9.4 the Sn2 Reaction

09_BRCLoudon_pgs4-3.qxd 11/26/08 12:25 PM Page 386

386 CHAPTER 9 • THE CHEMISTRY OF ALKYL HALIDES

9.7 What prediction does the rate law in Eq. 9.20 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 ma- terials and products against time.

9.4 THE SN2 REACTION

A. Rate Law and Mechanism of the SN2 Reaction Consider now the nucleophilic substitution reaction of ethoxide ion with methyl iodide in ethanol at 25 C. ° C H O H CI C H O CH I (9.23) 2 5 _ 3 C H OH 2 5 3 _ + L 2 5 L + The following rate law for this reaction was experimentally determined for this reaction:

rate k[CH3I][C2H5O_] (9.24) 4 1 1 = with k 6.0 10_ M_ s_ . That is, this is a second-order reaction that is ﬁrst order in each reactant.= X 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. Hence, the rate-limiting transition state of reaction 9.23 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:

H ‡ d d _ _ (9.25) C2H5O _ H3C I C2H5O "C I C2H5O CH3 I _ 213 L 213 213 3213 21 L + 3132 ΄ H H ΅ ) ) transition state 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 inter-

mediates) is called an SN2 mechanism. Reactions that occur by SN2 mechanisms are called SN2reactions.The meaning of the “nickname” SN2 is as follows:

SN2 substitution bimolecular nucleophilic (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 SN2 reaction, because it is concerted, involves no reactive intermediates. 09_BRCLoudon_pgs4-3.qxd 11/26/08 12:25 PM Page 387

9.4 THE SN2 REACTION 387

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 STUDY GUIDE LINK 9.1 Deducing about how they are arranged. Thus, the following two mechanisms for the SN2 reaction of Mechanisms from ethoxide ion with methyl iodide are equally consistent with the rate law. Rate Laws C H O

2 5 _ H H 132 % "C %C (9.26) H C H O H I I 2 5 _ L H 132 H frontside substitution backside substitution

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 rate- limiting step. 2. Mechanisms that are not consistent with the rate law are ruled out. 3. Of 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. However, 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 the- ory, 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.

PROBLEMS 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.

1 O 1 O S S H CHC NH H C C NH| 3 O 3 3 O _ 4 L L 1 L + 3 L L 1 3 + acetic acid O S rate k͓H3C C OH͔͓NH3͔ = LL 9.9 What rate law would be expected for the reaction of cyanide ion (_ CN) with ethyl bromide by the SN2 mechanism? 3 09_BRCLoudon_pgs4-3.qxd 11/26/08 12:25 PM Page 388

388 CHAPTER 9 • THE CHEMISTRY OF ALKYL HALIDES

B. Comparison of the Rates of SN2 Reactions and Brønsted Acid–Base Reactions In Sec. 3.4B, and again in Sec. 9.2, we learned about the close analogy between nucleophilic substitution reactions and acid–base reactions. The equilibrium constants for a nucleophilic substitution reaction and its acid–base analog are very similar, and the curved-arrow notations

for an SN2 reaction and its acid–base analog are identical. However, it is important to under- stand that their rates are very different. Most ordinary acid–base reactions occur instanta- neously—as fast as the reacting pairs can diffuse together. The rate constants for such reac- 8 10 1 1 tions are typically in the 10 –10 M_ s_ range. Although many nucleophilic substitution reactions occur at convenient rates, they are much slower than the analogous acid–base reactions. Thus, the reaction in Eq. 9.27a is completed in a little over an hour, but the correspond- ing acid–base reaction in Eq. 9.27b occurs within about a billionth of a second!

Nucleophilic substitution reaction:

.. ..

......

...... C2H5O H3C I C2H5O CH3 I.. (9.27a) + L C2H5OH L + (complete in about an hour)

Brønsted acid–base reaction:

.. ..

......

...... C2H5O HHI C2H5O I.. (9.27b) + L C2H5OH L + (complete in 10–9 second)

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. In other words, the Brønsted acid always wins.

PROBLEMS 9.10 Methyl iodide (0.1 M) and hydriodic acid (HI, 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 HBr (0.1 M) are allowed to react in aqueous THF with 1 M sodium

cyanide (Na|_CN). What products are observed? Are any products formed more rapidly than others? Explain.

C. Stereochemistry of the SN2 Reaction

The mechanism of the SN2 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 3. with a combination of (1) and (2); that is, mixed retention and inversion.

