Chapter 9 The Chemistry of Alkyl Halides

Transcription

1 Instructor Supplemental Solutions to Problems 2010 Roberts and Company Publishers Chapter 9 The Chemistry of Alkyl Halides 9.1 (b) The product is ethylammonium iodide. Solutions to In-Text Problems 9.2 (b) As in part (a), because there are two types of -hydrogens, two alkenes can be formed: 9.3 (b) Methyl iodide, H 3 C I, can form only a substitution product, dimethyl ether, H 3 C O CH 3. (d) (Bromomethyl)cyclopentane can form one substitution product and one elimination product. 9.4 (b) Because iodide ion is a weaker base than chloride ion, the equilibrium lies to the left. (d) Because methoxide ion is a much stronger base than chloride ion, the equilibrium lies to the right. 9.5 (b) The reaction is first order overall, and first order in alkyl halide. The rate constant has the dimensions of sec (b) We transform Eq. 9.22c to get the difference between the standard free energies of activation. G A G B = 2.30RT log k B k = (5.71) log(450) = 15.2 kj mol 1 A Therefore, reaction A has the higher G by 15.2 kj mol Because the S N 2 mechanism involves a molecule of alkyl halide and a molecule of nucleophile in a bimolecular reaction, the expected rate law is second order, first order in alkyl halide and first order in cyanide: rate = k[c 2 H 5 Br][ CN] 9.11 There is more than enough sodium cyanide to react with both the acid HBr and the alkyl halide. Therefore, the products are sodium bromide (NaBr, 0.2 M, half from the reaction with HBr and half from the reaction with ethyl bromide), ethyl cyanide (propionitrile, CH 3 CH 2 CN, 0.1 M), and unreacted sodium cyanide (0.8 M). However, 0.1

2 INSTRUCTOR SUPPLEMENTAL SOLUTIONS TO PROBLEMS CHAPTER 9 2 M NaBr is formed instantaneously, and the rest of the NaBr as well as the nitrile are formed much more slowly, because Brønsted acids reacts much more rapidly with bases than alkyl halides The reaction is an S N 2 reaction with inversion of configuration. Because the relative priorities of the groups attached to the asymmetric carbon are not changed, the product has the S configuration (a) The products of the S N 2 reaction between potassium acetate and ethyl iodide: (b) Potassium acetate is a better nucleophile in acetone because ethanol is a protic solvent and reduces the nucleophilicity of potassium acetate by hydrogen-bond donation. Consequently, potassium acetate in acetone reacts more rapidly with ethyl iodide than a solution of the same nucleophile in ethanol (a) The stepwise process involves formation of a methyl cation, which is very unstable. The instability of this cation, by Hammond s postulate, raises the energy of the transition state and retards the reaction. The concerted mechanism avoids formation of this high-energy intermediate. (b) A tertiary alkyl halide such as tert-butyl bromide, (CH 3 ) 3 C Br, can undergo the stepwise mechanism, because ionization gives a relatively stable tertiary carbocation in this case, (CH 3 ) 3 C +. This lowers the energy of the transition state (by Hammond s postulate). Section 9.6 describes this mechanism (b) The hydration rate of the deuterium-substituted styrene should differ very little, if at all, from that of styrene itself, because the deuteriums are not transferred in the rate-limiting step. A small effect of isotopic substitution occurs in this case because of the differential effect of deuterium and hydrogen on the rehybridization of carbon in the transition state. (The carbon bearing the deuteriums rehybridizes from sp 2 to sp 3 in the rate-limiting step.) However, this effect on rate amounts to only a few percent. Effects of this sort are called secondary deuterium isotope effects (b) Reasoning identical to that used in part (a) shows that the alkene formed has the E configuration. (We leave it to you to draw the appropriate structures.) In a stereospecific reaction with a given stereochemistry anti-elimination, in this case diastereomeric starting materials must give diastereomeric products In a stereospecific reaction with a given stereochemistry anti-elimination, in this case a diastereomeric product requires a diastereomeric starting material (either enantiomer). The easiest path to the answer is to convert the starting material in Eq. 9.40a into its diastereomer by the interchange of any two groups at one of the carbons. Either the following compound or its enantiomer would give the product of E configuration.

