9.4 the sn2 reaction - sapling learning€¦ · bon occur from opposite directions (backside...

386 CHAPTER 9 • THE CHEMISTRY OF ALKYL HALIDES

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 inethanol at 25 °C.

(9.23)

The following rate law for this reaction was experimentally determined for this reaction:

rate = k[CH3I][C2H5O_] (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 eachreactant.

The rate law of a reaction is important because it provides fundamental information aboutthe reaction mechanism. Specifically, the concentration terms of the rate law indicate whichatoms are present in the transition state of the rate-limiting step. Hence, the rate-limiting tran-sition state of reaction 9.23 consists of the elements of one methyl iodide molecule and oneethoxide ion. The rate law excludes some mechanisms from consideration. For example, anymechanism in which the rate-limiting step involves two molecules of ethoxide is ruled out bythe rate law, because the rate law for such a mechanism would have to be second order inethoxide.

The simplest possible mechanism consistent with the rate law is one in which the ethoxideion directly displaces the iodide ion from the methyl carbon:

Mechanisms like this account for many nucleophilic substitution reactions. A mechanism inwhich electron-pair donation by a nucleophile to an atom (usually carbon) displaces a leavinggroup 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 calledSN2 reactions. The meaning of the “nickname” SN2 is as follows:

(The word bimolecular means that the rate-limiting step of the reaction involves twospecies—in this case, one methyl iodide molecule and one ethoxide ion.) Notice that an SN2reaction, because it is concerted, involves no reactive intermediates.

substitution bimolecular

SN2

nucleophilic

(9.25)21 3C2H5O CH3C Ltransition state

"I213 I2133 I2133_ _21 3C2H5O L21C2H5O CH3! " +) )

H

H

H

‡d_ d_

C2H5O_ H3C I+ C2H5O CH3 I_+L LC2H5OH

9.7 What prediction does the rate law in Eq. 9.20 make about how the rate of the reaction changesas the reactants D and E are converted into F over time? Does the rate increase, decrease, orstay the same? Explain. Use your answer to sketch a plot of the concentrations of starting ma-terials and products against time.

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

9.4 THE SN2 REACTION 387

The rate law does not reveal all of the details of a reaction mechanism. Although the ratelaw indicates what atoms are present in the rate-limiting step, it provides no informationabout how they are arranged. Thus, the following two mechanisms for the SN2 reaction ofethoxide ion with methyl iodide are equally consistent with the rate law.

As far as the rate law is concerned, either mechanism is acceptable. To decide between thesetwo 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 experi-

ments.

Point (4) may seem disturbing because it means that a mechanism can be changed at a latertime. 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 mecha-nism 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 onchemical observations. Thus, when someone observes an experimental result different fromthat predicted by a mechanism, the mechanism must be modified to accommodate both thepreviously known facts and the new facts. The evolution of mechanisms is no different fromthe evolution of science in general. Knowledge is dynamic: theories (mechanisms) predict theresults of experiments, a test of these theories may lead to new theories, and so on.

PROBLEMS9.8 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.

9.9 What rate law would be expected for the reaction of cyanide ion (_3CN) with ethyl bromide bythe SN2 mechanism?

3NH3

acetic acid

C

O

LH3C HLL O11S + C

O

3 NH4LH3C L O11S +_ |

rate = k#H3C C

O

L L OH$#NH3$S

(9.26)C II

H

H

H

21 3C2H5O

"

frontside substitution backside substitution

%H

H

H

C L%_

21 3C2H5O _

STUDY GUIDE LINK 9.1Deducing

Mechanisms fromRate Laws



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 nucleophilicsubstitution reactions and acid–base reactions. The equilibrium constants for a nucleophilicsubstitution reaction and its acid–base analog are very similar, and the curved-arrow notationsfor 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-tions are typically in the 108–1010 M_1 s_1 range. Although many nucleophilic substitutionreactions occur at convenient rates, they are much slower than the analogous acid–base reac-tions. 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!

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.

C. Stereochemistry of the SN2 Reaction

The mechanism of the SN2 reaction can be described in more detail by considering its stereo-chemistry. The stereochemistry of a substitution reaction can be investigated only if the car-bon 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; or3. with a combination of (1) and (2); that is, mixed retention and inversion.