If approach of the nucleophile Nuc_ to an asymmetric carbon and departure of the leaving group X_ occur from more or less the 3same direction (frontside substitution), then a substitution reaction3 would result in a product with retention of conﬁguration at the asymmetric carbon. 09_BRCLoudon_pgs4-3.qxd 11/26/08 12:25 PM Page 389

9.4 THE SN2 REACTION 389

1 Nuc 1 1 R _ R d– ‡ R 3 Nuc % % % (9.28a) C X C 3 d– C Nuc _ X R2 L R2 X R2 L + 3 R3 R3 3 R3 transition state In 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.

1 1 1 R R ‡ L R

d– L d– Nuc % % _ CCX Nuc X Nuc C _ X (9.28b) 3 R2 R2 L 3 2 3 + 3 3 ΄ R 3 ΅ 3 R R R transition state 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 SN2 reaction and determining which enantiomer of the product is formed. If 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 SN2 reaction. The reaction follows a second- order rate law, ﬁrst order in _OH and ﬁrst order in the alkyl halide. When (R)-2-bromooctane

is used in the reaction, the product is (S)-2-octanol. CH3 L CH3

% L _OH CCBr HO Br _ (9.29) + H L H + (CH2)5CH3 (CH2)5CH3 (R)-2-bromooctane (S)-2-octanol

The stereochemistry of this SN2 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 SN2 reaction. In fact, inversion of stereochemical conﬁguration is generally observed in all SN2 reactions at carbon stereocenters. The stereochemistry of the SN2 reaction calls to mind the inversion of amines (Fig. 6.17, p. 256). In the hybrid orbital description of both processes, the central atom is turned “inside out,” and it is approximately sp2-hybridized at the transition state. In the transition state for amine inversion, the 2p orbital on the nitrogen contains an unshared electron pair. In the tran-

sition state for an SN2 reaction on carbon, the nucleophile and the leaving group are partially bonded to opposite lobes of the carbon 2p orbital (Fig. 9.2, p. 390).

Why is backside substitution preferred in the SN2 reaction? The hybrid orbital description of the reaction in Fig. 9.2 provides no information on this question, but a molecular orbital analy- sis does, as shown in Fig. 9.3 (p. 391) for the reaction of a nucleophile (Nuc ) with methyl chlo-

ride (CH3Cl). When a nucleophile donates electrons to an alkyl halide, the3 orbital containing the donated electron pair must initially interact with an unoccupied molecular orbital of the 09_BRCLoudon_pgs4-3.qxd 11/26/08 12:25 PM Page 390

390 CHAPTER 9 • THE CHEMISTRY OF ALKYL HALIDES

‡ sp2-hybridized carbon

R1 R1 R1 ␦ ␦ ϩ Nuc_ X_ Nuc C ϩ X Nuc _ C X C _ 3 R2 3 3 R2 2 R R R3 R3

120Њ

transition state

Figure 9.2 Stereochemistry of the SN2 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 MO of the nucleophile that contains the donated electron pair interacts with the unoccupied alkyl halide MO of lowest energy, called the LUMO (for “lowest unoccupied molecular orbital”). It happens that all of the bonding MOs of the alkyl halide are occupied; therefore, the alkyl halide LUMO is an antibonding MO, which is shown in Fig. 9.3. When backside substitution occurs (Fig. 9.3a), bonding overlap of the nucleophile orbital occurs with the alkyl halide LUMO; that is, wave peaks overlap. But in frontside substitution (Fig. 9.3b), the nucleophile orbital has both bonding and antibonding overlap with the LUMO; 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.

PROBLEM 9.12 What is the expected substitution product (including its stereochemical conﬁguration) in the SN2 reaction of potassium iodide in acetone solvent with the following compound? (D 2H deuterium, an isotope of hydrogen.) = = Cl (R)-CH3CH2CH2CHL L D

D. Effect of Alkyl Halide Structure on the SN2 Reaction

One of the most important aspects of the SN2 reaction is how the reaction rate varies with the structure of the alkyl halide. (Recall Eqs. 9.14 and 9.15, p. 382.) If an alkyl halide is very re-

active, its SN2 reactions occur rapidly under mild conditions. If 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. However, harsh conditions increase the likelihood of competing side reactions. Hence, 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 SN2 reaction. Typical reactivity data are given in Table 9.3. To put these data in some perspective: If the reaction of a methyl halide takes about one minute, then the reaction of a neopentyl halide under the same conditions takes about 23 years! 09_BRCLoudon_pgs4-3.qxd 11/26/08 12:25 PM Page 391

9.4 THE SN2 REACTION 391

methyl chloride methyl chloride

bonding overlap LUMO (antibonding) LUMO (antibonding) .. Nuc

bonding overlap antibonding overlap (a) backside substitution cancels bonding overlap ..

