9.4 THE S N 2 REACTION

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1 86 CAPTER 9 TE CEMSTRY F ALKYL ALDES 9.7 What prediction does the rate law in Eq make about how the rate of the reaction changes as the reactants D and E are converted into F over time? Does the rate increase, decrease, or stay the same? Explain. Use your answer to sketch a plot of the concentrations of starting materials and products against time. 9.4 TE S N 2 REACTN A. Rate Law and Mechanism of the S N 2 Reaction Consider now the nucleophilic substitution reaction of ethoxide ion with methyl iodide in ethanol at 25 C. C CL C 2 5 L C + C 2 5 The following rate law for this reaction was experimentally determined for this reaction: (9.2) rate = k[c ][C 2 5 ] (9.24) with k = 6.0 X 10 4 M 1 s 1. That is, this is a second-order reaction that is first order in each reactant. The rate law of a reaction is important because it provides fundamental information about the reaction mechanism. Specifically, the concentration terms of the rate law indicate which atoms are present in the transition state of the rate-limiting step. ence, the rate-limiting transition state of reaction 9.2 consists of the elements of one methyl iodide molecule and one ethoxide ion. The rate law excludes some mechanisms from consideration. For example, any mechanism in which the rate-limiting step involves two molecules of ethoxide is ruled out by the rate law, because the rate law for such a mechanism would have to be second order in ethoxide. The simplest possible mechanism consistent with the rate law is one in which the ethoxide ion directly displaces the iodide ion from the methyl carbon: C C L 21 d " d C C ) 21 C L C 21 transition state + ) (9.25) Mechanisms like this account for many nucleophilic substitution reactions. A mechanism in which electron-pair donation by a nucleophile to an atom (usually carbon) displaces a leaving group from the same atom in a concerted manner (that is, in one step, without reactive intermediates) is called an S N 2 mechanism. Reactions that occur by S N 2 mechanisms are called S N 2reactions.The meaning of the nickname S N 2 is as follows: substitution S N 2 nucleophilic bimolecular (The word bimolecular means that the rate-limiting step of the reaction involves two species in this case, one methyl iodide molecule and one ethoxide ion.) Notice that an S N 2 reaction, because it is concerted, involves no reactive intermediates.

2 9.4 TE S N 2 REACTN 87 STUDY GUDE LNK 9.1 Deducing Mechanisms from Rate Laws The rate law does not reveal all of the details of a reaction mechanism. Although the rate law indicates what atoms are present in the rate-limiting step, it provides no information about how they are arranged. Thus, the following two mechanisms for the S N 2 reaction of ethoxide ion with methyl iodide are equally consistent with the rate law. C " C frontside substitution C C L backside substitution (9.26) As far as the rate law is concerned, either mechanism is acceptable. To decide between these two possibilities, other types of experiments are needed (Sec. 9.4C). Let s summarize the relationship between the rate law and the mechanism of a reaction. 1. The concentration terms of the rate law indicate what atoms are involved in the ratelimiting step. 2. Mechanisms that are not consistent with the rate law are ruled out.. f the chemically reasonable mechanisms consistent with the rate law, the simplest one is provisionally adopted. 4. The mechanism of a reaction is modified or refined if required by subsequent experiments. Point (4) may seem disturbing because it means that a mechanism can be changed at a later time. Perhaps it seems that an absolutely true mechanism should exist for every reaction. owever, a mechanism can never be proved; it can only be disproved. The value of a mechanism lies not in its absolute truth but rather in its validity as a conceptual framework, or theory, that generalizes the results of many experiments and predicts the outcome of others. Mechanisms allow us to place reactions into categories and thus impose a conceptual order on chemical observations. Thus, when someone observes an experimental result different from that predicted by a mechanism, the mechanism must be modified to accommodate both the previously known facts and the new facts. The evolution of mechanisms is no different from the evolution of science in general. Knowledge is dynamic: theories (mechanisms) predict the results of experiments, a test of these theories may lead to new theories, and so on. PRBLEMS 9.8 The reaction of acetic acid with ammonia is very rapid and follows the simple rate law shown in the following equation. Propose a mechanism that is consistent with this rate law. S S CL C L L + N C L C L + N 4 acetic acid 1 S rate = k C LC L N What rate law would be expected for the reaction of cyanide ion ( CN) with ethyl bromide by the S N 2 mechanism?