If approach of the nucleophile Nuc3_ to an asymmetric carbon and departure of the leavinggroup X3_ occur from more or less the same direction (frontside substitution), then a substitu-tion reaction would result in a product with retention of configuration at the asymmetriccarbon.

9.10 Methyl iodide (0.1 M) and hydriodic acid (HI, 0.1 M) are allowed to react in ethanol solutionwith 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 sodiumcyanide (Na| _CN). What products are observed? Are any products formed more rapidlythan others? Explain.

PROBLEMS

(9.27b)C2H5O I+ C2H5O +L LC2H5OH

..

......

..

..

..

.. I

..

..

....

(complete in 10–9 second)

Brønsted acid–base reaction:

H H

(9.27a)C2H5O H3C I+ C2H5O CH3 +L LC2H5OH

..

......

..

..

..

.. I

..

..

....

(complete in about an hour)

Nucleophilic substitution reaction:

09_BRCLoudon_pgs4-3.qxd 11/26/08 12:25 PM 88


In contrast, if approach of the nucleophile and loss of the leaving group on an asymmetric car-bon occur from opposite directions (backside substitution), the other three groups on carbonmust invert, or “turn inside out,” to maintain the tetrahedral bond angle. This mechanismwould lead to a product with inversion of configuration at the asymmetric carbon.

The products of Eqs. 9.28a and 9.28b are enantiomers. Thus, the two types of substitution canbe distinguished by subjecting one enantiomer of a chiral alkyl halide to the SN2 reaction anddetermining 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, achiral 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-bromooctaneis used in the reaction, the product is (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 othernucleophiles 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 ofstereochemical 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 “insideout,” and it is approximately sp2-hybridized at the transition state. In the transition state foramine 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 partiallybonded 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 ofthe 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 (Nuc3) with methyl chlo-ride (CH3Cl). When a nucleophile donates electrons to an alkyl halide, the orbital containingthe donated electron pair must initially interact with an unoccupied molecular orbital of the

(9.29)_CH3CH3 LL

Br_H H

OH HO

(CH2)5CH3 (CH2)5CH3

C CL%Br +

(R)-2-bromooctane (S)-2-octanol

+

(9.28b)R2

R3

C

L L

X3X33 _Nuc 3_Nuc

R2

R3

C CLX

R2

R1

R3

Nuc! +transition state

"‡R1% R1%

d–d–

(9.28a)R2

R3

C L X3X3

3 _Nuc3_

NucR2

R1

R3

C L% R1% R1%X

R2

R3

CNuc +

transition state

‡

d–

d–



alkyl halide. The MO of the nucleophile that contains the donated electron pair interacts withthe unoccupied alkyl halide MO of lowest energy, called the LUMO (for “lowest unoccupiedmolecular 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. Whenbackside substitution occurs (Fig. 9.3a), bonding overlap of the nucleophile orbital occurs withthe 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 anti-bonding overlap (wave peak to wave trough) cancels the bonding overlap, and no net bondingcan occur. Because only backside substitution gives bonding overlap, this is always the ob-served substitution mode.

PROBLEM9.12 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.)

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 thestructure 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 un-reactive, then the severity of the reaction conditions (for example, the temperature) must be in-creased for the reaction to proceed at a reasonable rate. However, harsh conditions increase thelikelihood of competing side reactions. Hence, if an alkyl halide is unreactive enough, the re-action has no practical value.

Alkyl halides differ, in some cases by many orders of magnitude, in the rates with whichthey undergo a given SN2 reaction. Typical reactivity data are given in Table 9.3. To put thesedata in some perspective: If the reaction of a methyl halide takes about one minute, then the re-action of a neopentyl halide under the same conditions takes about 23 years!

(R)-CH3CH2CH2CH

D

LL Cl

120!

sp2-hybridized carbon

Nuc_"

X_"

transition state

C CCCCCCCCCCCC

R2RRR3RR

R1R1

XXNuc _3 #

‡

_3CR2RR

R22RRR3RR

R3RR

R1

X#Nuc CCC

Figure 9.2 Stereochemistry of the SN2 reaction.The green arrows show how the various groups change positionduring the reaction. (Nuc:_ = a general nucleophile.) Notice that the sterochemical configuration of the asymmet-ric carbon is inverted by the reaction.



