Rate Equations Containing More Than One Concentration

2 Rate Equations Containing More Than One Concentration 

The reaction rate now depends on two concentrations, those of species A and B. Moreover, there are three arbitrary constants in the rate equation, k, a, and P, that must be determined from the experimental data. Obviously, the depradence of —rA on both Ca and Cb cannot be determined using a single plot. Moreover, we caimot extract values of the three unknowns k, a, and p from two parameters, a slope and an intercept. 

To test rate equations containing more than one concentration graphically, the experiments leading to the kinetic data must be planned carefully, so as to isolate the effect of the individual concentrations. The analysis of the kinetic data then must be carried out in stages, one concentration at a time. 

Suppose that the data in Table 6-4 were taken during a smdy of the reaction 

Does the power-law rate equation given by Eqn. (6-8) fit these data If so, what are the approximate values of a, p, and kl 

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The application of any interpretation of kinetic data to reaction rate equations containing more than one concentration term can be somewhat complex. Consider the reaction... 

As noted above, the application of any interpretation of kinetic data to reaction rate equations containing more than one concentration term can be somewhat complex. For runs (l)-(3), the concentrations of B and C are constant (for each run at the initial conditions specified). Therefore, columns (3) and (4) in Table 13.24... 

Rate Equations Containing More Than One Concentration (Reprise)... 

Intermediate in complexity and accuracy between true mechanisms and abstract models are empirical rate law models. Here, the modeler eschews the identification of elementary steps and, instead, works with experimentally established rate laws for the component overall stoichiometric processes that make up a particular reaction. Each process may consist of several elementary steps and involve many reaction intermediates, but it enters the model only as a single empirical rate equation, and only those species that appear in the rate equation need be included in the model. Assuming that the empirical rate laws have been accurately determined, this approach will give results for the species contained in the rate laws that are identical to the results from the full mechanism, so long as no intermediate builds up to a significant concentration and so long as the component processes are independent of one another. This last requirement implies that no intermediate that is omitted from the model is involved in more than one process, and that there are no cross-reactions between intermediates involved in different processes. 

In the sedimentation-equilibrium method a lower centrifugal field is applied and the processes of sedimentation and diffusion are brought to equilibrium [13]. In this case the governing equation contains sedimentation equilibrium concentrations of species at different positions from the axis of rotation, but one does not need to know D. It should be pointed out that sedimentation and diffusion are more complicated when the species are electrically charged. This is because the smaller counterions sediment at a slower rate than do the colloidal-sized species. This creates an electric potential gradient that tends to speed up the counter-ions and to drag the colloidal species. The reverse effect occurs for diffusion. 

In the monomolecular layer systems described so far, diffusion of the cosubstrate through the film is not a rate-limiting factor. This is true in the case of a free-moving cosubstrate, but also, at least at low scan rates, with cosubstrates attached to the structure. When several layers are coated on the electrode, diffusion of the cosubstrate may become rate limiting even if it is not attached to the structure. The diffusion rate of the two cosubstrate forms increases with its concentration. One may thus expect that the enzymatic reaction, rather than diffusion, tends to be the rate-determining step upon raising the cosubstrate concentration and that this situation is reached all the more easily that the number of layers is small. Under such conditions, the separation of the cyclic voltammetric current in two independent contributions [equation (5.29)] is still valid. icat is thus proportional to the total amount of enzyme contained in the film per unit surface area and therefore to the number, N, of monomolecular layers deposited on the electrode ... 

One can see immediately that this approach will be a little more detailed than the previous section, since the bubble mechanics are contained in the basic material balance. Various simplifications of equation (8-164) are possible according to the reactor type by deleting terms for a steady-state CSTR the time derivative is zero, for a batch reactor the flow rate terms are zero, etc. For the gas phase the situation is complicated by the fact that the configuration (and concentration) of bubbles can be a function of both time and position that is, the total mass of j in a given bubble, PVt,yj RT), can depend on both position z and time t. 

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