We have seen how chemical kinetics allows chemists to evaluate the impact that changing the substituents attached to the reaction center has on the rates of Sn2 reactions. We have also seen how the rates of bimolecular nucleophilic aliphatic substitution reactions change when the nucleophile or the leaving group is changed. In this topic we will look at the stereochemistry of bimolecular nucleophilic aliphatic substitution reactions. In particular, we will consider one experiment which established unequivocally that Sn2 reactions proceed with inversion of configuration.
The term Walden inversion is used to describe the stereochemical outcome of aliphatic bimolecular nucleophilic substitution reactions. For many years chemists suspected that a bimolecular nucleophilic substitution reaction at a chiral carbon atom produced a product that had the opposite stereochemistry from that of the reactant. This suspicion was based upon numerous results in which the optical rotation of the product had the opposite sign from that of the reactant. In other words, a reactant that was levorotatory produced a product that was dextrorotatory or vice versa. For example, the specific rotations of the enantiomers of 2-bromooctane are -34.6o and +34.6o. The specific rotations of the enantiomers of 2-octanol are -9.9o and +9.9o. When a sample of 2-bromooctane with a specific rotation of -34.6o was treated with NaOH, the 2-octanol that was produced had an optical rotation of +9.9o. Figure 1 illustrates these points.
Goin' Around In Circles
The problem was that when this work was done the investigators did not know whether the stereochemistry at the reaction center was R or S. Nor did they know the configuration at the chiral center in the product. Since there is no a priori connection between the sign of optical rotation and the stereochemical configuration for different compounds, it was not possible to conclude with certainty that the change in the sign of the specific rotation reflected a change in stereochemical configuration at the reaction center.
In 1935, E.D. Hughes and his colleagues published an article in the Journal of the Chemical Society (1935),1525-1529 entitled Aliphatic Substitution and the Walden Inversion. Part I, which demonstrated unequivocally that bimolecular nucleophilic aliphatic substitution reactions proceed with complete inversion of configuration at the reaction center.
Scheme 1 animates the simple, yet elegant experiment that Hughes and his colleagues performed. I* represents a radioactive isotope of iodine. The specific rotation of (R)-(-)-2-iodooctane is -38.5o.
An Elegant Experiment
Exercise 1 The investigators made the following assumption: Every substitution occurs with inversion of configuration. If that assumption is true, how many of the initial 100 molecules of (R)-(-)-2-iodooctane shown in Scheme 1 would have to react before the optical rotation of the sample would drop to 0? How many of the initial 100 molecules of (R)-(-)-2-iodooctane have to react before the exchange of radioactive iodine for non-radioacive iodine is complete? Will the rate of racemization be faster or slower than the rate of isotope exchange? Given the initial assumption, what is the predicted value of kracemization/kexchange?
This experiment actually involved separate sets of measurements. The rate of racemization was measured by mixing the reactants in a polarimeter tube and measuring the decrease in specific rotation as a function of time. The rate constant for racemization, ka, was 2.62+0.03 x 10-3 M-1sec-1.
Exercise 2 Why doesn't the optical activity of the mixture change once half of the (R)-(-)-2-iodooctane molecules have been converted into (S)-(+)-2-iodooctane? Why doesn't the final value of the specific rotation become +38.5o?
To determine the rate of isotope exchange they quenched the reaction by adding ice water and extracting the aqueous solution with carbon tetrachloride, thus separating the NaI from the 2-iodooctane.
Exercise 3 After the extraction the aqueous layer contained .
They used a Geiger counter to measure the radioactivity in both the NaI and the 2-iodooctane. The rate constant for isotope exchange, kex, was 1.36+0.11 x 10-3 M-1sec-1. In other words, within experimental error the rate ratio ka/ kex was 2/1! This result is exactly what you would predict if you assume that each substitution occurs with inversion of configuration at the reaction center.
In our discussion of substituent effects we saw that the rate of bimolecular substitution decreases as the number of substituents attached to the reaction center increases. We offered a preliminary interpretation of this result, namely that attachment of substituents to the reaction center blocked access of the nucleophile to the back side of the bond between the reaction center and the leaving group. The exchange experiment confirms our thesis and allows us to refine our description of the Sn2 mechanism. Figure 2 offers a view of the spatial and the hybridization changes that attend the displacement of the leaving group from the reaction center by the nucleophile.