Jumat, 09 Oktober 2009

The Sn2 Reaction: Solvent Effects

So far we have examined five aspects of the Sn2 mechanism:

Of necessity, our discussions of some of these variables included consideration of the role of the solvent in an Sn2 reaction. In this topic we will look at that role more closely. Since we will be focusing on relative rates of substitution, we will be interested in the effect of the solvent on activation energies. In particular, we will develop a formalism for assessing the relative stabilization that the solvent affords the reactants in comparison to the transition state. Our approach requires the classification of Sn2 reactions into four charge types.

Charge Types in Sn2 Reactions

We have seen that there are two types of nucleophiles, those in which the central atom is neutral and those in which it is negatively charged. The same applies to the leaving group; the central atom may be neutral or it may bear a formal charge of -1. Thus there are four combinations of nucleophile-leaving group charge types:

  1. The nucleophile and the leaving group are both neutral
  2. The nucleophile is neutral and the leaving group is negative.
  3. The neucleophile is negative and the leaving group is neutral.
  4. The nucleophile and the leaving group are both negative.

Figure 1 presents specific examples of each of these four situations.

Figure 1

Take Charge

Before we go any further we must make an important distinction. When a leaving group is neutral, its central atom bears a formal positive charge in the reactant. As the bond between the central atom of the substrate and the central atom of the leaving group breaks, the electron pair goes with the central atom of the leaving group, thereby reducing its formal charge from +1 to 0. This is the situation in reactions 1 and 3 in Figure 1.

When a leaving group is negative, its central atom is uncharged in the reactant. As the bond between the central atom of the substrate and the central atom of the leaving group breaks, the electron pair goes with the central atom of the leaving group, thereby reducing its formal charge from 0 to -1. This is the situation in reactions 2 and 4 in Figure 1.

Now let's look at some rate data. Table 1 summarizes the relative rates of the first three reactions in Figure 1as the solvent is changed from ethanol to water.

Table 1

Reaction Rates as a Function of Solvent Polarity

Reaction
Volume % Water in Ethanol

T, oC
0
20
40
100
1
45
6.67 x 105
......
......
0.65 x 105
2
55
1.73 x 107
23.6 x 107
66.7 x 107
......
3
100
7240 x 104
178 x 104
15.1 x 104
0.37 x 104


Exercise 1 The the ethanol/water solvent system is least polar when it contains % water. It is most polar when it contains % water.

Exercise 2 For reaction 1, the rate of substitution increases as the polarity of the solvent .

Exercise 3 For reaction 2, the rate of substitution increases as the polarity of the solvent .

Exercise 4 For reaction 3, the rate of substitution increases as the polarity of the solvent .


To understand the effect that changing a solvent will have on the rate of an Sn2 reaction, we have to appreciate the change in the charge distribution that occurs as the reaction progresses from the reactants to the transition state. Figure 2 illustrates this point for the first reaction shown in Figure 1.

Figure 2

Changing Charge Distribution

Initially all of the charge is localized on the sulfur atom of the leaving group. As the bond between the nucleophile and the substrate begins to form, the nitrogen atom begins to acquire positive charge. As the bond between the leaving group and the substrate begins to break, the charge on the sulfur atom starts to diminish. In the transition state the unit of positive charge that was initially localized on the sulfur atom has been distributed between the sulfur and the nitrogen; each has approximately half of the charge. Since the electric field associated with a localized charge is more intense than when the charge is spread out, the charge-dipole interaction between the reactants and the solvent will be greater initially than in the transition state. Furthermore, the greater the dipole associated with the solvent, i.e. the more polar the solvent, the greater the charge-dipole interaction will be. What this means is that, for reactions of charge type 1, increasing the polarity of the solvent stabilizes the reactants more than it does the transition state. This results in an increase in the activation energy as the polarity of the solvent increases, which, in turn, results in a decrease in reaction rate as the solvent polarity increases. Figure 3 compares the reaction coordinate diagrams for reaction 1 in ethanol and water.

Figure 3

Understanding Solvent Effects

The symbol DER stands for the change in energy of the reactants that occurs when the solvent is changed from ethanol to water. DETS stands for the change in energy of the transition state.


Exercise 5 Draw a picture of the charge-dipole interactions between the reactant and two molecules of water for reaction 1.

Exercise 6 Draw a reaction coordinate diagram for reaction 1 in the absence of solvent. Would you expect the rate to be greater in the absence of a solvent or in ethanol? without a solvent in ethanol


Table 2 presents another comparison of solvent effects on the rate of reaction 1. It also includes activation energies so that you can get a feel for the relationship between changes in activation energies and changes in rates.

Table 2

Another Set of Solvents

Solvent
H2O
CH3OH
CH3CH2OH
CH3NO2
krel
1
6
10
119
EA, kcal/mol
23.1
21.6
20.6
18.0

Table 3 presents rate data for reaction 4 in Figure 1.

Table 3

More Rate Data

Solvent
HCONH2

formamide

HCONHCH3

N-methylformamide

HCON(CH3)2

N,N-dimethylformamide

Dielectric Constant
109
189
38.3
Dipole moment
3.73
3.83
3.82
krel
12.5
45.3
1,200,000

Exercise 7 Draw Lewis structures for formamide, N-methylformamide, and N,N-dimethylformamide.

Exercise 8 Select the solvents that are protic formamide N-methylformamide N,N-dimethylformamide.

Exercise 9 According to the data in Table 2 the correlation between the dielectric constant of the solvent and the reaction rate is direct inverse non-existent.

Exercise 10 According to the data in Table 2 the correlation between the dipole moment of the solvent and the reaction rate is direct inverse non-existent.

Exercise 11 Draw the structure of the transition state for reaction 4.

Exercise 12 Considering the nature of charge-dipole interactions, what property of the solvents in Table 2 can you correlate with krel?

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