3 88 CAPTER 9 TE CEMSTRY F ALKYL ALDES B. Comparison of the Rates of S N 2 Reactions and Brønsted AciBase Reactions n Sec..4B, and again in Sec. 9.2, we learned about the close analogy between nucleophilic substitution reactions and acibase reactions. The equilibrium constants for a nucleophilic substitution reaction and its acibase analog are very similar, and the curved-arrow notations for an S N 2 reaction and its acibase analog are identical. owever, it is important to understand that their rates are very different. Most ordinary acibase reactions occur instantaneously as fast as the reacting pairs can diffuse together. The rate constants for such reactions are typically in the M 1 s 1 range. Although many nucleophilic substitution reactions occur at convenient rates, they are much slower than the analogous acibase reactions. Thus, the reaction in Eq. 9.27a is completed in a little over an hour, but the corresponding acibase reaction in Eq. 9.27b occurs within about a billionth of a second! Nucleophilic substitution reaction: C C L C 2 5 L C + C 2 5 (complete in about an hour) (9.27a) Brønsted acibase reaction: C L C 2 5 L + C 2 5 (complete in 10 9 second) (9.27b) This means that if an alkyl halide and a Brønsted acid are in competition for a Brønsted base, the Brønsted acid reacts much more rapidly. n other words, the Brønsted acid always wins. PRBLEMS 9.10 Methyl iodide (0.1 M) and hydriodic acid (, 0.1 M) are allowed to react in ethanol solution with 0.1 M sodium ethoxide. What products are observed? 9.11 Ethyl bromide (0.1M) and Br (0.1 M) are allowed to react in aqueous TF with 1 M sodium cyanide (Na CN). What products are observed? Are any products formed more rapidly than others? Explain. C. Stereochemistry of the S N 2 Reaction The mechanism of the S N 2 reaction can be described in more detail by considering its stereochemistry. The stereochemistry of a substitution reaction can be investigated only if the carbon at which substitution occurs is a stereocenter in both reactants and products (Sec. 7.9B). A substitution reaction can occur at a stereocenter in three stereochemically different ways: 1. with retention of configuration at the stereocenter; 2. with inversion of configuration at the stereocenter; or. with a combination of (1) and (2); that is, mixed retention and inversion. f approach of the nucleophile Nuc to an asymmetric carbon and departure of the leaving group X occur from more or less the same direction (frontside substitution), then a substitution reaction would result in a product with retention of configuration at the asymmetric carbon.

4 9.4 TE S N 2 REACTN 89 R 2 R 1 C LX R Nuc R 1 R 2 R C Nuc X transition state R 1 C L Nuc + R 2 R X (9.28a) n contrast, if approach of the nucleophile and loss of the leaving group on an asymmetric carbon occur from opposite directions (backside substitution), the other three groups on carbon must invert, or turn inside out, to maintain the tetrahedral bond angle. This mechanism would lead to a product with inversion of configuration at the asymmetric carbon. Nuc R 1 CLX R 2 R R 1 Nuc C X Nuc C + L R 2 R 1 R transition state L R 2 R X (9.28b) The products of Eqs. 9.28a and 9.28b are enantiomers. Thus, the two types of substitution can be distinguished by subjecting one enantiomer of a chiral alkyl halide to the S N 2 reaction and determining which enantiomer of the product is formed. f both paths occur at equal rates, then the racemate will be formed. What are the experimental results? The reaction of hydroxide ion with 2-bromooctane, a chiral alkyl halide, to give 2-octanol is a typical S N 2 reaction. The reaction follows a secondorder rate law, first order in and first order in the alkyl halide. When (R)-2-bromooctane is used in the reaction, the product is (S)-2-octanol. + C L L C CL Br C + Br (9.29) (C 2 ) 5 C (C 2 ) 5 C (R)-2-bromooctane (S)-2-octanol The stereochemistry of this S N 2 reaction shows that it proceeds with inversion of configuration. Thus, the