The data in Table 9.3 show, first, that increased alkyl substitution at the b-carbon retardsan SN2 reaction. As Fig. 9.4 on p. 392 shows, these data are consistent with a backside substi-tution mechanism. When a methyl halide undergoes substitution, approach of the nucleophileand departure of the leaving group are relatively unrestricted. However, when a neopentylhalide reacts with a nucleophile, both the nucleophile and the leaving group experience severevan der Waals repulsions with hydrogens of the methyl substituents. These van der Waalsrepulsions raise the energy of the transition state and therefore reduce the reaction rate. Thisis another example of a steric effect. Recall from Sec. 5.6D that a steric effect is any effect ona chemical phenomenon (such as a reaction) caused by van der Waals repulsions. Thus, SN2reactions of branched alkyl halides are retarded by a steric effect. Indeed, SN2 reactions ofneopentyl halides are so slow that they are not practically useful.

methyl chlorideLUMO (antibonding)

..

..

Nuc

Nuc

(a) backside substitution

(b) frontside substitution

bonding overlap

bonding overlapantibonding overlapcancels bonding overlap

methyl chlorideLUMO (antibonding)

Figure 9.3 In the SN2 reaction, the orbital containing the nucleophile electron pair interacts with the unoccu-pied molecular orbital of lowest energy (LUMO) in the alkyl halide. (a) Backside substitution leads to bondingoverlap. (b) Frontside substitution gives both bonding and antibonding overlaps that cancel. Therefore, backsidesubstitution is always observed.

Effect of Alkyl Substitution in the Alkyl Halide on the Rate of a Typical SN2 Reaction

RL Name of R Relative rate*

CH3— methyl 145

Increased alkyl substitution at the b-carbon:CH3CH2CH2— propyl 0.82(CH3)2CHCH2— isobutyl 0.036(CH3)3CCH2— neopentyl 0.000012

Increased alkyl substitution at the a-carbon:CH3CH2— ethyl 1.0(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.

TABLE 9.3

R LBr I_+ R L I Br_+acetone

25 °C



The data in Table 9.3 help explain why elimination reactions compete with the SN2reactions of secondary and tertiary alkyl halides (Sec. 9.1C): these halides react so slowly inSN2 reactions that the rates of elimination reactions are competitive with the rates of substitu-tion. The rates of the SN2 reactions of tertiary alkyl halides are so slow that elimination is theonly reaction observed. The competition between b-elimination and SN2 reactions will beconsidered 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 ofnucleophiles 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 anucleophile because both are aspects of its Lewis basicity. That is, in either role a Lewis basedonates an electron pair. (Be sure to review the definitions of these terms in Sec. 3.4A.) Let’sfirst examine some data for the SN2 reactions of methyl iodide with anionic nucleophiles ofdifferent basicity to see whether this expectation is met in practice. Some data for the reactionof 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

IBr Br

BrBr

I

II

d–d–

d–d–

d–

d–d–

d–

van der Waals repulsions

van der Waals repulsions

(a) Br + CH3 I (b) Br + (CH3)3C ICH2

Figure 9.4 Transition states for SN2 reactions.The upper panels show the transition states as ball-and-stick mod-els, 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 be-cause of the severe van der Waals repulsions of both the nucleophile and the leaving group with the pink hydro-gens of the methyl substituents.These repulsions are indicated with red brackets in the models.



of the periodic table. Figure 9.5 shows a very rough trend toward faster reactions with themore basic nucleophiles.

Let’s now consider some data for the same reaction with anionic nucleophiles from differentperiods (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

Increasing nucleophile basicity

Incr

easi

ng S

N2

reac

tion

rat

e

line of slope = 1

SO42_

AcO_

F_

PhO_CH3O_

NO3_

N3_

_CN

-2 0 2 4 6 8 10 12 14 16

(pKa of Nuc H)basicity of Nuc ..

log

k fo

r N

uc

..

+C

H3

I

-2

-3

-4

-5

-6

-7

-8

-9

Figure 9.5 The dependence of nucleophile SN2 reactivity on nucleophile basicity for a series of nucleophiles inmethanol solvent. Reactivity is measured by log k for the reaction of the nucleophile with methyl iodide. Basicityis measured by the pKa of the conjugate acid of the nucleophile. The blue dashed line of slope = 1 shows thetrend to be expected if a change of one log unit in basicity resulted in the same change in nucleophilicity. Thesolid blue line shows the actual trend for a series of nucleophiles (blue squares) in which the reacting atom isLO_.The black circles show the reactivity of other nucleophilic anions in which the reacting atoms are from pe-riod 2 of the periodic table, the same period as oxygen.

