Reaction rates, energy barriers, catalysis

REACTION RATES, ENERGY BARRIERS, CATALYSIS, AND EQUILIBRIUM 219... 

Each of the rate terms, k+ and k, in Eq. (9.16) is related to concentrations in a way that one would predict if the probability of reaction were dependent on the collision of randomly moving particles the rate is proportional to the product of the number of entities involved in the reaction. All other factors that determine the reaction rate (energy barriers, temperature dependence, the effect of other species in solution, catalysis, etc.) are represented in the rate constant, k, which has units necessary to balance the left- and right-hand sides of the rate expression. Because ion interaction effects that are accounted for by activity coefficients in chemical equilibrium calculations (Chapter 3) are all incorporated into the rate constant, concentrations and not activities are used on the right-hand side of the reaction rate equation. 

Enzymes accelerate reaction rates by lowering the activation barrier AGp. While they may undergo transient modification during the process of catalysis, enzymes emerge unchanged at the completion of the reaction. The presence of an enzyme therefore has no effect on AG for the overall reaction, which is a function solely of the initial and final states of the reactants. Equation (25) shows the relationship between the equilibrium constant for a reaction and the standard free energy change for that reaction ... 

Catalysis relies on changes in the kinetics of chemical reactions. Thermodynamics acts as an arrow to show the way to the most stable products, but kinetics defines the relative rates of the many competitive pathways available for the reactants, and can therefore be used to make metastable products from catalytic processes in a fast and selective way. Indeed, cafalysis work by opening alternative mechanistic routes with lower activation energy barriers than those of the noncatalyzed reactions. As an example, Figure 1 illustrates how the use of metal catalysts facilitates the dissociation of molecular oxygen, and with that the oxidation of carbon monoxide. Thanks to the availability of new pathways, catalyzed reactions can be carried out at much faster rates and at lower temperatures than noncatalyzed reactions. Note, however, that a catalyst can shorten the time needed to achieve thermodynamic equihbrium, but caimot shift the position of that equihbrium, and therefore cannot catalyze a thermodynamicaUy unfavorable reaction. ... 

Under saturating substrate concentrations, the rate of the enzyme-catalyzed reaction will be governed by the activation energy for the conversion of the ES complex to the EP complex. It is clear that if the substrate is bound more tightly by the enzyme, then the size of this activation energy barrier wiU increase, which leads to a reduced rate. Therefore, for optimum rates of catalysis, enzymes should bind the substrate fairly weakly, but they should selectively bind the transition state of the reaction. 

Catalysis and control is crucial here. For a chemical reaction to take place, it is generally necessary that the molecules collide in the correct orientation and with sufficient energy to overcome the activation energy barrier (Ea), which leads to reaction products. This reaction is encapsulated in the classic empirical Arrhenius rate law ... 

From the analytical viewpoint, we are in rested primarily in homogeneous catalysis, particularly where the rate of the catalyzed reaction is proportional to the concentration of catalyst. A catalyst may operate either by lowering the energy barrier for both the forward and back reactions or by introducing an alternative reaction path. 

Each pathway corresponds to a different mechanism, a different rate law, and a different activation energy. Figure 12 shows the potential energy profiles for the uncatalyzed reaction and for catalysis by three different catalysts. Because the catalyzed pathways have lower activation energy barriers, the catalysts speed up the rate of the reaction. 

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