJ/mol (-32.7kcal/mol)

Problem 50SP Peroxides are often added to free-radical reactions as initiators because the oxygen–oxygen bond cleaves homolytically rather easily. For example, the bond-dissociation enthalpy of the O-O bond in hydrogen peroxide( H-O-O-H) is only 213 kJ mol (51 kcal mol). Give a mechanism for the hydrogen peroxide-initiated reaction of cyclopentane with chlorine. The BDE for HO-Cl is 210 kJ mol (50 kcal/mol).

Problem 51SP When dichloromethane is treated with strong NaOH, an intermediate is generated that reacts like a carbene. Draw the structure of this reactive intermediate, and propose a mechanism for its formation.

When a small amount of iodine is added to a mixture of chlorine and methane, it prevents chlorination from occurring. Therefore, iodine is a free-radical inhibitor for this reaction. Calculate \(\Delta H^{\circ}\) values for the possible reactions of iodine with species present in the chlorination of methane, and use these values to explain why iodine inhibits the reaction. (The bond-dissociation enthalpy is \(211 \mathrm{~kJ} / \mathrm{mol}$ or $50 \mathrm{kcal} / \mathrm{mol}\).) Equation Transcription: Text Transcription: \Delta H^{\circ} 211 kJ/mol or 50 kcal/mol

Tributyltin hydride \(\left(B u_{3} S n H\right)\) is used synthetically to reduce alkyl halides, replacing a halogen atom with hydrogen. Free-radical initiators promote this reaction, and free-radical inhibitors are known to slow it or stop it. Your job is to develop a mechanism, using the following reaction as the example. 1. Propose initiation and propagation steps to account for this reaction. 2. Calculate values of \(\Delta H\) for your proposed steps to show that they are energetically feasible. (Hint: A trace of \(B r_{2}\) and light suggests it’s there only as an initiator, to create Then decide which atom can be abstracted most favorably from the starting materials by the That should complete the initiation. Now decide what energetically favored propagation steps will accomplish the reaction.) Equation Transcription: Text Transcription: (Bu3SnH) \Delta H B r_{2}

When healthy, Earth’s stratosphere contains a low concentration of ozone \(\left(O_{3}\right)\) that absorbs potentially harmful ultraviolet \((U V)\) radiation by the cycle shown at right. Chlorofluorocarbon refrigerants, such as Freon 12 \(\left(C F_{2} C l_{2}\right)\), are stable in the lower atmosphere, but in the stratosphere they absorb high-energy UV radiation to generate chlorine radicals. The presence of a small number of chlorine radicals appears to lower ozone concentrations dramatically. The following reactions are all known to be exothermic (except the one requiring light) and to have high rate constants. Propose two mechanisms to explain how a small number of chlorine radicals can destroy large numbers of ozone molecules. Which of the two mechanisms is more likely when the concentration of chlorine atoms is very small? Equation Transcription: Text Transcription: (O3) (UV) (CF2Cl2)

Deuterium (D) is the hydrogen isotope of mass number 2, with a proton and a neutron in its nucleus. The chemistry of deuterium is nearly identical to the chemistry of hydrogen, except that the \(C-D\) bond is slightly stronger than the bond by \(5.0 \mathrm{~kJ} / \mathrm{mol}(1.2 \mathrm{kcal} / \mathrm{mol})\). Reaction rates tend to be slower if a \(C-D\) bond (as opposed to a bond) is broken in a rate-limiting step. This effect, called a kinetic isotope effect, is clearly seen in the chlorination of methane. Methane undergoes free-radical chlorination 12 times as fast as tetradeuteriomethane \(\left(C D_{4}\right)\). Faster: \(C H_{4}+C l \cdot \rightarrow C H_{3} C l+H C l\) relative rate = 12 Slower: \(C D_{4}+C l \cdot \rightarrow C D_{3} C l+D C l\) relative rate = 1 (a) Draw the transition state for the rate-limiting step of each of these reactions, showing how a bond to hydrogen or deuterium is being broken in this step. (b) Monochlorination of deuterioethane \(\left(C_{2} H_{5} D\right)\) leads to a mixture containing \(93 \% C_{1} H_{4} D C l\) and \(7 \% C_{2} H_{5} C l\). Calculate the relative rates of abstraction per hydrogen and deuterium in the chlorination of deuterioethane. (c) Consider the thermodynamics of the chlorination of methane and the chlorination of ethane, and use the Hammond postulate to explain why one of these reactions has a much larger isotope effect than the other. Equation Transcription: Text Transcription: C-D 5.0 kJ/mol (1.2 kcal/mol) C-D (CD4) CH4+Cl \cdot \rightarrow CH3Cl+HCl CD4+Cl \cdot \rightarrow CD3Cl+DCl (C2H5D) 93% C1H4DCl 7% C2H5Cl