Dependence of SN2 Reaction Rate on the Basicity of the Nucleophile

k (second-order rateNucleophile (name) pKa of conjugate acid* constant, M_1 s_1) log k

CH3O_ (methoxide) 15.1 2.5 X 10_4 -3.6

PhO_ (phenoxide) 9.95 7.9 X 10_5 -4.1

_CN (cyanide) 9.4 6.3 X 10_4 -3.2

AcO_ (acetate) 4.76 2.7 X 10_6 -5.6

N3_ (azide) 4.72 7.8 X 10_5 -4.1

F_ (fluoride) 3.2 5.0 X 10_8 -7.3

SO42_ (sulfate) 2.0 4.0 X 10_7 -6.4

NO3_ (nitrate) -1.2 5.0 X 10_9 -8.3

*pKa values in water

TABLE 9.4

Nuc L CH3 I_+25 °CH3C L INuc _ +3

CH3OH



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 nucle-ophiles, 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 inpolar, protic solvents (such as water and alcohols):

1. In a series of nucleophiles in which the nucleophilic atoms are from the same period ofthe 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 morenucleophilic.

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 rela-tionship of basicity and nucleophilicity within a group of the periodic table. The solvent in allof the cases shown in Tables 9.4 and 9.5 and Fig. 9.5 is methanol, a protic solvent. In a proticsolvent, hydrogen bonding occurs between the protic solvent molecules (as hydrogen bonddonors) and the nucleophilic anions (as hydrogen bond acceptors). The strongest Brønstedbases are the best hydrogen bond acceptors. For example, fluoride ion forms much strongerhydrogen 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 SN2reaction to take place, a hydrogen bond between the solvent and the nucleophile must be bro-ken (Fig. 9.6). More energy is required to break a strong hydrogen bond to fluoride ion than isrequired to break a relatively weak hydrogen bond to iodide ion. This extra energy is reflectedin a greater free energy of activation—the energy barrier—and, as a result, the reaction offluoride ion is slower. To use a football analogy, the nucleophilic reaction of a strongly hydro-gen-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 nu-cleophilicity and basicity were exactly correlated, the graph would follow the dashed blue lineof slope = 1. Focus on the blue curve, which shows the trend for nucleophiles that all have

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

k (second-order rateNucleophile pKa of conjugate acid* constant, M_1 s_1) log k

Group 6A NucleophilesPhS_ 6.52 1.1 +0.03

PhO_ 9.95 7.9 X 10_5 -4.1

Group 7A NucleophilesI_ -10 3.4 X 10_3 -2.5

Br_ -8 8.0 X 10_5 -4.1

Cl_ -6 3.0 X 10_6 -5.5

F_ 3.2 5.0 X 10_8 -7.3

*pKa values in water

TABLE 9.5

Nuc L CH3 I_+H3C L INuc _ +3 25 °CCH3OH



LO_ as the reacting atom (blue squares). The downward curvature shows that the nucle-ophiles 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. Thestrongest bases form the strongest hydrogen bonds with the protic solvent methanol, and oneof these hydrogen bonds has to be broken for the nucleophilic reaction to occur. The strongerthe 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 hy-drogen 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 oxygennucleophiles. That is, fluoride ion is a worse nucleophile than an oxygen anion with the samebasicity. The hydrogen bonds of fluoride with protic solvents are exceptionally strong, andhence its nucleophilicity is correspondingly reduced. Conversely, the hydrogen bonds of azideion and the carbon of cyanide ion with protic solvents are weaker than those of the oxygen an-ions, 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 car-ried 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 sol-vent to a polar aprotic solvent accelerates the reactions of all nucleophiles, but the increase ofthe 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 asthe nucleophile is converted from an essentially useless reaction in a protic solvent—one thattakes years—to a very rapid reaction in the polar aprotic solvent. Other polar aprotic solventshave effects of a similar magnitude, and similar accelerations occur in the SN2 reactions ofother alkyl halides. The effect on rate is due mostly to the solvent proticity—whether the sol-vent is protic. Fluoride ion is by far the most strongly hydrogen-bonded halide anion in Table9.5; consequently, the change of solvent has the greatest effect on the rates of its SN2 reactions.

