Kinetics versus Thermodynamics

Kinetics versus Thermodynamics

The rate of a reaction and its thermodynamic favorability are two different topics, although they are closely related. This is true of all reactions, whether or not a catalyst is involved. The difference between the energies of the reactants (the initial state) and the energies of the products (the Þnal state) of a reaction gives the energy change for that reaction, expressed as the standard freeenergy change, or ∆G°. Energy changes can be described by several relatedthermodynamic quantities. We shall use standard free energy changes for our discussion; the question of whether a reaction is favored depends on ∆G°. Enzymes, like all catalysts, speed up reactions, but they cannot alter the equilibrium constant or the free energy change. The reaction rate depends on the free energy of activation or activation energy (∆G°¹), the energy input required to initiate the reaction. The activation energy for an uncatalyzed reaction is higher than that for a catalyzed reaction; in other words, an uncatalyzed reaction requires more energy to get started. For this reason, its rate is slower than that of a catalyzed reaction.

The reaction of glucose and oxygen gas to produce carbon dioxide and water is an example of a reaction that requires a number of enzymatic catalysts:

Glucose + 6O₂ - >  6CO₂ + 6H₂O

This  reaction  is  thermodynamically  favorable  (spontaneous  in  the thermodynamic sense) because its free energy change is negative (  ∆G° = -2880 kJ mol^-1 = -689 kcal mol^-1).

If a reaction is spontaneous, does that mean it will be fast?

Note that the term spontaneous does not mean Òinstantaneous.Ó Glucose is stable in air with an unlimited supply of oxygen. The energy that must be supplied to start the reaction (which then proceeds with a release of energy)Ñthe activation energyÑis conceptually similar to the act of pushing an object to the top of a hill so that it can then slide down the other side.

Activation energy and its relationship to the free energy change of a reaction can best be shown graphically. In Figure 6.1a, the x coordinate shows the extent to which the reaction has taken place, and the y coordinate indicates free energy for an idealized reaction. The activation energy profile shows the interme- diate stages of a reaction, those between the initial and final states. Activation energy profiles are essential in the discussion of catalysts. The activation energy directly affects the rate of reaction, and the presence of a catalyst speeds up a reaction by changing the mechanism and thus lowering the activation energy. Figure 6.1a plots the energies for an exergonic, spontaneous reaction, such as the complete oxidation of glucose. At the maximum of the curve connect-ing the reactants and the products lies the transition state with the necessary amount of energy and the correct arrangement of atoms to produce products. The activation energy can also be seen as the amount of free energy required to bring the reactants to the transition state.

The analogy of traveling over a mountain pass between two valleys is frequently used in discussions of activation energy profiles. The change in energy corresponds to the change in elevation, and the progress of the reaction cor- responds to the distance traveled. The analogue of the transition state is the top of the pass. Considerable effort has gone into elucidating the intermediate stages in reactions of interest to chemists and biochemists and determining the pathway or reaction mechanism that lies between the initial and final states. Reaction dynamics, the study of the intermediate stages of reaction mecha- nisms, is currently a very active field of research.

The most important effect of a catalyst on a chemical reaction is appar-ent from a comparison of the activation energy profiles of the same reaction, catalyzed and uncatalyzed, as shown in Figure 6.1b. The standard free energy change for the reaction, G¡, remains unchanged when a catalyst is added, but the activation energy, G¡^à, is lowered. In the hill-and-valley analogy, the cata-lyst is a guide that finds an easier path between the two valleys. A similar com-parison can be made between two routes from San Francisco to Los Angeles. The highest point on Interstate 5 is Tejon Pass (elevation 4400 feet) and is analogous to the uncatalyzed path. The highest point on U.S. Highway 101 is not much over 1000 feet. Thus, Highway 101 is an easier route and is analogous to the catalyzed pathway. The initial and final points of the trip are the same, but the paths between them are different, as are the mechanisms of catalyzed and uncatalyzed reactions. The presence of an enzyme lowers the activation energy needed for substrate molecules to reach the transition state. The con-centration of the transition state increases markedly. As a result, the rate of the catalyzed reaction is much greater than the rate of the uncatalyzed reaction. Enzymatic catalysts enhance a reaction rate by many powers of 10.

The biochemical reaction in which hydrogen peroxide (H₂O₂) is converted to water and oxygen provides an example of the effect of catalysts on activation energy.

2H₂O₂ - > 2H₂O + O₂

The activation energy of this reaction is lowered if the reaction is allowed to proceed on platinum surfaces, but it is lowered even more by the enzyme catalase. Table 6.1 summarizes the energies involved.

Will a reaction go faster if you raise the temperature?

Raising the temperature of a reaction mixture increases the energy available to with temperature occurs only to a limited extent with biochemical reactions. It reaction increases with temperature. One might be tempted to assume that this is universally true for biochemical reactions. In fact, increase of reaction rate is helpful to raise the temperature at Þrst, but eventually there comes a point at which heat denaturation of the enzyme is reached. Above this temperature, adding more heat denatures more enzyme and slows down the reaction. Figure 6.2 shows a typical curve of temperature effect on an enzyme- catalyzed reaction. The preceding Biochemical Connections box describes another way in which the speciÞcity of enzymes is of great use.

Summary

Thermodynamics of a biochemical reaction refers to whether a reaction is spontaneous. A spontaneous reaction has a negative Gibbs free energy or  G¡.

Kinetics refers to how fast a reaction occurs. A reaction may have a nega- tive  G¡ and still not happen quickly.

Enzymes speed up a reaction by lowering the activation energy of a reac-tion. They help the substrate and enzyme attain the transition state, the high point on an energy diagram for the reaction.