Substrate limitations, quantitative description

A quantitative description of relations between structural parameters of solid catalysts or substrates on one side and reaction rates or adsorption equilibria on the other side, even if valid only in limited areas, may form an important step in the development of a general theory of catalysis. Some years ago, Boudart 1) noticed that such correlations in heterogeneous catalysis can be divided into two broad classes. In the first type a series of catalysts is tested by means of a standard reaction and some kinetic parameter is related to a property of the solid catalyst. In correlations of the second type, the reactivity of a series of compounds is studied on a single catalyst and some kinetic parameter is related to a property of the reacting molecules. Boudart pointed out that correlations of the first type are more frequent in the literature than those of the second type. He also presented some examples of both types. Correlations between the substrate structure and its reactivity were qualitative or semiquantitative. 

Substrate limitations have been documented and quantitatively described ( U, 2, 17 ). Dooley et al. (11) present an excellent description of modeling a reaction in macroreticular resin under conditions where diffusion coefficients are not constant. Their study was complicated by the fact that not all the intrinsic variables could be measured independently several intrinsic parameters were found by fitting the substrate transport with reaction model to the experimental data. Roucls and Ekerdt (16) studied olefin hydrogenation in a gel-form resin. They were able to measure the intrinsic kinetic parameters and the diffusion coefficient independently and demonstrate that the substrate transport with reaction model presented earlier is applicable to polymer-immobilized catalysts. Finally, Marconi and Ford (17) employed the same formalism discussed here to an immobilized phase transfer catalyst. The reaction was first-order and their study presents a very readable application of the principles as well as presents techniques for interpreting substrate limitations in trlphase systems. 

Before proceeding to a ReactLab based mechanistic analysis it is informative to briefly outline the classical approach to the quantitative analysis of this and similar basic enzyme mechanisms. The reader is referred to the many kinetics textbooks available for a more detailed description of these methods. The scheme in equation (5) was proposed by Michaelis and Menten in 1913 to aid in the interpretation of kinetic behaviour of enzyme-substrate reactions (Menten and Michaelis 1913). This model of the catalytic process was the basis for an analysis of measured initial rates (v) as a function of initial substrate concentration in order to determine the constants Km (The Michaelis constant) and Vmax that characterise the reaction. At low [S], v increases linearly, but as [S] increases the rise in v slows and ultimately reaches a limiting value Vmax-... 

By the kinetic mechanism of enzyme reactions, we understand (a) the kinetic mechanism, which is a qualitative description of the order of substrate combination and product release from the enzyme, and (b) the determination of rate-limiting steps from quantitative analysis of the kinetic mechanism. 

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