hydrogen bonds between nucleophile and solvent

X213 3 3_ CH3I

transition state

+ +

‡

OHH

O

H

H

bond to carbon

X213 I

H

C

H

HH

H

"H2O

$) O

H$)

H

O$)O

H

H$%% O

HH%% O

HH%%

)

d_d_

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

3x113_



As the data demonstrate, eliminating the possibility of hydrogen bonding to nucleophilesstrongly accelerates their SN2 reactions.

What we’ve learned, then, is that SN2 reactions of nucleophilic anions with alkyl halidesare much faster in polar aprotic solvents than they are in protic solvents. If this is so, why notuse 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 dissolvesa salt that contains the nucleophilic anion of interest. We must also remove the solvent fromthe products when the reaction is over. Protic solvents, precisely because they are protic, dis-solve significant quantities of salts. Methanol and ethanol, two of the most commonly usedprotic 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 tempera-ture can be used without introducing side reactions, the use of protic solvents is often the mostpractical solvent for an SN2 reaction. Except for acetone and acetonitrile (which dissolve rel-atively few salts), many of the commonly used polar aprotic solvents have very high boilingpoints and are difficult to remove from the reaction products. Furthermore, the solubility ofsalts in polar aprotic solvents is much more limited because they lack the protic character thatsolvates 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 DiagnosisPositron emission tomography, or “PET,” is a widely used technique for cancer detection. In PET, a glu-cose derivative containing an isotope that emits positrons is injected into the patient. A glucose de-rivative is used because rapidly growing tumors have a high glucose requirement and thereforetake up glucose to a greater extent than normal tissue. The emission of positrons (b| particles, orpositive 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 gammarays that retreat from the site of collision in opposite directions, and these are detected ultimately aslight.The light emission pinpoints the site of glucose uptake—that is, the tumor.

Solvent Dependence of Nucleophilicity in the SN2 Reaction

In methanol In DMF‡

Reaction is Reaction isNucleophile pKa* k, M_1 s_1 over in—† k, M_1 s_1 over in—†

I_ -10 3.4 X 10_3 17 min 4.0 X 10_1 8.7 s

Br_ -8 8.0 X 10_5 12 h 1.3 2.7 s

CI_ -6 3.0 X 10_6 13 days 2.5 1.4 s

F_ 3.2 5.0 X 10_8 2.2 years >3 <1.2 s

_CN 9.4 6.3 X 10_4 1.5 h 3.2 X 102 0.011 s

*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)

TABLE 9.6

Nuc L CH3 I_+25 °CH3C L INuc _ +3



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

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 theemitting isotope doesn’t last very long in the body. But it places constraints on the chemistry used toprepare FDG.Thus, 18F, which is generated from H2

18O as an aqueous solution of K| 18F_, must be pro-duced at or near the PET facility and used to prepare FDG quickly in the PET facility. An SN2 reaction isused to prepare an FDG derivative using 18F-fluoride as the nucleophile. Like other SN2 reactions, thisreaction occurs with inversion of configuration.

(9.30a)

(The leaving group is a triflate group, which we’ll discuss in Sec. 10.3A.) This synthesis cannot be car-ried out in water as a solvent because fluoride ion in protic solvents is virtually unreactive as a nucle-ophile. To solve this problem, water is completely removed from the aqueous fluoride solution andis replaced by acetonitrile, a polar aprotic solvent (Table 8.2, p. 341). Fluoride ion in anhydrous ace-tonitrile is a potent nucleophile, and to make it even more nucleophilic, a cryptand (Fig. 8.7, p. 353) isadded to sequester the potassium counterion. This prevents the potassium ion from forming ionpairs with the fluoride ion.The “naked” and highly nucleophilic fluoride ion reacts rapidly with man-nose triflate tetraacetate to form FDG tetraacetate, as shown in Eq. 9.30a.