reaction occurs by backside substitution of hydroxide ion on the alkyl halide. Recall that backside substitution is also observed for the reaction of bromide ion and other nucleophiles with the bromonium ion intermediate in the addition of bromine to alkenes (Sec. 7.9C). As you can now appreciate, that reaction is also an S N 2 reaction. n fact, inversion of stereochemical configuration is generally observed in all S N 2 reactions at carbon stereocenters. The stereochemistry of the S N 2 reaction calls to mind the inversion of amines (Fig. 6.17, p. 256). n the hybrid orbital description of both processes, the central atom is turned inside out, and it is approximately sp 2 -hybridized at the transition state. n the transition state for amine inversion, the 2p orbital on the nitrogen contains an unshared electron pair. n the transition state for an S N 2 reaction on carbon, the nucleophile and the leaving group are partially bonded to opposite lobes of the carbon 2p orbital (Fig. 9.2, p. 90). Why is backside substitution preferred in the S N 2 reaction? The hybrid orbital description of the reaction in Fig. 9.2 provides no information on this question, but a molecular orbital analysis does, as shown in Fig. 9. (p. 91) for the reaction of a nucleophile (Nuc) with methyl chloride (C Cl). When a nucleophile donates electrons to an alkyl halide, the orbital containing the donated electron pair must initially interact with an unoccupied molecular orbital of the

5 90 CAPTER 9 TE CEMSTRY F ALKYL ALDES sp 2 -hybridized carbon R 1 R 1 R 1 Nuc R C R 2 X Nuc C R 2 R X Nuc C R R 2 X 120 transition state Figure 9.2 Stereochemistry of the S N 2 reaction.the green arrows show how the various groups change position during the reaction. (Nuc: = a general nucleophile.) Notice that the sterochemical configuration of the asymmetric carbon is inverted by the reaction. alkyl halide. The M of the nucleophile that contains the donated electron pair interacts with the unoccupied alkyl halide M of lowest energy, called the LUM (for lowest unoccupied molecular orbital ). t happens that all of the bonding Ms of the alkyl halide are occupied; therefore, the alkyl halide LUM is an antibonding M, which is shown in Fig. 9.. When backside substitution occurs (Fig. 9.a), bonding overlap of the nucleophile orbital occurs with the alkyl halide LUM; that is, wave peaks overlap. But in frontside substitution (Fig. 9.b), the nucleophile orbital has both bonding and antibonding overlap with the LUM; the antibonding overlap (wave peak to wave trough) cancels the bonding overlap, and no net bonding can occur. Because only backside substitution gives bonding overlap, this is always the observed substitution mode. PRBLEM 9.12 What is the expected substitution product (including its stereochemical configuration) in the S N 2 reaction of potassium iodide in acetone solvent with the following compound? (D = 2 = deuterium, an isotope of hydrogen.) (R)-C C 2 C 2 C L Cl L D D. Effect of Alkyl alide Structure on the S N 2 Reaction ne of the most important aspects of the S N 2 reaction is how the reaction rate varies with the structure of the alkyl halide. (Recall Eqs and 9.15, p. 82.) f an alkyl halide is very reactive, its S N 2 reactions occur rapidly under mild conditions. f an alkyl halide is relatively unreactive, then the severity of the reaction conditions (for example, the temperature) must be increased for the reaction to proceed at a reasonable rate. owever, harsh conditions increase the likelihood of competing side reactions. ence, if an alkyl halide is unreactive enough, the reaction has no practical value. Alkyl halides differ, in some cases by many orders of magnitude, in the rates with which they undergo a given S N 2 reaction. Typical reactivity data are given in Table 9.. To put these data in some perspective: f the reaction of a methyl halide takes about one minute, then the reaction of a neopentyl halide under the same conditions takes about 2 years!

