Integrated rate equations consecutive reactions

Our consecutive reaction here has the general form A - B -> C. Deriving an integrated rate equation for a consecutive reaction is performed in much the same way as for a simple one-step reaction (see Section 8.2), although its complexity will prevent us from attempting a full derivation for ourselves here. 

The rate of change of C has been given already as Equation (8.42). Equations (8.42) and (8.43) show why the derivation of integrated rate equations can be difficult for consecutive reactions while we can readily write an expression for the rate of forming C, the rate expression requires a knowledge of [B], which first increases, then decreases. The problem is that [B] is itself a function of time. 

The adsorption of CO occurs sequentially with Au CO as an intermediate product. As the carbon monoxide concentration in the trap is constant, all reaction steps are taken to be pseudo-first-order in the simulations. Purely consecutive reaction steps do not fit the experimental data, and it is therefore essential to introduce a final equilibrium (1.2). The fits of the integrated rate equations to the data are represented by the solid lines in Fig. 1.36b and are an excellent match to the experimental results. 

Fig. 6. Normalized ion intensity curves for ions in moist nitrogen. Fno = 2 Torr, PhjO = 1.6 X 10 Torr, 300°K. Successive intensity maxima indicate sequence N2 - N4 H20 -> H (H20)2 > H (H20)3 H (H20)4. Dashed lines represent theoretical curves calculated from integrated rate equations for consecutive reactions including reversible steps using average rate constants of Table II. In experiments where only position of equilibrium is to be studied, higher water concentrations are used so that equilibrium is established in less than 50 /zsec.

Consecutive reactions involving one first-order reaction and one second-order reaction, or two second-order reactions, are very difficult problems. Chien has obtained closed-form integral solutions for many of the possible kinetic schemes, but the results are too complex for straightforward application of the equations. Chien recommends that the kineticist follow the concentration of the initial reactant A, and from this information rate constant k, can be estimated. Then families of curves plotted for the various kinetic schemes, making use of an abscissa scale that is a function of c kit, are compared with concentration-time data for an intermediate or product, seeking a match that will identify the kinetic scheme and possibly lead to additional rate constant estimates. 

In the case of a CL reaction, such as A + R —> P + hv, the response curve corresponds to two first-order consecutive reaction steps taking into account the possible rate equations that can be formulated for each reaction step, the integrated equation can be formulated as [27] ... 

Rate laws derived for reaction schemes consisting of any number and combination of consecutive, parallel and independent first-order reaction steps can be integrated in closed form to give a sum of exponential terms, so that the total absorbance A of a solution in which these reactions proceed can also be expressed as a sum of exponential terms (Equation 3.9), but see last paragraph of this Section. 

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