The acetate (L OAc) groups are used for several reasons. One reason is that they make the man-nose derivative more soluble in acetonitrile than it would be if L OH groups were present. But themost important reason they are used is that if OL H groups were present they would themselvesform hydrogen bonds with 18F_, thus reducing its nucleophilicity and preventing the nucleophilicreaction from taking place.The acetate groups are rapidly removed in a subsequent ester hydrolysisreaction (Sec. 21.7A) to give FDG itself.

OAcOCH2 OSO2CF3

OAcAcO

AcO

AcO

mannose triflate 1,3,4,6-tetraacetate

FDG 1,3,4,6-tetraacetate

triflate group

F18 .... ..

..

F18 .... ..

..

..

..

OSO2CF3....

AcOCH2

OAcAcO

AcO+

anhydrous acetonitrile

Kryptofix [2.2.2](a cryptand)

inversion of configuration a polar aprotic solvent

a cryptand is usedto bind K+

= acetate = H3C C

O

O

O

OOHOCH2 HOCH2

OH

OH

OHHO

HO HOHO

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

D-glucopyranose(glucose)

F18



Figure 9.7 shows the PET image of a malignant lung tumor. PET is so sensitive that it has led to thedetection of some cancers at an earlier and less invasive stage than previously possible. As we’veseen, PET hinges on the rapid synthesis of FDG, which in turn hinges on the clever use of polar apro-tic solvents and ion-complexing agents to enhance the nucleophilicity of fluoride ion.

PROBLEMS9.13 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.

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

9.15 Which nucleophile, 3N(C2H5)3 or 3P(C2H5)3, reacts most rapidly with methyl iodide in ethanolsolvent? Explain, and give the product formed in each case.

F. Leaving-Group Effects in the SN2 Reaction

In many cases, when an alkyl halide is to be used as a starting material in an SN2 reaction, achoice of leaving group is possible. That is, an alkyl halide might be readily available as analkyl chloride, alkyl bromide, or alkyl iodide. In such a case, the halide that reacts most rapidlyis usually preferred. The reactivities of alkyl halides can be predicted from the close analogybetween SN2 reactions and Brønsted acid–base reactions. Recall that the ease of dissociatingan HLX bond within the series of hydrogen halides depends mostly on the HLX bond en-ergy (Sec. 3.6A), and, for this reason, HL I is the strongest acid among the hydrogen halides.Likewise, SN2 reactivity depends primarily on the carbon–halogen bond energy, which fol-lows the same trend: Alkyl iodides are the most reactive alkyl halides, and alkyl fluorides arethe least reactive.

Relative reactivities in SN2 reactions:

RLF << RLCl < RLBr < RL I (9.31)

In other words, the best leaving groups in the SN2 reaction are those that give the weakestbases 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 soslowly that they are useless as leaving groups in most SN2 reactions. In contrast, chloride, bro-

potassium acetate

C$O3 3LH3C

K|*

O3 31 _

(9.30b)

FDG1,3,4,6-tetraacetate

FDG

.. ....

O3M HCl

4 H2O

AcOCH2

OAcAcO

AcOF

18 .. ....

OHOCH2

OHHO

HOF

18

+ +

hydrolytic removalof acetate groups

4 AcOH



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 arethe most reactive of these. On a laboratory scale, alkyl bromides, which are in most cases lessexpensive than alkyl iodides, usually represent the best compromise between expense and re-activity. For reactions carried out on a large scale, the lower cost of alkyl chlorides offsets thedisadvantage of their lower reactivity.

Halides are not the only groups that can be used as leaving groups in SN2 reactions. Section10.3A 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 mech-anism. 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 inthe alkyl halide.

2. The mechanism involves a backside substitution reaction of the nucleophile with thealkyl 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, thestrongest bases are generally the most reactive nucleophiles.

5. The solvent has a significant effect on nucleophilicity. SN2 reactions are generallyslower in protic solvents than in aprotic solvents, and the effect is particularly great foranions containing nucleophilic atoms from the second period.

6. The fastest SN2 reactions involve leaving groups that give the weakest bases as products.

malignancy as visualized by PET

Figure 9.7 The PET image of a malignant lung tumor.The positron-emitting 18F is incorporated in the structureof FDG, a glucose derivative. FDG uptake, like glucose uptake, is enhanced in malignant tumors because they arerapidly growing and require more glucose than normal tissues.


9.4 the sn2 reaction - sapling learning€¦ · bon occur from opposite directions (backside...

Documents