CHEM 240
Bioanalytical
Chemistry

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Lecture 21. Reaction mechanisms

Monday 15 March 2010

Reaction mechanisms. Elementary reactions, molecularity. Relationship between reaction mechanism, elementary reactions, and rate law. Intermediates and transition states. Kinetics and chemical equilibrium. The rate-determining step of a mechanism.

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Lecture 21 Chemistry topic

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Reaction coordinate diagrams

Reaction coordinate diagrams and the transition state

Here we develop the key conceptual relationship between activation energy of a reaction and what chemists refer to as the transition state for an elementary step. We make use of reaction coordinate diagrams, which are a representation of the "energy landscape" of a reaction mechanism.

As an initial illustration of these concepts, we choose the SN2 reaction, familiar from the study of organic chemistry. The SN2 mechanism represents the simplest type of mechanism, in that it occurs in one step. The overall reaction is the same as the elementary reaction of the single, bimolecular step.
Reaction coordinate diagram for an SN2 reaction

The lower half of the figure above shows a reaction coordinate diagram for an SN2 mechanism between the nucleophile ammonia and methyl iodide. The energy of the reacting molecules is plotted along the vertical axis as they progress along a horizontal "reaction coordinate" in going from reactant to product species (left to right). Above the reaction coordinate diagram are three corresponding frames from a movie of the reaction between two molecules. The first frame shows the two molecules moving toward one another in the right orientation and with sufficient energy to react upon collision. The curved red arrows show how the electron pairs move in the forward direction of reaction. The next frame shows the transition state for the reaction (symbolized by a double dagger, ‡), which is the highest energy species along the reaction coordinate. Note that the activation energy for the forward reaction is the difference in energy between the reactants and the transition state. The movie frame shows the bonds between the carbon and nitrogen and carbon and iodine as lengthened dashed lines, indicating partially forming and breaking bonds. The final frame shows the iodide ion leaving group and the protonated methylamine product moving apart. If we run the movie backwards, we will see the reverse reaction with iodide the nucleophile attacking methylammonium cation. In this case, the activation energy for the reverse reaction, Ea, rev, is the difference in energy between the products and the transition state.

Finally, the energy change for the reaction, DErxn, is the energy change for the overall reaction, Eproducts,Ereactants, which we could measure by calorimetry. It is also the difference between the activation energies, Ea, fwd,Ea, rev. This is an important idea that provides a basis for the understanding of the relationship between kinetics and thermodynamics in chemistry. (See also: Chemical equilibrium and reaction rates).

As an introduction to reaction coordinate diagrams, those for an SN2 mechanism are nice because of the simplicity of the mechanism. What about a slightly more complicated, two-step mechanism - also from organic chemistry - the SN1 mechanism? In the reaction of tert-butyl chloride and hydroxide ion to form tert-butyl alcohol and chloride ion, the first step for the mechanism is the relatively slow formation of a tert-butyl carbocation. This high-energy intermediate then rapidly reacts with hydroxide to form the alcohol in the second step. The figure below shows a reaction coordinate diagram for an SN1 reaction.
Reaction coordinate diagram for an SN1 reaction mechanism
Since the an SN1 mechanism consists of two elementary steps, there are two transition states in the reaction coordinate diagram. Since the energy of activation for the first step is so much higher than that for the second step, the first step of the an SN1 mechanism is the rate-limiting or rate-determining step.

Catalysis and enzymes

We want to understand how catalysts affect reaction rates. Usually the catalyst provides an alternate mechanism for the reaction, one with a lower activation energy (so that kcat > kuncat). The reaction coordinate diagram for this situation is shown below. Note that the energy change in the catalyzed reaction remains the same as that for the uncatalyzed reaction, meaning that a catalyst does not alter the conditions under which the reaction is at equilibrium. This is determined by DErxn, the energy change for the reaction. The position of equilibrium is not affected, but the approach to equilibrium is more rapid, from the product side as well. The reaction coordinate diagram shows that the energy of activation for the reverse reaction is lowered by the catalyst as well.

Reaction coordinate diagram showing catalzed and uncatalzed reactions
The above diagram can help us understand how enzymes - the biological catalysts - can achieve such phenomenal absolute reaction rates and degrees of rate acceleration (catalyzed rate compared with uncatalyzed rate of the same reaction). Enzymes are most commonly protein molecules adapted to speed up a specific reaction, and since the chemical processes of life are so complex and varied, there are very many types of enzymes in biochemistry.
 
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[ E-mail: cronk@gonzaga.edu ]