6 9.4 TE S N 2 REACTN 91 bonding overlap methyl chloride LUM (antibonding) methyl chloride LUM (antibonding) Nuc (a) backside substitution antibonding overlap cancels bonding overlap bonding overlap Nuc (b) frontside substitution Figure 9. n the S N 2 reaction, the orbital containing the nucleophile electron pair interacts with the unoccupied molecular orbital of lowest energy (LUM) in the alkyl halide. (a) Backside substitution leads to bonding overlap. (b) Frontside substitution gives both bonding and antibonding overlaps that cancel. Therefore, backside substitution is always observed. TABLE 9. Effect of Alkyl Substitution in the Alkyl alide on the Rate of a Typical S N 2 Reaction RL Name of R Relative rate* C methyl 145 ncreased alkyl substitution at the b-carbon: C C 2 C 2 propyl 0.82 (C ) 2 CC 2 isobutyl 0.06 (C ) CC 2 neopentyl ncreased alkyl substitution at the a-carbon: C C 2 ethyl 1.0 (C ) 2 C isopropyl (C ) C tert-butyl ; *All rates are relative to that of ethyl bromide. Estimated from the rates of closely related reactions. R L Br + 25 C R L + Br acetone The data in Table 9. show, first, that increased alkyl substitution at the b-carbon retards an S N 2 reaction. As Fig. 9.4 on p. 92 shows, these data are consistent with a backside substitution mechanism. When a methyl halide undergoes substitution, approach of the nucleophile and departure of the leaving group are relatively unrestricted. owever, when a neopentyl halide reacts with a nucleophile, both the nucleophile and the leaving group experience severe van der Waals repulsions with hydrogens of the methyl substituents. These van der Waals repulsions raise the energy of the transition state and therefore reduce the reaction rate. This is another example of a steric effect. Recall from Sec. 5.6D that a steric effect is any effect on a chemical phenomenon (such as a reaction) caused by van der Waals repulsions. Thus, S N 2 reactions of branched alkyl halides are retarded by a steric effect. ndeed, S N 2 reactions of neopentyl halides are so slow that they are not practically useful.

7 92 CAPTER 9 TE CEMSTRY F ALKYL ALDES van der Waals repulsions Br Br van der Waals repulsions Br Br (a) Br + C (b) Br + (C ) C C 2 Figure 9.4 Transition states for S N 2 reactions.the upper panels show the transition states as ball-and-stick models, and the lower panels show them as space-filling models. (a) The reaction of methyl bromide with iodide ion. (b) The reaction of neopentyl bromide with iodide ion.the S N 2 reactions of neopentyl bromide are very slow because of the severe van der Waals repulsions of both the nucleophile and the leaving group with the pink hydrogens of the methyl substituents.these repulsions are indicated with red brackets in the models. The data in Table 9. help explain why elimination reactions compete with the S N 2 reactions of secondary and tertiary alkyl halides (Sec. 9.1C): these halides react so slowly in S N 2 reactions that the rates of elimination reactions are competitive with the rates of substitution. The rates of the S N 2 reactions of tertiary alkyl halides are so slow that elimination is the only reaction observed. The competition between b-elimination and S N 2 reactions will be considered in more detail in Sec. 9.5G. E. Nucleophilicity in the S N 2 Reaction As Table 9.1 (p. 79) illustrates, the S N 2 reaction is especially useful because of the variety of nucleophiles that can be employed. owever, nucleophiles differ significantly in their reactivities. What factors govern nucleophilicity in the S N 2 reaction and why? We might expect some correlation between nucleophilicity and the Brønsted basicity of a nucleophile because both are aspects of its Lewis basicity. That is, in either role a Lewis base donates an electron pair. (Be sure to review the definitions of these terms in Sec..4A.) Let s first examine some data for the S N 2 reactions of methyl iodide with anionic nucleophiles of different basicity to see whether this expectation is met in practice. Some data for the reaction of methyl iodide with various nucleophiles in methanol solvent are given in Table 9.4 and plotted in Fig Notice in this table that the nucleophilic atoms are all from the second period

8 9.4 TE S N 2 REACTN 9 TABLE 9.4 Dependence of S N 2 Reaction Rate on the Basicity of the Nucleophile k (second-order rate Nucleophile (name) pk a of conjugate acid* constant, M 1 s 1 ) log k C (methoxide) X Ph (phenoxide) X CN (cyanide) X Ac (acetate) X N (azide) X F (fluoride) X S 4 2 (sulfate) X N (nitrate) X *pk a values in water Nuc + C L 25 C C Nuc L C + -2 ncreasing nucleophile basicity log k for Nuc + C - line of slope = 1 CN S 4 F N N Ac Ph C basicity of Nuc (pk a of Nuc ) ncreasing S N 2 reaction rate Figure 9.5 The dependence of nucleophile S N 2 reactivity on nucleophile basicity for a series of nucleophiles in methanol solvent. Reactivity is measured by log k for the reaction of the nucleophile with methyl iodide. Basicity is