Initial rate expressions

Under initial rate conditions [P] and [Q] = 0) and no abortive complexes being formed, the initial-rate expression is... 

The steady-state initial rate expression, in the absence of products and abortive complexes, is ... 

An enzyme reaction scheme in which there are two substrates (A and B) and three products (P, Q, and R) and in which the substrates bind and the products are released in an ordered fashion. This reaction scheme is exemphfied by the malic enzyme The initial rate expression, in the absence of abortive complexes and products, is identical to the corresponding equation for the ordered Bi Bi mechanism. See Multisubstrate Mechanisms Ordered Bi Bi Mechanism... 

For non-rapid-equilibrium cases (i.e., steady-state cases) the enzyme rate expression is much more complex, containing terms with [A] and with [I]. Depending on the relative magnitude of those terms in the initial rate expression, there may be nonlinearity in the standard double-reciprocal plot. In such cases, computer-based numerical analysis may be the only means for obtaining estimates of the magnitude of the kinetic parameters involving the partial inhibition. See Competitive Inhibition... 

A procedure that assists in the characterization of binding mechanisms for sequential (/.e., non-ping pong) reactions . The same general initial rate expression applies to the steady-state ordered Bi Bi reaction, the rapid-equilibrium random Bi Bi reaction, and the Theorell-... 

A good illustration of the influence of an impurity can be provided by noting the effect on initial-rate kinetics by the presence of a particular type of inhibitor in the substrate stock solution. Substrates and competitive inhibitors are often structural analogs of each other. It would not be surprising if an unknown competitive inhibitor was present with the substrate. Hence, upon serial dilutions of the stock substrate solution, the inhibitor concentration would be in constant ratio relative to the substrate. Thus, the initial rate expression in the presence of a competitive inhibitor,... 

Initial rates, expressed as percentage of final uptake/min. c Standard conditions, using ethanethiol. 

Empirical Rate Expression and Search for a Reaction Mechanism. Based on the steady state results, the initial rate expression can be represented as ... 

Despite the technical difficulties of measuring the initial rate when even traces of peracid must be absent for meaningful results to be obtained. Combe et al. [15—19] obtained pi values at 123 °C. They considered that when the initial oxygen was in excess and the peracid concentration effectively zero, the essential steps in the initial oxidation reactions were (la), (2), (3) and (4a). Combination of these lead to the initial rate expression... 

For the oxidation in boric acid coated vessels at 440 °C Baldwin et al. [23] proposed a scheme comprising (22), (11), (15), (20) and (16) from which the initial rate expression... 

Latest investigations by pressure measurement revealed that, at higher temperatures and lower pressures, there is a definite deviation from the f order. It was established that the initial rate expression can be described by Eqn. (2) (Figs. 3 and 4). 

In Sections 3.2 and 3.4, the approach based on one rate-determining step with the other steps in quasi-equilibrium was applied to simplify the derivation of rate expressions. A further simplification of the rate expressions is obtained when the product concentrations or partial pressures are negligibly small, i.e., at low conversions of a pure reactant feed stream. Similarly, at high conversions, when nearly only product is present, the rate expressions can also be simplified. Applying e single-site model, Eqns. (3.17)-(3.19), for the reaction A B at low conversion, the following expressions (often called "initial rate expressions") are obtained, provided that the feed contains pure A. 

An excellent illustration of the LHHW theory is catalytic cracking of n-alkanes over ZSM-5 [8]. For this reaction, the observed activation energy decreases from 140 to -50 ( ) kj/mol when the carbon number increases from 3 to 20. The decrease appeared to linearly depend on the carbon number as shown in Fig. 3.11. This dependence can be interpreted from a kinetic analysis that showed that the hydrocarbons (A) are adsorbed weakly under the experimental conditions. The initial rate expression for a rate-determining surface reaction applies (3.30), which in the limiting case of weak adsorption of A reduces to Eqn. (3.52). The activation energy is then represented by equation (3.53). 

S (a) For the reaction in Problem 2.3, show that the initial rate expression, assuming that iwth surface reaction and desorption of K are rate controlling, is... 

Equations given in Table 2 are relatively long and complex by comparison to initial-rate expressions. It is generally cumbersome, if not completely impractical, to obtain kinetic constants for each step from isotope exchange data instead, one deals with the equations to obtain qualitative patterns of rate behavior. 

If there is only A in the feed with no products (Cb = Cc = 0), the initial rate expressions can be rewritten directly from Eqs. 3.8 through 3.10 with the aid of the ideal gas law ... 

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