3 INSTRUCTOR SUPPLEMENTAL SOLUTIONS TO PROBLEMS CHAPTER (b) In this case, the nucleophile is the conjugate base of ethanethiol, sodium ethanethiolate. Although a polar aprotic solvent could be used, ethanol would probably be the most convenient solvent (for solubility reasons). Because the nucleophile is from the third period, the reaction would occur at a convenient rate in a protic solvent; hence, experimental convenience determines the choice of solvent. The nucleophile would be easily formed from ethanethiol with one equivalent of sodium ethoxide, as shown in Eq. 8.13, text p Because a-substitution in the base promotes a greater proportion of elimination, the order is C > A > B (b) This tertiary alkyl halide will undergo the S N 1 E1 process to give substitution products that result from the Lewis acid base association reactions of both water and ethanol, respectively, with the carbocation intermediate; and this carbocation can lose a b-proton to solvent (water or ethanol, abbreviated ROH below) to form two alkenes. Of the two alkenes, D will be formed in greater amount because it has a greater number of alkyl substituents at the double bond (b) A less stable carbocation, by the same reasoning as in part (a), should have a shorter lifetime; a greater fraction will not last past the ion-pair stage, which reacts with the solvent by inversion (b) 2-Bromobutane is a secondary alkyl halide, and potassium tert-butoxide is a strong, highly branched base. Entry 7 of Table 9.7 covers this case. Thus, the E2 reaction is the major process that occurs. Two possible alkenes, 1-butene and 2-butene, can form. Either or both can be considered as correct answers. A significant amount of 1-butene is formed because the large base molecule reacts at the least sterically hindered hydrogen. (d) We leave it to you to show the formation of the 2-butenes. Bromocyclohexane is a secondary alkyl halide; methanol is a polar, protic solvent; and there is no strong base present. Entry 9 of Table 9.7 covers this situation; both S N 1 product A and E1 product B are formed.

4 INSTRUCTOR SUPPLEMENTAL SOLUTIONS TO PROBLEMS CHAPTER (a) 9.31 (a) 9.32 (b) 9.33 (b) Cyclopropane formation occurs at the face of the ring opposite to the methyl group for steric reasons.

5 INSTRUCTOR SUPPLEMENTAL SOLUTIONS TO PROBLEMS CHAPTER 9 5 Solutions to Additional Problems 9.34 The first step in any problem that requires structures is to draw the structures: (b) (d) (f) (h) Compound (5) can exist as diastereomers because it has two asymmetric carbons. Compound (3) is least reactive to sodium methoxide in methanol because it cannot undergo a b-elimination it has no b-hydrogens and the three b-substituents make it virtually unreactive in the S N 2 reaction, much like neopentyl bromide. Compound (2) will give an E2 but no S N 2 reaction with sodium methoxide in methanol. Compound (2) will give the fastest S N 1 reaction because it is the only tertiary alkyl halide The first thing to do is to draw out the structures. The order of increasing S N 2 reaction rates is C < B < E < D < A. Alkyl halides with three -substituents (C) are virtually unreactive in S N 2 reactions. Secondary alkyl halides with no b- substituents (B) react more slowly than primary alkyl halides with two b- substituents (E), and the latter react more slowly than unbranched primary alkyl halides (D). Methyl halides (A) react most rapidly (b) (d) 9.40 (a) 9.41 (b) (d) 9.43 Allow the appropriate alkoxide, (CH 3 ) 3 CCH 2 O Na +, to react with ethyl iodide, CH 3 CH 2 I. Using sodium ethoxide with neopentyl bromide, (CH 3 ) 3 CCH 2 Br, won t work; why? 9.45 (b) The reaction conditions favor a solvolysis reaction, which occurs by an S N 1 E1 mechanism accompanied by rearrangement.

6 INSTRUCTOR SUPPLEMENTAL SOLUTIONS TO PROBLEMS CHAPTER 9 6 The S N 1 product A, derived from the Lewis acid base association reaction of solvent with the first-formed carbocation, should have largely inverted configuration at carbon-2, because the carbocation will be a backside-solvated ion pair; this carbocation will react faster with the solvent molecule than the bromide ion is replaced by a second solvent molecule. (See Fig. 9.13, text p. 419.) The stereochemistry of carbon-3 is unaffected. The substitution product B, derived from the rearranged tertiary carbocation, should be mostly racemic, although the exact stereochemical outcome is difficult to predict exactly. Compounds C and D are E1 products. The stereochemistry at carbon-3 of alkene C is the same as in the starting alkyl halide. Alkene D should be the major alkene product because it has the larger number of substituents on the double bond (b) Proceed the same way as in part (a). Because the starting materials are diastereomers, the products must also be diastereomers if the elimination is anti If this compound were to undergo solvolysis, it would have to form carbocation A: As a model will verify, the four asterisked carbons cannot become coplanar because of the constraints of the bicyclic ring system. Yet sp 2 hybridization requires trigonal-planar geometry. Remember: hybridization and geometry are connected. If a molecule can t achieve the geometry for a given hybridization, then that hybridization will not occur. Because sp 2 hybridization is the lowest-energy hybridization for a carbocation, the inability to achieve this hybridization raises the energy of the carbocation. But that s not all. Solvation of the carbocation can only occur from one side, because the back side of the electron-deficient carbon is blocked by part of the ring system. The absence of effective solvation, then, also raises the energy of this carbocation. Any solvolysis reaction involving such an unstable carbocation is slow.

