Kinetic constraints

Chemistry can be viewed as a balance between thermodynamic and kinetic factors which dictate the course of chemical reactions and the stability of compounds. Chemists seeking to achieve particular goals, manipulate these factors using chemical or physical means. The papers in this symposium on "High Energy Processes in Organometallic Chemistry" describe recent attempts to apply mainly physical means to get around the thermodynamic and kinetic constraints of conventional organometallic chemistry. 

In the above section, we have shown that the whole apparatus of a cell is organised by thermodynamic and kinetic constraints on concentrations of all its chemical components. We know, in fact, that individually and cooperatively the organic and inorganic molecules and ions are controlled in a cell in a given state provided that external conditions of material and energy availability are fixed. This is known as a homeostatic steady state and not an equilibrium condition. Now there are two kinds of constraints, which we mentioned in Chapter 3. The first is equilibrium, which applies when combinations of components are in balanced concentration with their free entities... 

Aagaard, P. and H. C. Helgeson, 1982, Thermodynamic and kinetic constraints on reaction rates among minerals and aqueous solutions, I. Theoretical considerations. American Journal of Science 282,237-285. 

Biologically mediated redox reactions tend to occur as a series of sequential subreactions, each of which is catalyzed by a specific enzyme and is potentially reversible. But despite favorable thermodynamics, kinetic constraints can slow down or prevent attainment of equilibrium. Since the subreactions generally proceed at unequal rates, the net effect is to make the overall redox reaction function as a imidirectional process that does not reach equilibrium. Since no net energy is produced imder conditions of equilibrium, organisms at equilibrium are by definition dead. Thus, redox disequilibrium is an opportunity to obtain energy as a reaction proceeds toward, but ideally for the sake of the organism does not reach, equilibrium. 

Although the cyclic siloxanes are more bioaccumulative in fish because they cannot eliminate them through breath as fast as land mammals, other factors such as metabolism, kinetic constraints, or reduced dietary absorption limit these compounds potential for bioaccumulation [284]. 

Application of the collected thermodynamic data to model the oxidative alteration pathway of U02 under repositoiy conditions by using the PHREEQC code (Parkhurst Appelo 1999) is given in Fig. 1 la and b. Once the thermodynamic framework is set for the geochemical evolution of the repositoiy system, we have to take into consideration that for many of the processes involved, there will be some kinetic constraints. This is illustrated by Table 2, where a comparison of the expected lifetime for some of the phases expected in the repositoiy system is made. 

Secondary phases predicted by thermochemical models may not form in weathered ash materials due to kinetic constraints or non-equilibrium conditions. It is therefore incorrect to assume that equilibrium concentrations of elements predicted by geochemical models always represent maximum leachate concentrations that will be generated from the wastes, as stated by Rai et al. (1987a, b 1988) and often repeated by other authors. In weathering systems, kinetic constraints commonly prevent the precipitation of the most stable solid phase for many elements, leading to increasing concentrations of these elements in natural solutions and precipitation of metastable amorphous phases. Over time, the metastable phases convert to thermodynamically stable phases by a process explained by the Guy-Lussac-Ostwald (GLO) step rule, also known as Ostwald ripening (Steefel Van Cappellen 1990). The importance of time (i.e., kinetics) is often overlooked due to a lack of kinetic data for mineral dissolution/... 

Assume the gases are at 298 K and that other standard conditions prevail, and determine whether the prevalence of reaction 1 at nearambient conditions is a result of thermodynamic or kinetic constraints. 

However, this reaction is expected to be endothermic due to a more negative potential for the NO, H+/HNO couple (147, 164). Dehydrative dimerization of HNO to N20 [Eq. 6 8 x 106M 1s 1 (106)] is substantially faster then deprotonation to 3NO- [Eq. 10 5 x 104M l s OH ] (106)]. These kinetic constraints indicate that 3NO and subsequent ONOO- formation (Eq. 9) does not occur until the HNO concentration drops to the low nanomolar range, which is below the current observation threshold. Furthermore, the oxidative chemistry from Angeli s salt was found to be pH-independent (167), suggesting that HNO not NO- reacts with O2 to form the oxidant and cytotoxic species. Although the nature of the oxidative intermediate has not been determined, it is apparent that the HNO/O2 reaction is fundamentally different than that of the NO/O2 (and the NO /02) reaction in resultant reactive intermediates and product formation. 

Equation (30) describes the material balance of transformations of the /-th system component. The kinetic constraint (32) is similar to (10), but it includes the relationships between the constrained functions (rates of reactions, the most attainable concentrations of reagents, etc.) and the degrees of completeness of reactions. 

Unfortunately it is not always possible to use only linear inequalities. In further studies we will have to include into the kinetic constraints both the equations of nonlinear chemical kinetics and the nonlinear equations of transfer processes. Nonconvexity of the problem solved and possible multivaluedness of its solutions, in case the constraints on radiant heat exchange are included into MEIS, are shown in the work by Kaganovich et al. (2005a). 

Model (53)-(57) does not include kinetic constraint that corresponds to constraint (10) in the general model (7)-(12). Graphical illustrations of the efficiency of including constraints on macroscopic kinetics into MEIS are given in Section 5. This section focuses on the geometrical explanation of... 

When setting the constraints on macroscopic kinetics in MEIS the idea of tree is useful even from the viewpoint of interpreting the applied method for formalization of these constraints. It (the idea) can help represent even the deformation of the region of feasible solutions in the thermodynamic space and the deformation of extremely simple representation of this region (a thermodynamic tree), and the projection of limited kinetic trajectories on the tree. In other words the use of the tree notion helps reveal the interrelations between kinetics and kinetic constraints, on the one hand, and thermodynamics, on the other. 

Simplification of the solution or complete exclusion of the problem of dividing the variables into fast and slow is a great computational advantage of MEIS in comparison with the models of kinetics and nonequilibrium thermodynamics. The problem is eliminated, if there are no constraints in the equilibrium models on macroscopic kinetics. Indeed, the searches for the states corresponding to final equilibrium of only fast variables and states including final equilibrium coordinates of both types of variables with the help of these models do not differ from one another algorithmically. With kinetic constraints the division problem is solved by one of the three methods presented in Section 3.4, which are applied in the majority of cases to slow variables limiting the results of the main studied process. 

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