measured by the pka of the conjugate acid of the nucleophile. The blue dashed line of slope = 1 shows the trend to be expected if a change of one log unit in basicity resulted in the same change in nucleophilicity. The solid blue line shows the actual trend for a series of nucleophiles (blue squares) in which the reacting atom is L.The black circles show the reactivity of other nucleophilic anions in which the reacting atoms are from period 2 of the periodic table, the same period as oxygen. of the periodic table. Figure 9.5 shows a very rough trend toward faster reactions with the more basic nucleophiles. Let s now consider some data for the same reaction with anionic nucleophiles from different periods (rows) of the periodic table. These data are shown in Table 9.5 ( p. 94). f we are expecting a similar correlation of nucleophilic reactivity and basicity, we get a surprise. Notice that the

9 94 CAPTER 9 TE CEMSTRY F ALKYL ALDES TABLE 9.5 Dependence of S N 2 Reaction Rate on the Basicity of Nucleophiles from Different Periods of the Periodic Table Nuc + C L 25 C C Nuc L C + k (second-order rate Nucleophile pk a of conjugate acid* constant, M 1 s 1 ) log k Group 6A Nucleophiles PhS Ph X Group 7A Nucleophiles X Br X Cl -6.0X F X *pk a values in water sulfide nucleophile is more than three orders of magnitude less basic than the oxide nucleophile, and yet it is more than four orders of magnitude more reactive. Similarly, for the halide nucleophiles, the least basic halide ion (iodide) is the best nucleophile. Let s generalize what we ve learned so far. The following apply to nucleophilic anions in polar, protic solvents (such as water and alcohols): 1. n a series of nucleophiles in which the nucleophilic atoms are from the same period of the periodic table, there is a rough correlation of nucleophilicity with basicity. 2. n a series of nucleophiles in which the nucleophilic atoms are from the same group (column) but different periods of the periodic table, the less basic nucleophiles are more nucleophilic. The interaction of the nucleophile with the solvent is the most significant factor that accounts for both of these generalizations. Let s start with generalization 2 the inverse relationship of basicity and nucleophilicity within a group of the periodic table. The solvent in all of the cases shown in Tables 9.4 and 9.5 and Fig. 9.5 is methanol, a protic solvent. n a protic solvent, hydrogen bonding occurs between the protic solvent molecules (as hydrogen bond donors) and the nucleophilic anions (as hydrogen bond acceptors). The strongest Brønsted bases are the best hydrogen bond acceptors. For example, fluoride ion forms much stronger hydrogen bonds than iodide ion. When the electron pairs of a nucleophile are involved in hydrogen bonding, they are unavailable for donation to carbon in an S N 2 reaction. For the S N 2 reaction to take place, a hydrogen bond between the solvent and the nucleophile must be broken (Fig. 9.6). More energy is required to break a strong hydrogen bond to fluoride ion than is required to break a relatively weak hydrogen bond to iodide ion. This extra energy is reflected in a greater free energy of activation the energy barrier and, as a result, the reaction of fluoride ion is slower. To use a football analogy, the nucleophilic reaction of a strongly hydrogen-bonded anion with an alkyl halide is about as likely as a tackler bringing down a ball carrier when both of the tackler s arms are being held by opposing linemen. The data in Fig. 9.5 and generalization 1 can be understood with a similar argument. f nucleophilicity and basicity were exactly correlated, the graph would follow the dashed blue line of slope = 1. Focus on the blue curve, which shows the trend for nucleophiles that all have

10 9.4 TE S N 2 REACTN 95 $ $ hydrogen bonds between ) nucleophile and solvent ) " d X21 + C X21 C + 2 $ ) $ ) transition state bond to carbon d Figure 9.6 An S N 2 reaction of methyl iodide involving a nucleophile ( x1 1 ) in a protic solvent requires breaking a hydrogen bond between the solvent and the nucleophile.the energy required to break this hydrogen bond becomes part of the standard free energy of activation of the substitution reaction and thus retards the reaction. L as the reacting atom (blue squares). The downward curvature shows that the nucleophiles of higher basicity do not react as rapidly with an alkyl halide as their basicity predicts, and the deviation from the line of unit slope is greatest for the most basic nucleophiles. The strongest bases form the strongest hydrogen bonds with the protic solvent methanol, and one of these hydrogen bonds has to be broken for the nucleophilic reaction to occur. The stronger the hydrogen bond to solvent, the greater is the rate-retarding effect on nucleophilicity. The data for nucleophiles shown with the black circles in Fig. 9.5 reflect the effects of hydrogen bonding to nucleophilic atoms that come from different groups within the