The Rate of a Reaction Depends on the Activation Energy Necessary to Energize the Reactants into a Transition State
As a chemical reaction proceeds, reactants approach each other; some bonds begin to form while others begin to break. One way to think of the state of the molecules during this transition is that there are strains in the electronic configurations of the atoms and their bonds. The collection of atoms moves from the relatively stable state of the reactants to this transient, intermediate, and higher-energy state during the course of the reaction (Figure 2-30). The state during a chemical reaction at which the system is at its highest energy level is called the transition state, and the collection of reactants in that state is called the transition-state intermediate. The energy needed to excite the reactants to this higher-energy state is called the activation energy of the reaction. The activation energy is usually represented by ΔG‡, which is analogous to the representation of the change in Gibbs free energy (ΔG) already discussed. From the transition state, the collection of atoms can either release energy as the reaction products are formed or release energy as the atoms go “backward” and re-form the original reactants. The velocity (V) at which products are generated from reactants during the reaction under a given set of conditions (temperature, pressure, reactant concentrations) will depend on the concentration of material in the transition state, which in turn will depend on the activation energy, and on the characteristic rate constant (v) at which the material in the transition state is converted to products. The higher the activation energy, the lower the fraction of reactants that reach the transition state, and the slower the overall rate of the reaction. The relationship between the concentration of reactants, v, and V is
V = v [reactants] × 10–(ΔG‡/2.3RT)
From this equation, we can see that lowering the activation energy—that is, decreasing the free energy of the transition state ΔG‡—leads to an acceleration of the overall reaction rate V. A reduction in ΔG‡ of 1.36 kcal/mol leads to a tenfold increase in the rate of the reaction, whereas a 2.72 kcal/mol reduction increases the rate a hundredfold. Thus relatively small changes in ΔG‡ can lead to large changes in the overall rate of the reaction.
FIGURE 2-30 Activation energy of uncatalyzed and catalyzed chemical reactions. This hypothetical reaction pathway (blue) depicts the changes in free energy, G, as a reaction proceeds. A reaction will take place spontaneously if the free energy (G) of the products is less than that of the reactants (ΔG < 0). However, all chemical reactions proceed through one (shown here) or more high-energy transition states, and the rate of a reaction is inversely proportional to the activation energy (ΔG‡), which is the difference in free energy between the reactants and the transition state. In a catalyzed reaction (red), the free energies of the reactants and products are unchanged, but the free energy of the transition state is lowered, thus increasing the velocity of the reaction.
Catalysts such as enzymes (discussed further in Chapter 3) accelerate reaction rates by lowering the relative energy of the transition state and thus the activation energy required to reach it (see Figure 2-30). The relative energies of reactants and products determine if a reaction is thermodynamically favorable (negative ΔG), whereas the activation energy determines how rapidly products form—that is, the reaction kinetics. Thermodynamically favorable reactions will not occur at appreciable rates if the activation energies are too high.