Variable-concentration kinetic

Alibrandi, G., Variable-concentration kinetics, J. Chem. Soc., Chem. Commun. 2709-2710 (1994). 

Figure 12 shows the variable-concentration kinetic profile obtained for the reaction of the platinum complex with SC15L. The modulating function was [SCN ] = at., with a = 0.048 M/s. Even in this case the reaction is accelerated in the first part of the kinetics, but this is caused by the increasing concentration of nucleophile. The dependence function for this reaction is given as... 

Ahbrandi, G., D Aliberti, S., and Tresoldi, G. (2003), Spectrophotometric variable-concentration kinetic experiments applied to inorganic reactions, Ini. I Chem. Kinet., 35, 497-502. 

Based on this feature, aggregation states of transition-state structures for base-promoted isomerization of oxiranes have been established by kinetic studies of LDA-mediated isomerizations of selected oxiranes in nonpolar media in the presence of variable concentrations of coordinating solvents (ligands). Results reported provide the idealized rate law V = [ligand]" [base] [oxtrane] for a-deprotonation and v = fc[ligand]°[base] / [oxirane]... 

Figure 14 shows the variable-pH kinetic (VpHK) profile obtained spectrophoto-metrically for the reaction of hydrolysis of aspirin with pH varying in the range 2-10 at T = 342.5 K. The variable-concentration conditions were realized by adding a concentrated solution of NaOH (0.6 M) to the thermostatted reaction vessel containing the aqueous solution of acetylsahcylic acid and a buffer composed of acetic acid (0.01 M), fosforic acid (0.01 M), and boric acid (0.01 M). In this way an almost linear increase of pH was generated. The absorbance was read by an optical fiber cell and stored in a computer. The pH was monitored by a pH sensor connected to a computer. 

Remark 13. The concepts of entirety and independence are quite distinct. We shall assume henceforth that all reactions are proper and will not add this qualification each time. If variable concentrations of species other than the sfs have to be introduced, or if the/r, g depend explicitly on time, the kinetics are not entire. 

Example 13.5 The Belousov-Zhabotinsky reaction scheme Field et al. (1972) explained the qualitative behavior of the Belousov-Zhabotinsky reaction, using the principles of kinetics and thermodynamics. A simplified model with three variable concentrations producing all the essential features of the Belousov-Zhabotinsky reaction was published by Field and Noyes (1974). Some new models of Belousov-Zhabotinsky reaction scheme consist of as main as 22 reaction steps. With the defined symbols X = HBr02, Y = Br, Z = Ce4+, B = organic, A = B1O3 (the rate constant contains H+), FKN Model (Field et al., 1972) consists of the following steps summarized by Kondepudi and Priogogine (1999) ... 

Experimental kinetic data derived by variables (concentration, temperature, nature of the solvent, presence of other solutes, structural variations of the reactants, etc.), refer to a reaction rate. Reaction mechanism is always only indirectly derived from primary data. Stoichiometry of the reaction, even when this is a simple one, cannot be directly related with its mechanism, and when the reaction occurs through a series of elementary steps, the possibility that the experimental rate law may be interpreted in terms of alternative mechanism increases. Therefore, to resolve ambiguities as much as possible, one must use all the physicochemical information available on the system. Particularly useful here is information on the structural relations between the reactants, the intermediate, and the reaction products. 

Here t is the time element of the dynamic (kinetic) system, x is the variable, concentration of a chemical element of the reaction. 

The terms in Equation 5-16 contain the relative adsorptivity of the catalyst for the individual components of the reaction mixture. For a complete derivation of the kinetics of a catal5dic reaction, that is, the functional relationship between r and the variables concentration, temperature, and pressure, the reaction mechanism must be known. It often sufficient to formulate the kinetic equation in terms of the slowest, rate-determining elementary step [2]. In this way, multiparameter equations can often be replaced by equivalent rate expressions that describe the influence of the most important experimental variables with sufficient accuracy. For irreversible reactions in which the rate of mass transport is decisive, simple expressions of the type shown in Equation 5-17 are often sufficient. 