Nuc

(b) frontside substitution

Figure 9.3 In the SN2 reaction, the orbital containing the nucleophile electron pair interacts with the unoccupied molecular orbital of lowest energy (LUMO) 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 9.3 Effect of Alkyl Substitution in the Alkyl Halide

on the Rate of a Typical SN2 Reaction

25 °C R Br I R I Br _ acetone _ L + L + R Name of R Relative rate* L CH3—methyl145 Increased alkyl substitution at the b-carbon:

CH3CH2CH2—propyl0.82 (CH3)2CHCH2—isobutyl0.036 (CH3)3CCH2—neopentyl0.000012 Increased alkyl substitution at the a-carbon:

CH3CH2—ethyl1.0 (CH3)2CH— isopropyl 0.0078 † (CH3)3C— tert-butyl ;0.0005

*All rates are relative to that of ethyl bromide. †Estimated from the rates of closely related reactions.

The data in Table 9.3 show, ﬁrst, that increased alkyl substitution at the b-carbon retards

an SN2 reaction. As Fig. 9.4 on p. 392 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. However, 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, SN2 reactions of branched alkyl halides are retarded by a steric effect. Indeed, SN2 reactions of neopentyl halides are so slow that they are not practically useful. 09_BRCLoudon_pgs4-3.qxd 11/26/08 12:25 PM Page 392

392 CHAPTER 9 • THE CHEMISTRY OF ALKYL HALIDES

van der Waals repulsions

d– d– d– d– I I Br Br

van der Waals repulsions

d– d– d– d–

I Br Br I

(a) Br + CH3 I (b) Br + (CH3)3C CH2 I

Figure 9.4 Transition states for SN2 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 SN2 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 9.3 help explain why elimination reactions compete with the SN2 reactions of secondary and tertiary alkyl halides (Sec. 9.1C): these halides react so slowly in

SN2 reactions that the rates of elimination reactions are competitive with the rates of substitution. The rates of the SN2 reactions of tertiary alkyl halides are so slow that elimination is the only reaction observed. The competition between b-elimination and SN2 reactions will be considered in more detail in Sec. 9.5G.

E. Nucleophilicity in the SN2 Reaction

As Table 9.1 (p. 379) illustrates, the SN2 reaction is especially useful because of the variety of nucleophiles that can be employed. However, nucleophiles differ signiﬁcantly in their reactiv-

ities. What factors govern nucleophilicity in the SN2 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. 3.4A.) Let’s

ﬁrst examine some data for the SN2 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 plot- ted in Fig. 9.5. Notice in this table that the nucleophilic atoms are all from the second period 09_BRCLoudon_pgs4-3.qxd 11/26/08 12:25 PM Page 393

9.4 THE SN2 REACTION 393

TABLE 9.4 Dependence of SN2 Reaction Rate on the Basicity of the Nucleophile

25 °C Nuc H C I Nuc CH I _ 3 CH OH 3 _ 3 + L 3 L + k (second-order rate 1 1 Nucleophile (name) pKa of conjugate acid* constant, M_ s_ )log k

4 CH3O_ (methoxide) 15.1 2.5 10_ 3.6 X - 5 PhO_ (phenoxide) 9.95 7.9 10_ 4.1 X - 4 _CN (cyanide) 9.4 6.3 10_ 3.2 X - 6 AcO_ (acetate) 4.76 2.7 10_ 5.6 X - 5 N3_ (azide) 4.72 7.8 10_ 4.1 X - 8 F_ (ﬂuoride) 3.2 5.0 10_ 7.3 X - 2 7 SO4_ (sulfate) 2.0 4.0 10_ 6.4 X - 9 NO3_ (nitrate) 1.2 5.0 10_ 8.3 - X -

*pKa values in water

Increasing nucleophile basicity 2 - 3 line of slope = 1 CN - _ CH3O I _ 4 N 3 3 PhO - _ _ CH 5 2 reaction2 rate +

- N .. AcO 6 _ 2 - SO4_

for Nuc for 7 k

F S Increasing - _

log 8 - NO _3 9 - 2 0 2 4 6 8 10 12 14 16

- .. basicity of Nuc (pKa of Nuc H)

Figure 9.5 The dependence of nucleophile SN2 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

O_.The black circles show the reactivity of other nucleophilic anions in which the reacting atoms are from pe- Lriod 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. 394). If we are expect- ing a similar correlation of nucleophilic reactivity and basicity, we get a surprise. Notice that the 09_BRCLoudon_pgs4-3.qxd 11/26/08 12:25 PM Page 394