7 INSTRUCTOR SUPPLEMENTAL SOLUTIONS TO PROBLEMS CHAPTER (b) The scheme in part (a) shows that complexation of the cation by the crown ether is essential for the reaction to occur, because this is the only way to obtain the dissolved anion. Because [18]-crown-6 does not bind the smaller lithium cation it is selective for the larger potassium cation lithium fluoride is not solubilized by the crown ether, and is therefore unreactive whether the crown ether is present or not (a) The thiosulfate dianion contains two types of nucleophilic atoms: the anionic oxygen and the anionic sulfur. Hence, alkylation could occur at the oxygen or the sulfur: (b) In a hydrogen-bonding solvent such as methanol, the more weakly basic atom is the better nucleophile. (The principle is the same as in the solution to Problem 9.51.) Hence, product B is the major one observed. (What solvent change could you make to obtain more of product A?) 9.54 The reaction between methyl iodide and sodium ethoxide is an S N 2 process that has the following rate law: rate = k[ch 3 I][CH 3 CH 2 O ] This means that the rate of the reaction depends on the concentration of the nucleophile. In the first case, the nucleophile concentration changes during the reaction from 0.1 M to 0 M; in the second case, the nucleophile concentration changes from 0.5 M to 0.4 M. In the second case, the reaction is faster because the concentration of the nucleophile is higher at all times during the reaction. However, in either case, there is sufficient nucleophile present to react completely with the alkyl halide. If we wait long enough, the yield of the reaction will be the same in either case The fact that protonolysis reactions of the corresponding Grignard reagents give the same hydrocarbon indicates that the two compounds have the same carbon skeleton. The conditions of ethanol and no added base are S N 1 conditions. Since compound A reacts rapidly to give a solution containing bromide ion, it must be an alkyl halide that readily undergoes an S N 1 reaction, and therefore it is probably a tertiary alkyl bromide. Because the two alkyl halides give the same ether, the product from compound B must be formed in a rearrangement. The only tertiary alkyl halide with the formula C 5 H 11 Br is 2-bromo-2-methylbutane, and this is therefore compound A: Two possible alkyl halides with the same carbon skeleton as A could rearrange in respective S N 1 reactions to give the same carbocation, and hence the same ether product, as A; these are labeled B1 and B2 below. (An S N 1 reaction of B1 would be very slow, if it occurred at all.)

8 INSTRUCTOR SUPPLEMENTAL SOLUTIONS TO PROBLEMS CHAPTER 9 8 However, only B2 can react in an E2 reaction with sodium ethoxide to give an alkene that furnishes acetone as one of its ozonolysis products: Consequently, compound B2 is compound B, 2-bromo-3-methylbutane Compound A has no conformation in which the b-hydrogens and the bromine are anti, whereas in compound B, the b-hydrogens are anti to the bromine in the more stable conformation (shown). For this reason, compound B should more readily undergo the E2 reaction The reaction of butylamine with 1-bromobutane is a typical S N 2 reaction. (Bu = the butyl group = CH 3 CH 2 CH 2 CH 2 ): This mechanism is consistent with the second-order rate law, because the rate law requires one molecule of amine and one molecule of alkyl halide in the transition state. The second reaction is also a nucleophilic substitution reaction, but, because it is intramolecular (that is, the nucleophile and carbon at which it reacts are part of the same molecule), the reaction is first-order (a) Bromine addition to alkenes is anti; consequently, the stereochemistry of compound B is as follows:

9 INSTRUCTOR SUPPLEMENTAL SOLUTIONS TO PROBLEMS CHAPTER 9 9 (b) Draw the structure of compound B in a conformation in which the butyl (Bu) group and the Br that remains after the elimination are on opposite sides of the molecule, because this is the way they are in the alkene product. This shows that the trimethylsilyl group and the bromine are anti; consequently, the elimination shown is an anti-elimination. (c) Diastereomeric starting materials must give diastereomeric products if the stereochemistry of the two reactions remains the same. The E stereoisomer of compound A therefore would give the diastereomer of compound B (as the racemate), and the subsequent elimination would give the Z stereoisomer of compound C. This can be shown by the analysis used in parts (a) and (b) with the positions of the trimethylsilyl group and the hydrogen interchanged.