same period (row) of the periodic table. For example, fluoride ion lies below the trend line for the oxygen nucleophiles. That is, fluoride ion is a worse nucleophile than an oxygen anion with the same basicity. The hydrogen bonds of fluoride with protic solvents are exceptionally strong, and hence its nucleophilicity is correspondingly reduced. Conversely, the hydrogen bonds of azide ion and the carbon of cyanide ion with protic solvents are weaker than those of the oxygen anions, and their nucleophilicities are somewhat greater. f hydrogen bonding by the solvent tends to reduce the reactivity of very basic nucleophiles, it follows that S N 2 reactions might be considerably accelerated if they could be carried out in solvents in which such hydrogen bonding is not possible. Let s examine this proposition with the aid of some data shown in Table 9.6 (p. 96). The two solvents, methanol (e = ) and N,N-dimethylformamide (DMF, e = 7; structure in Table 8.2, p. 41), were chosen for the comparison because their dielectric constants are nearly the same; that is, their polarities are very similar. As you can see from the data in this table, changing from a protic solvent to a polar aprotic solvent accelerates the reactions of all nucleophiles, but the increase of the reaction rate for fluoride ion is particularly noteworthy a factor of n fact, the acceleration of the reaction with fluoride ion is so dramatic that an S N 2 reaction with fluoride ion as the nucleophile is converted from an essentially useless reaction in a protic solvent one that takes years to a very rapid reaction in the polar aprotic solvent. ther polar aprotic solvents have effects of a similar magnitude, and similar accelerations occur in the S N 2 reactions of other alkyl halides. The effect on rate is due mostly to the solvent proticity whether the solvent is protic. Fluoride ion is by far the most strongly hydrogen-bonded halide anion in Table 9.5; consequently, the change of solvent has the greatest effect on the rates of its S N 2 reactions.

11 96 CAPTER 9 TE CEMSTRY F ALKYL ALDES TABLE 9.6 Solvent Dependence of Nucleophilicity in the S N 2 Reaction Nuc + C L 25 C Nuc L C + n methanol n DMF Reaction is Reaction is Nucleophile pk a * k, M 1 s 1 over in k, M 1 s 1 over in X min 4.0 X s Br X h s C -6.0 X days s F X years > <1.2 s CN X h.2 X s *pk a values of the conjugate acid in water Time required for 97 completion of the reaction DMF = N,N-dimethylformamide (see Table 8.2, p. 41) As the data demonstrate, eliminating the possibility of hydrogen bonding to nucleophiles strongly accelerates their S N 2 reactions. What we ve learned, then, is that S N 2 reactions of nucleophilic anions with alkyl halides are much faster in polar aprotic solvents than they are in protic solvents. f this is so, why not use polar aprotic solvents for all such S N 2 reactions? ere we must be concerned with an element of practicality. To run an S N 2 reaction in solution, we must find a solvent that dissolves a salt that contains the nucleophilic anion of interest. We must also remove the solvent from the products when the reaction is over. Protic solvents, precisely because they are protic, dissolve significant quantities of salts. Methanol and ethanol, two of the most commonly used protic solvents, are cheap, are easily removed because they have relatively low boiling points, and are relatively safe to use. When the S N 2 reaction is rapid enough, or if a higher temperature can be used without introducing side reactions, the use of protic solvents is often the most practical solvent for an S N 2 reaction. Except for acetone and acetonitrile (which dissolve relatively few salts), many of the commonly used polar aprotic solvents have very high boiling points and are difficult to remove from the reaction products. Furthermore, the solubility of salts in polar aprotic solvents is much more limited because they lack the protic character that solvates anions. owever, for the less reactive alkyl halides, or for the S N 2 reactions of fluoride ion, polar aprotic solvents are in some cases the only practical alternative. mportance of the Solvent Effect in an S N 2 Reaction Used in Cancer Diagnosis Positron emission tomography, or PET, is a widely used technique for cancer detection. n PET, a glucose derivative containing an isotope that emits positrons is injected into the patient. A glucose derivative is used because rapidly growing tumors have a high glucose requirement and therefore take up glucose to a greater extent than normal tissue. The emission of positrons (b particles, or positive electrons) is detected when they collide with nearby electrons (b particles). This antimatter matter reaction results in annihilation of the two particles and the production of two gamma rays that retreat from the site of collision in opposite directions, and these are detected ultimately as light.the light emission pinpoints the site of glucose uptake that is, the tumor.