394 CHAPTER 9 • THE CHEMISTRY OF ALKYL HALIDES

TABLE 9.5 Dependence of SN2 Reaction Rate on the Basicity of Nucleophiles from Different Periods of the Periodic Table

25 °C Nuc H C I Nuc CH I _ 3 CH OH 3 _ 3 + L 3 L + k (second-order rate 1 1 Nucleophile pKa of conjugate acid* constant, M_ s_ )log k

Group 6A Nucleophiles

PhS_ 6.52 1.1 0.03 + 5 PhO_ 9.95 7.9 10_ 4.1 X - Group 7A Nucleophiles 3 I_ 10 3.4 10_ 2.5 - X - 5 Br_ 88.010_ 4.1 - X - 6 Cl_ 63.010_ 5.5 - X - 8 F_ 3.2 5.0 10_ 7.3 X -

*pKa 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. In 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. In 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 ac- counts 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. In 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 hy-

drogen bonding, they are unavailable for donation to carbon in an SN2 reaction. For the SN2 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 car- rier 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. If 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 = 09_BRCLoudon_pgs4-3.qxd 11/26/08 12:25 PM Page 395

9.4 THE SN2 REACTION 395

bond to carbon H H ‡ O hydrogen bonds between O $ nucleophile and solvent $ H) H) H O O O d " d H % %H X _ H % %H CH3I H % %H X _ C I _ H2O 3321 ++3 21 3 H H H H $O $O H) H) transition state

Figure 9.6 An SN2 reaction of methyl iodide involving a nucleophile (x1 _ ) in a protic solvent requires breaking a hydrogen bond between the solvent and the nucleophile.The energy 3required13 to break this hydrogen bond be- comes part of the standard free energy of activation of the substitution reaction and thus retards the reaction.

O_ as the reacting atom (blue squares). The downward curvature shows that the nucle- ophilesL 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. If hydrogen bonding by the solvent tends to reduce the reactivity of very basic nucle-

ophiles, it follows that SN2 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 propo- sition with the aid of some data shown in Table 9.6 (p. 396). The two solvents, methanol (e 33) and N,N-dimethylformamide (DMF, e 37; structure in Table 8.2, p. 341), were cho- sen= for the comparison because their dielectric constants= are nearly the same; that is, their po- larities 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 108. In fact, the accel-

eration of the reaction with ﬂuoride ion is so dramatic that an SN2 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. Other polar aprotic solvents

have effects of a similar magnitude, and similar accelerations occur in the SN2 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 SN2 reactions. 09_BRCLoudon_pgs4-3.qxd 11/26/08 12:25 PM Page 396

396 CHAPTER 9 • THE CHEMISTRY OF ALKYL HALIDES

TABLE 9.6 Solvent Dependence of Nucleophilicity in the SN2 Reaction

25 °C Nuc _ H3C I Nuc CH3 I_ 3 + L L + In methanol In DMF‡

Reaction is Reaction is 1 1 † 1 1 † Nucleophile pKa* k, M_ s_ over in— k, M_ s_ over in—

3 1 I_ 10 3.4 10_ 17 min 4.0 10_ 8.7 s - X X 5 Br_ 88.010_ 12 h 1.3 2.7 s - X 6 CI_ 63.010_ 13 days 2.5 1.4 s - X 8 F_ 3.2 5.0 10_ 2.2 years 3 1.2 s X > < 4 2 _CN 9.4 6.3 10_ 1.5 h 3.2 10 0.011 s X X

*pKa values of the conjugate acid in water †Time required for 97% completion of the reaction ‡DMF N,N-dimethylformamide (see Table 8.2, p. 341) =

As the data demonstrate, eliminating the possibility of hydrogen bonding to nucleophiles

strongly accelerates their SN2 reactions. What we’ve learned, then, is that SN2 reactions of nucleophilic anions with alkyl halides are much faster in polar aprotic solvents than they are in protic solvents. If this is so, why not

use polar aprotic solvents for all such SN2 reactions? Here we must be concerned with an ele- ment of practicality. To run an SN2 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 SN2 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 SN2 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. However, for the less reactive alkyl halides, or for the SN2 reactions of ﬂuo- ride ion, polar aprotic solvents are in some cases the only practical alternative.

