The detailed description of the changes that occur during nucleophilic aliphatic substitution reactions has emerged as the result of thousands of experiments conducted by thousands of chemists over the past 75 years or more. Of all the investigations that have been run, none has proven more informative than those involving reaction kinetics, i.e. the measurement of the rates of chemical reactions and the investigation of the dependence of reaction rates on the reaction parameters. This topic outlines the basics of kinetic studies. In the four subsequent topics we will consider experiments that were designed to test the effect of each of the following parameters on the rates of nucleophilic aliphatic substitution reactions:
- the substituent(s) connected to the substrate
- the leaving group
- the nucleophile
- the solvent
Kinetic Experiments
The objective of a kinetics experiment is to determine the rate of a chemical reaction. To do this, you measure changes in the concentration of one of the reactants or products as a function of time. We'll use the reaction of bromomethane with sodium hydroxide shown in Equation 1to illustrate the approach.
Figure 1 diagrams a simple apparatus for measuring the change in the concentration of hydroxide ion as it reacts with the alkyl bromide.
Figure 1
A Simple Set-Up for Measuring Reaction Kinetics
To measure the rate of the reaction you simply mix precisely known concentrations of the alkyl bromide and sodium hydroxide solutions and recordthe pH at carefully timed intervals.
Exercise 1 Why isn't it necessary to measure changes in the concentration of bromomethane as well as sodium hydroxide in order to measure the rate of reaction 1?
Exercise 2 The chemical shift of the methyl group in the 1H-NMR spectrum of bromomethane is 2.68 ppm while that of the methyl group in methanol is 3.34 ppm. How would you use 1H-NMR to determine the kinetics of reaction 1?
Exercise 3 The boiling points of methanol and bromomethane are 68 and 4oC, respectively. How would you use gas chromatography to determine the kinetics of reaction 1?
More important than the rate of the reaction is the dependence of the rate on the concentrations of the reactants. In order to determine this you have to perform a series of experiments in which you vary the concentration of the alkyl halide. Then you perform another series in which you vary the concentration of the sodium hydroxide. Such measurements allow you to determine the order of the reaction. If the rate of a reaction doubles when you double the concentration of the alkyl halide, the reaction is said to be first order with respect to alkyl halide. If the rate of a reaction doubles when you double the concentration of the NaOH, the reaction is said to be first order with respect to hydroxide. A reaction that is first order with respect to both the reagent and the reactant is said to be second order overall. Such a reaction is described as a bimolecular reaction because its rate depends upon the concentration of both reactants.
Kinetic Equations
In our introduction to chemical reactions, we described two alternative reaction profiles. They are reiterated in Figure 2.
Figure 2
Different Strokes for Different Folks
The diagram in the left-hand panel describes what chemists call a 1-step or concerted reaction, while that in the right-hand panel is typical of a non-concerted, 2-step process. Reactions with these types of profiles display fundamentally different kinetic behaviors, i.e. the mathematical equations that describe the changes in concentrations of reactants with time are different. By plotting the change in pH as some mathematical function of time, it is possible to determine the rate constant of the reaction. The rate constant is a proportionality factor which allows chemists to express the relationship between concentration and reaction rate as a mathematical equality. Scheme 1 compares the forms of the equations that describe the kinetics of reactions that display the profiles shown in Figure 2.
Scheme1
Everybody's Always Giving Me Orders
In both cases [-OH]o refers to the initial concentration of hydroxide ion while [-OH]t stands for the amount of hydroxide remaining at some later time, t. If a reaction is second order, a plot of 1/[-OH]t vs t will be a straight line. The slope of the line will equal k2, while the intercept will be 1/[-OH]o. When a reaction displays first order kinetics, a plot of log [-OH]t vs t will be a straight line with a slope of -k1/2.303 and an intercept of log[-OH]t.
Figure 3 compares plots of simulated experimental data for reaction 1. Since the plot of 1/[-OH] vs t is a straight line, while the plot of log [-OH] vs t is not, we can conclude that this is a second order reaction. This means that both CH3Br and -OH are involved in the transition state leading to the formation of the products in reaction 1. Nucleophilic aliphatic substitution reactions that display second order kinetics are labeled Sn2 reactions, where Sn2 is an abbreviation for substitution, nucleophilic, bimolecular.
Figure 3
Getting Your Act in Order
Figure 4 animates a typical experiment. The matrix of red dots represents the hydroxide ion concentration. Initially there are 1000 dots representing the initial experimental concentration of sodium hydroxide, which was 0.1000 M. The pH of a 0.1000 molar solution of hydroxide ion is 13. As the hydroxide ions react with the bromomethane, the pH decreases. As we've just seen, for this reaction a plot of 1/[-OH] vs time gives a straight line, indicating that the nucleophilic aliphatic substitution reaction of bromomethane with sodium hydroxide is a bimolecular reaction.
Figure 4
A Simple Kinetics Experiment
Towards a Reaction Mechanism
The fact that the reaction of bromomethane with hydroxide ion displays second order kinetics must mean that both species are involved in the rate determining step of the reaction. In other words, the structure of the transition state must contain both reactants. Scheme 2 presents a description of the transformation of reactants to products that is consistent with this conclusion.
Scheme 2
From Fact to Theory
Exercise 4 According to VSEPR theory, what is the most likely geometry of the transition state shown in Scheme 2?
linear trigonal planar pyramidal tetrahedral trigonal bipyramidal octahedral
Exercise 5 According to VSEPR theory, which of the following geometries would best represent the structure of the transition state shown in Scheme 2?
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Exercise 6 Given your answer to Exercise 5, what is the hybridization of the reaction center in the transition state of an Sn2 reaction? sp sp2 sp3
Let's be clear about the symbolism in Scheme 2. First, the dashed lines indicate that the bond between the oxygen and carbon atoms is beginning to form. It is a partial single bond. Similarly, the bond between the carbon and bromine is beginning to break. The bond-making and bond-breaking are occurring simultaneously. The reaction is described as a concerted process. The d-Br---C---d-OH notation implies that the formal negative charge that was initially associated with the oxygen atom of the hydroxide ion is shared between the oxygen and the bromine atoms in the transition state. The charge is being transferred from the oxygen to the bromine. Finally, the configuration of atoms in which the C-O bond is not fully formed, and the C-Br bond is not fully broken corresponds to the point of maximum potential energy on the reaction profile diagram.
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