12 9.4 TE S N 2 REACTN 97 The glucose derivative used in PET is 2-18 fluoro-2-deoxy-d-glucopyranose, or FDG, which contains the positron-emitting isotope 18 F ( fluorine-18 ).The structure of FDG is so similar to the structure of glucose that FDG is also taken up by cancer cells. C 2 C 2 18 F 2-( 18 F)-fluoro-2-deoxy-D-glucopyranose (FDG) D-glucopyranose (glucose) The half-life of 18 F is only about 110 minutes.this means that half of it has decayed after 110 minutes, 75 has decayed after 220 minutes, and so on.this short half-life is good for the patient because the emitting isotope doesn t last very long in the body. But it places constraints on the chemistry used to prepare FDG.Thus, 18 F, which is generated from 2 18 as an aqueous solution of K 18 F,must be produced at or near the PET facility and used to prepare FDG quickly in the PET facility. An S N 2 reaction is used to prepare an FDG derivative using 18 F-fluoride as the nucleophile. Like other S N 2 reactions, this reaction occurs with inversion of configuration. triflate group AcC 2 S 2 CF Ac Ac inversion of configuration 18 F Ac a cryptand is used to bind K + Kryptofix [2.2.2] (a cryptand) anhydrous acetonitrile a polar aprotic solvent Ac Ac AcC 2 18 FDG 1,,4,6-tetraacetate F + Ac S 2 CF mannose triflate 1,,4,6-tetraacetate Ac = acetate = C C (9.0a) (The leaving group is a triflate group, which we ll discuss in Sec. 10.A.) This synthesis cannot be carried out in water as a solvent because fluoride ion in protic solvents is virtually unreactive as a nucleophile. To solve this problem, water is completely removed from the aqueous fluoride solution and is replaced by acetonitrile, a polar aprotic solvent (Table 8.2, p. 41). Fluoride ion in anhydrous acetonitrile is a potent nucleophile, and to make it even more nucleophilic, a cryptand (Fig. 8.7, p. 5) is added to sequester the potassium counterion. This prevents the potassium ion from forming ion pairs with the fluoride ion.the naked and highly nucleophilic fluoride ion reacts rapidly with mannose triflate tetraacetate to form FDG tetraacetate, as shown in Eq. 9.0a. The acetate (L Ac) groups are used for several reasons. ne reason is that they make the mannose derivative more soluble in acetonitrile than it would be if L groups were present. But the most important reason they are used is that if L groups were present they would themselves form hydrogen bonds with 18 F,thus reducing its nucleophilicity and preventing the nucleophilic reaction from taking place.the acetate groups are rapidly removed in a subsequent ester hydrolysis reaction (Sec. 21.7A) to give FDG itself.