Importance of the Solvent Effect in an SN2 Reaction Used in Cancer Diagnosis Positron emission tomography, or “PET,”is a widely used technique for cancer detection. In 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 antimat- ter–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. 09_BRCLoudon_pgs4-3.qxd 11/26/08 12:25 PM Page 397

9.4 THE SN2 REACTION 397

The glucose derivative used in PET is 2-18ﬂuoro-2-deoxy-D-glucopyranose,or FDG,which contains the positron-emitting isotope 18F (“ﬂuorine-18”).The structure of FDG is so similar to the structure of glucose that FDG is also taken up by cancer cells.

HOCH2 HOCH2 O O HO HO HO OH HO OH 18F OH

18 2-( F)-fluoro-2-deoxy-D-glucopyranose D-glucopyranose (FDG) (glucose)

The half-life of 18F 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 18 18 18 prepare FDG.Thus, F,which is generated from H 2 O as an aqueous solution of K| F_,must be pro-

duced at or near the PET facility and used to prepare FDG quickly in the PET facility.An SN2 reaction is 18 used to prepare an FDG derivative using F-ﬂuoride as the nucleophile. Like other SN2 reactions, this reaction occurs with inversion of conﬁguration.

a cryptand is used +

triflate group to bind K

.. ..

AcOCH2 OSO2CF3 AcOCH2

Kryptofix [2.2.2] O ..

O .. AcO (a cryptand) AcO + OSO.. CF

OAc OAc 2 3

AcO anhydrous acetonitrile AcO

18 .. ..

18 .. .. F.. F inversion of a polar aprotic solvent FDG 1,3,4,6-tetraacetate configuration

mannose triflate 1,3,4,6-tetraacetate O

AcO = acetate = H3C C O (9.30a)

(The leaving group is a triflate group, which we’ll discuss in Sec.10.3A.) 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. 341). Fluoride ion in anhydrous acetonitrile is a potent nucleophile,and to make it even more nucleophilic,a cryptand (Fig.8.7,p.353) 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. 9.30a. The acetate ( OAc) groups are used for several reasons. One reason is that they make the mannose derivative Lmore soluble in acetonitrile than it would be if OH groups were present. But the most important reason they are used is that if O H groups wereL present they would themselves 18 L form hydrogen bonds with 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. 09_BRCLoudon_pgs4-3.qxd 11/26/08 12:25 PM Page 398

398 CHAPTER 9 • THE CHEMISTRY OF ALKYL HALIDES

AcOCH2 HOCH2 O O AcO 3M HCl HO

AcO OAc + 4 H2O HO OH + 4 AcOH (9.30b)

......

18 .. 18

.. F.. F FDG hydrolytic removal FDG 1,3,4,6-tetraacetate of acetate groups

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.

PROBLEMS 9.13 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.°

9.14 (a) Give the structure of the SN2 reaction product between ethyl iodide and potassium acetate. O 3 3 H3C C* L O K $ _ | 3 1 3 potassium acetate

(b) In which solvent would you expect the reaction to be faster: acetone or ethanol? Explain.

9.15 Which nucleophile, N(C2H5)3 or P(C2H5)3, reacts most rapidly with methyl iodide in ethanol solvent? Explain, and3 give the product3 formed in each case.

F. Leaving-Group Effects in the S N2 Reaction

In many cases, when an alkyl halide is to be used as a starting material in an SN2 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. In 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 SN2 reactions and Brønsted acid–base reactions. Recall that the ease of dissociating an H X bond within the series of hydrogen halides depends mostly on the H X bond energy (Sec.L 3.6A), and, for this reason, H I is the strongest acid among the hydrogenL halides.

Likewise, SN2 reactivity depends primarilyL 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 SN2 reactions: R F R Cl R Br R I (9.31) L << L < L < L In other words, the best leaving groups in the SN2 reaction are those that give the weakest bases as products. Fluoride is the strongest base of the halide ions; consequently, alkyl ﬂuo-

rides are the least reactive of the alkyl halides in SN2 reactions. In fact, alkyl ﬂuorides react so slowly that they are useless as leaving groups in most SN2 reactions. In contrast, chloride, bro- 09_BRCLoudon_pgs4-3.qxd 11/26/08 12:25 PM Page 399

9.4 THE SN2 REACTION 399

malignancy as visualized by PET

Figure 9.7 The PET image of a malignant lung tumor.The positron-emitting 18F 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 SN2 reactions, and alkyl iodides are the most reactive of these. On 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.

Halides are not the only groups that can be used as leaving groups in SN2 reactions. Section 10.3A will introduce a variety of alcohol derivatives that can also be used as starting materi-

als for SN2 reactions.

G. Summary of the SN2 Reaction

Primary and some secondary alkyl halides undergo nucleophilic substitution by the SN2 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. 3. 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. SN2 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 SN2 reactions involve leaving groups that give the weakest bases as products.