Free Energy of Activation and the Action of Catalysts

In a first-order chemical reaction, the conversion of A to P occurs because, at any given instant, a fraction of the A molecules has the energy necessary to achieve a reactive condition known as the transition state. In this state, the probability is very high that the particular rearrangement accompanying the A ® P transition will occur. This transition state sits at the apex of the energy profile in the energy diagram describing the energetic relationship between A and P (Figure 14.5).

Figure 14.5 •Energy diagram for a chemical reaction (A ® P) and the effects of (a) raising the temperature from T₁ to T₂ or (b) adding a catalyst. Raising the temperature raises the average energy of A molecules, which increases the population of A molecules having energies equal to the activation energy for the reaction, thereby increasing the reaction rate. In contrast, the average free energy of A molecules remains the same in uncatalyzed versus catalyzed reactions (conducted at the same temperature). The effect of the catalyst is to lower the free energy of activation for the reaction.

The average free energy of A molecules defines the initial state and the average free energy of P molecules is the final state along the reaction coordinate. The rate of any chemical reaction is proportional to the concentration of reactant molecules (A in this case) having this transition-state energy. Obviously, the higher this energy is above the average energy, the smaller the fraction of molecules that will have this energy, and the slower the reaction will proceed. The height of this energy barrier is called the free energy of activation, DG^‡. Specifically, DG^‡ is the energy required to raise the average energy of one mole of reactant (at a given temperature) to the transition-state energy. The relationship between activation energy and the rate constant of the reaction, k, is given by the Arrhenius equation:

k = Ae^{- DG‡/RT} (14.5)

where A is a constant for a particular reaction (not to be confused with the reactant species, A, that we’re discussing). Another way of writing this is 1/k = (1/A)e ^DG‡/RT. That is, k is inversely proportional to e ^DG‡/RT. Therefore, if the energy of activation decreases, the reaction rate increases.

Decreasing DG^‡ Increases Reaction Rate

We are familiar with two general ways that rates of chemical reactions may be accelerated. First, the temperature can be raised. This will increase the average energy of reactant molecules, which in effect lowers the energy needed to reach the transition state (Figure 14.5a). The rates of many chemical reactions are doubled by a 10°C rise in temperature. Second, the rates of chemical reactions can also be accelerated by catalysts. Catalysts work by lowering the energy of activation rather than by raising the average energy of the reactants (Figure 14.5b). Catalysts accomplish this remarkable feat by combining transiently with the reactants in a way that promotes their entry into the reactive, transition-state condition. Two aspects of catalysts are worth noting: (a) they are regenerated after each reaction cycle (A ® P), and so can be used over and over again; and (b) catalysts have no effect on the overall free energy change in the reaction, the free energy difference between A and P (Figure 14.5b).

Date: 2016-01-03; view: 901