13 98 CAPTER 9 TE CEMSTRY F ALKYL ALDES Ac Ac AcC 2 18 F FDG 1,,4,6-tetraacetate Ac C M Cl + 4 Ac 18 F hydrolytic removal of acetate groups FDG (9.0b) Figure 9.7 shows the PET image of a malignant lung tumor. PET is so sensitive that it has led to the detection of some cancers at an earlier and less invasive stage than previously possible. As we ve seen, PET hinges on the rapid synthesis of FDG, which in turn hinges on the clever use of polar aprotic solvents and ion-complexing agents to enhance the nucleophilicity of fluoride ion. PRBLEMS 9.1 When methyl bromide is dissolved in ethanol, no reaction occurs at 25 C. When excess sodium ethoxide is added, a good yield of ethyl methyl ether is obtained. Explain (a) Give the structure of the S N 2 reaction product between ethyl iodide and potassium acetate. * C L C $ n other words, the best leaving groups in the S N 2 reaction are those that give the weakest bases as products. Fluoride is the strongest base of the halide ions; consequently, alkyl fluorides are the least reactive of the alkyl halides in S N 2 reactions. n fact, alkyl fluorides react so slowly that they are useless as leaving groups in most S N 2 reactions. n contrast, chloride, bropotassium acetate 1 K (b) n which solvent would you expect the reaction to be faster: acetone or ethanol? Explain Which nucleophile, N(C 2 5 ) or P(C 2 5 ), reacts most rapidly with methyl iodide in ethanol solvent? Explain, and give the product formed in each case. F. Leaving-Group Effects in the S N 2 Reaction n many cases, when an alkyl halide is to be used as a starting material in an S N 2 reaction, a choice of leaving group is possible. That is, an alkyl halide might be readily available as an alkyl chloride, alkyl bromide, or alkyl iodide. n such a case, the halide that reacts most rapidly is usually preferred. The reactivities of alkyl halides can be predicted from the close analogy between S N 2 reactions and Brønsted acibase reactions. Recall that the ease of dissociating an LX bond within the series of hydrogen halides depends mostly on the LX bond energy (Sec..6A), and, for this reason, L is the strongest acid among the hydrogen halides. Likewise, S N 2 reactivity depends primarily on the carbon halogen bond energy, which follows the same trend: Alkyl iodides are the most reactive alkyl halides, and alkyl fluorides are the least reactive. Relative reactivities in S N 2 reactions: RLF << RLCl < RLBr < RL (9.1)

14 9.4 TE S N 2 REACTN 99 malignancy as visualized by PET Figure 9.7 The PET image of a malignant lung tumor. The positron-emitting 18 F is incorporated in the structure of FDG, a glucose derivative. FDG uptake, like glucose uptake, is enhanced in malignant tumors because they are rapidly growing and require more glucose than normal tissues. mide, and iodide ions are much less basic than fluoride ion; alkyl chlorides, alkyl bromides, and alkyl iodides all have acceptable reactivities in typical S N 2 reactions, and alkyl iodides are the most reactive of these. n a laboratory scale, alkyl bromides, which are in most cases less expensive than alkyl iodides, usually represent the best compromise between expense and reactivity. For reactions carried out on a large scale, the lower cost of alkyl chlorides offsets the disadvantage of their lower reactivity. alides are not the only groups that can be used as leaving groups in S N 2 reactions. Section 10.A will introduce a variety of alcohol derivatives that can also be used as starting materials for S N 2 reactions. G. Summary of the S N 2 Reaction Primary and some secondary alkyl halides undergo nucleophilic substitution by the S N 2 mechanism. Let s summarize six of the characteristic features of this mechanism. 1. The reaction rate is second order overall: first order in the nucleophile and first order in the alkyl halide. 2. The mechanism involves a backside substitution reaction of the nucleophile with the alkyl halide and inversion of stereochemical configuration.. The reaction rate is decreased by alkyl substitution at both the a- and b-carbon atoms; alkyl halides with three b-branches are unreactive. 4. When the nucleophilic atoms come from within the same row of the periodic table, the strongest bases are generally the most reactive nucleophiles. 5. The solvent has a significant effect on nucleophilicity. S N 2 reactions are generally slower in protic solvents than in aprotic solvents, and the effect is particularly great for anions containing nucleophilic atoms from the second period. 6. The fastest S N 2 reactions involve leaving groups that give the weakest bases as products.