Create kinetics connection Connection Type to share variables, parameters, and distribution domains across models with the same connection Connection Types Folder right click New Entity - Name kinetics connection. This connection needs to make accessible variable concentration c and reaction rate R. Since c and R are dependent on N and M parameters and xdomain distribution domain, they also need to be passed to the kinetics connection. The parameter diffusion length is also used in both submodels, MainReactor and Kinetics. Here, there are two options Either SET this parameter in the flow sheet model so that it will propagate to both submodels or SET it in one of the snbmodels and pass via the connection (the recommended option is used here as shown in Figure 9.18). 

Let us now consider the transient kinetics of the changes in the concentrations S and P, as weU as the thermodynamic functions G(f) and Hit), that take place after simultaneous imposing (or ceasing) of the input and output fluxes. Let us assume that at the initial moment of time t = 0 the mixture of S and P had the component concentrations S(0) = Sq and P(0) = Pq. In a general case, this initial state may be a nonequilibrium one. We assume that at the moment of time t = 0 two fluxes instantaneously appear, Jj p and Jo corresponding to the input of S into the reaction mixture and the output of P from the mixture. The concentrations of S and P change with switching on the fluxes, symbolized on Scheme (2.42) by open channels inp and out. The deterministic kinetic equations for the variable concentrations. Sit) and Pit), can be written as follows ... 

The fitting of non-linear regression equations to time-toxicity data from standard aquatic acute toxicity tests can generate quantifiable first-order, one-compartment kinetics constants when the bioconcentration factor is obtained from other sources and introduced into the equation. The relationship between toxicity-based and bioconcentration-based kinetic parameters is a function of the internal toxicant concentration of endpoint achieved in each of these two experimental protocols. This is a fixed internal concentration of about 0.006 mol L" for acute toxicity and a hydrophobicity-related variable concentration for bioconcentration, for the organisms and organic chemicals studied herein. Therefore, the difference between the endpoints, which is proportional to Kg, can be used to convert toxicity-based kinetic data to bioconcentration-based kinetic data and vice versa. 

It is clear that, based on small perturbations of concentrations, lifetimes can be related to chemical kinetic systems. These lifetimes do not belong to species, however, but to combinations of species concentrations defined by the left eigenvectors of the Jacobian, called modes. A matrix Jacobian of size x has eigenvalues, and therefore, the number of modes is identical to the number of variables. In the case of a linear system (in reaction kinetics, this means that the mechanism consists of first-order and zeroth-order reactions only), the Jacobian is constant and does not depend on the values of variables (concentrations). If the system is nonlinear, which is the case for most reaction kinetic systems, the Jacobian depends on the values of variables, i.e. the timescales depend on the concentrations. In other words, the set of timescales belong to a given point in the space of concentrations (phase space) and are different from location to location (or from time point to time point if the concentrations change in time). 

In both cases the late stages of kinetics show power law domain growth, the nature of which does not depend on the mitial state it depends on the nature of the fluctuating variable(s) which is (are) driving the phase separation process. Such a fluctuating variable is called the order parameter for a binary mixture, tlie order parameter o(r,0 is tlie relative concentration of one of the two species and its fluctuation around the mean value is 5e(/,t) = c(r,t) - c. In the disordered phase, the system s concentration is homogeneous and the order... 

Excitable media are some of tire most commonly observed reaction-diffusion systems in nature. An excitable system possesses a stable fixed point which responds to perturbations in a characteristic way small perturbations return quickly to tire fixed point, while larger perturbations tliat exceed a certain tlireshold value make a long excursion in concentration phase space before tire system returns to tire stable state. In many physical systems tliis behaviour is captured by tire dynamics of two concentration fields, a fast activator variable u witli cubic nullcline and a slow inhibitor variable u witli linear nullcline [31]. The FitzHugh-Nagumo equation [34], derived as a simple model for nerve impulse propagation but which can also apply to a chemical reaction scheme [35], is one of tire best known equations witli such activator-inlribitor kinetics ... 

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