Kinetic modeling zero order reaction rate

The speed of autoxidation was compared for different carotenoids in an aqueous model system in which the carotenoids were adsorbed onto a C-18 solid phase and exposed to a continnons flow of water saturated with oxygen at 30°C. Major products of P-carotene were identified as (Z)-isomers, 13-(Z), 9-(Z), and a di-(Z) isomer cleavage prodncts were P-apo-13-carotenone and p-apo-14 -carotenal, and also P-carotene 5,8-epoxide and P-carotene 5,8-endoperoxide. The degradation of all the carotenoids followed zero-order reaction kinetics with the following relative rates lycopene > P-cryptoxanthin > (E)-P-carotene > 9-(Z)-p-carotene. 

Zero Order. It may seem somewhat at odds with the law of mass action to talk about rates that are independent of the concentration of reactant, but apparent zero-order reactions do occur, particularly in the description of the overall kinetics of some closed reaction sequences. We consider the model reaction,... 

Because the forms of these expressions match, we can see that if we plot [A] (on the y axis) as a function of t (on the x axis), we will get a straight line. We can also see that the slope of that line (yn) must be equal to -k and the y intercept (b) must be equal to [A]q, the initial concentration of reactant A. Equation 11.4 provides us a model of the behavior expected for a system obeying a zero-order rate law. To test this model, we simply need to compare it with data for a particular reaction. So we could measure the concentration of reactant A as a function of time, and then plot [A] versus t. If the plot is linear, we could conclude that we were studying a zero-order reaction. The catalytic destruction of N2O in the presence of gold is an example of this type of kinetics. A graphical analysis of the reaction is shown in Figure 11.6. 

A constant rate (zero-order kinetic behaviour) maintained during all, or the greater part of the process may be accounted for [487] by the following reaction models, illustrated in Fig. 5. These alternatives may be distinguished by microscopic observations. 

Initially, it could be postulated that the reaction could be zero order, first order or second order in the concentration of A and B. However, given that all the reaction stoichiometric coefficients are unity, and the initial reaction mixture has equimolar amounts of A and B, it seems sensible to first try to model the kinetics in terms of the concentration of A. This is because, in this case, the reaction proceeds with the same rate of change of moles for the two reactants. Thus, it could be postulated that the reaction could be zero order, first order or second order in the concentration of A. In principle, there are many other possibilities. Substituting the appropriate kinetic expression into Equation 5.47 and integrating gives the expressions in Table 5.5 ... 

Isomerization of jS-isophorone to a-isophorone has been represented as a model reaction for the characterization of solid bases 106,107). The reaction involves the loss of a hydrogen atom from the position a to the carbonyl group, giving an allylic carbanion stabilized by conjugation, which can isomerize to a species corresponding to the carbanion of a-isophorone (Scheme 9). In this reaction, zero-order kinetics has been observed at 308 K for many bases, and consequently the initial rate of the reaction is equal to the rate constant. The rate of isomerization has been used to measure the total number of active sites on a series of solid bases. Figueras et al. (106,107) showed that the number of basic sites determined by CO2 adsorption on various calcined double-layered hydroxides was proportional to the rate constants for S-isophorone isomerization (Fig. 3), confirming that the reaction can be used as a useful tool for the determination of acid-base characteristics of oxide catalysts. 

Based on the Langmuir-Hinshelwood expression derived for a unimolecular reaction system (6) Rate =k Ks (substrate) /[I + Ks (substrate)], Table 3 shows boththe apparent kinetic rate and the substrate concentration were used to fit against the model. Results show that the initial rate is zero-order in substrate and first order in hydrogen concentration. In the case of the Schiff s base hydrogenation, limited aldehyde adsorption on the surface was assumed in this analysis. Table 3 shows a comparison of the adsorption equilibrium and the rate constant used for evaluating the catalytic surface. 

Kinetic Considerations. The reaction kinetics are masked by a desorption process as shown below and are further complicated by rate deactivation. The independence of the 400-sec rate on reactant mole ratio is not indicative of zero-order kinetics but results because of the nature of the particular kinetic, desorption, and rate decay relationships under these conditions. It would not be expected to be more generally observed under widely varying conditions. The initial rate behavior is considered more indicative of the intrinsic kinetics of the system and is consistent with a model involving competitive adsorption between the two reactants with the olefin being more strongly adsorbed. Such kinetic behavior is consistent with that reported by Venuto (16). Kinetic analysis depends on the assumption that quasi-steady state behavior holds for the rate during rate decay and that the exponential decay extrapolation is valid as time approaches zero. Detailed quantification of the intrinsic kinetics was not attempted in this work. 

In the sixth and last step, the system is still considered to be purely conductive, with heat exchange at the wall to the surroundings and the zero-order approximation of the kinetics is replaced by a more realistic kinetic model. This technique is very powerful in autocatalytic reaction, since a zero-order approximation leads to the very conservative assumption that the maximum heat release rate is realized at the beginning of the exposure and maintained at this level, respectively increasing with temperature, during the whole time period. In reality, the maximum heat release rate is delayed, and only achieved later on. Thus, heat losses may lead to a decreasing temperature during the induction time of the autocatalytic reaction. 

The reaction model assumed is one in which free-radical polymerisation is compartmentalised within a fixed number of reaction loci, all of which have similar volumes. As has been pointed out above, new radicals are generated in the external phase only. No nucleation of new reaction loci occurs as polymerisation proceeds, and the number of loci is not reduced by processes such as particle agglomeration. Radicals enter reaction loci from the external phase at a constant rate (which in certain cases may be zero), and thus the rate of acquisition of radicals by a single locus is kinetic-ally of zero order with respect to the concentration of radicals within the locus. Once a radical enters a reaction locus, it initiates a chain polymerisation reaction which continues until the activity of the radical within the locus is lost. Polymerisation is assumed to occur almost exclusively within the reaction loci, because the solubility of the monomer in the external phase is assumed to be low. The volumes of the reaction loci are presumed not to increase greatly as a consequence of polymerisation. Two classes of mechanism are in general available whereby the activity of radicals can be lost from reaction loci ... 

In the reactive case, r is not equal to zero. Then, Eq. (3) represents a nonhmoge-neous system of first-order quasilinear partial differential equations and the theory is becoming more involved. However, the chemical reactions are often rather fast, so that chemical equilibrium in addition to phase equilibrium can be assumed. The chemical equilibrium conditions represent Nr algebraic constraints which reduce the dynamic degrees of freedom of the system in Eq. (3) to N - Nr. In the limit of reaction equilibrium the kinetic rate expressions for the reaction rates become indeterminate and must be eliminated from the balance equations (Eq. (3)). Since the model Eqs. (3) are linear in the reaction rates, this is always possible. Following the ideas in Ref. [41], this is achieved by choosing the first Nr equations of Eq. (3) as reference. The reference equations are solved for the unknown reaction rates and afterwards substituted into the remaining N - Nr equations. 

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