Pseudoequilibrium

Hemiequilibria, a pseudoequilibrium that can occur when a fast-acting agonist equilibrates with a receptor system where a slow acting antagonist is present. The agonist will occupy the nonantagonist bound receptors quickly and... 

Frequently the rate constants k for the forward reaction A B and 2 for the reverse reaction are much larger than 3, so that the pseudo-equilibrium A B is strongly coupled and the reaction B C serves merely to drain off the product C from the equilibrium. If we define the pseudoequilibrium constant ATab = k lk2, then the rate of formation of C is... 

We attribute the form of this rate law to be due to the pseudoequilibrium 6. We refer to 6 as a pseudo-equilibrium, because it is in fact a steady state rather than a true equilibrium. If... 

Since the excellent work of Moore and Watson (6, who cross-linked natural rubber with t-butylperoxide, most workers have assumed that physical cross-links contribute to the equilibrium elastic properties of cross-linked elastomers. This idea seems to be fully confirmed in work by Graessley and co-workers who used the Langley method on radiation cross-linked polybutadiene (.7) and ethylene-propylene copolymer (8) to study trapped entanglements. Two-network results on 1,2-polybutadiene (9.10) also indicate that the equilibrium elastic contribution from chain entangling at high degrees of cross-linking is quantitatively equal to the pseudoequilibrium rubber plateau modulus (1 1.) of the uncross-linked polymer. 

Continuous generation simply means that the intermediate is continuously replenished by some method and examined under pseudoequilibrium conditions. For instance, Whyman (4) was able, using a special IR cell working at high pressure and temperature, to monitor the behavior of several species of importance in the thermal hydro formyl at ion catalytic cycle. Similarly, Koemer von Gustorf and colleagues (5) have monitored the photochemical... 

Lemkowitz et al. (4) used a similar model to that proposed by Van Krevelen et al. They correlated the equilibria in the C02+NH3+Urea+H20 system. The pseudoequilibrium constant for urea formation, as well as... 

Kent and Eisenberg (5) also correlated solubility data in the system S+CC +alkanoleimines+ O using pseudo-equilibrium constants based on molarity. Instead of using ionic characterization factors, they accepted published values of all but two pseudoequilibrium constants and found these by fitting data for MEA and DEA solutions. They were able to obtain excellent fits by this approach and also discovered that the fitted pseudo-equilibrium constants showed an Arrhenius dependence on temperature. 

The Km value for a particular enzyme-substrate combination under a given set of reaction conditions is the concentration of substrate at which the enzyme is working at exactly 50% of V ax- From O Eq. 1, it is tempting to assume that Km represents a dissociation constant for the ES complex. However, this is only true if kp (also referred to as /c2 or kcat) is very small relative to k i. When is large relative to /c i. Km is essentially a kinetic constant for the formation of product. Thus, Km is a dynamic or pseudoequilibrium constant, related to ki, and k (Segel, 1993) ... 

If the diffusion of the condensed oxide vapor into the particle is slow compared with the other two steps and if condensation is reversible, the outer surface layer of the particle reaches equilibrium, or pseudoequilibrium, with the oxide vapor, and further uptake is governed by... 

It expresses the velocity (v) of a single-substrate reaction (Equation C1. 1.1) in terms of substrate concentration at time zero ([S]) and the kinetic constants KM and V. is defined as the limiting maximal velocity for the reaction, which is observed when all of the enzyme is present as ES. KM, known as the Michaelis constant, is a pseudoequilibrium constant, which equals the concentration of substrate at which the reaction velocity equals one-half Vtrax (Figure Cl. 1.1). 

Solubility values based on a plateau in the dissolution rate curve, when dissolution of the metastable form is essentially complete and the system reaches a pseudoequilibrium state befori conversion to the stable solid state, are reasonably accurate. Those based on peaks in these curves obtained by Ltting exponential functions to estimate the plateau that might be reached in the absenc< of conversion should only be considered estimates ofthe metastable form solubility. The quantitative gain in these systems may be estimated more accurately by comparing initial dissolution rates for the two forms. In most cases, amorphous form solubilities must be estimated by these techniques due to their rapid crystallization when in contact with solvents. 

From this point of view, the obvious issues that need addressing are those of the achievement of the equilibrium or pseudoequilibrium condition (i.e. the critical chemical kinetics in the medium), of the nature and rate of the slow step in the chain of processes that link the principal metal species to the physiological response (i.e. the actual physiological mechanism of metal action) and, of course, the environmental meaning of it all. 

AH solutions from pH = 1 to higher pH values by the pH-jump technique or by exciting Ct solutions by a light flash. Such species reach a pseudoequilibrium on a time scale of seconds and then undergo a very slow, thermal transformation to Ct. 39 ... 

In some cases, the reaction rates are very fast and a pseudoequilibrium approach is used to model the system (4.30). This approach consists of assuming that the concentration of species is always close to the equilibrium conditions and hence, they can be calculated using equilibrium constants from the values of other species present in the reaction system. This approach is especially important for the modeling processes in which the reaction rates are fast and when the kinetic rates are ill-defined (because of a large number of species or a lack of experimental data that makes difficult the kinetic analysis)... 

According to this reaction the stoichiometry of the process can be modeled according to (4.45). To calculate the concentration of every model species in a batch system, the mass balance of the pollutant species (4.46) that of the reagent species (4.47) and the pseudoequilibrium constant (4.48) should also be considered. 

These equations are solved for every time step in the simulation. Hence, it is assumed that the system is always on the equilibrium conditions (pseudoequilibrium approach). Model parameters are calculated by mathematical fitting. The good results obtained in the validation, together with the physical meaning of the parameters, are the two main advantages of this model, which can help to understand better the fundamentals of the electrochemical coagulation processes. 

The concentration of any of these species depends on the total concentration of dissolved aluminum and on the pH, and this makes the system complex from the mathematical point of view and consequently, difficult to solve. To simplify the calculations, mass balances were applied only to a unique aluminum species (the total dissolved aluminum, TDA, instead of the several species considered) and to hydroxyl and protons. For each time step (of the differential equations-solving method), the different aluminum species and the resulting proton and hydroxyl concentration in each zone were recalculated using a pseudoequilibrium approach. To do this, the equilibrium equations (4.64)-(4.71), and the charge (4.72), the aluminum (4.73), and inorganic carbon (IC) balances (4.74) were considered in each zone (anodic, cathodic, and chemical), and a nonlinear iterative procedure (based on an optimization method) was applied to satisfy simultaneously all the equilibrium constants. In these equations (4.64)-(4.74), subindex z stands for the three zones in which the electrochemical reactor is divided (anodic, cathodic, and chemical). 

The application of a 50 percent Murphree vapor-phase efficiency on a y-x diagram is illustrated in Fig. 13-31. A pseudoequilibrium curve is drawn halfway (on a vertical line) between the operating lines and the true equilibrium curve. The true equilibrium curve is used for the first stage (the partial reboiler is assumed to be an equilibrium stage), but for all other stages the vapor leaving each stage is assumed to approach the equilibrium value only 50 percent of the way. Consequently, the steps in Fig. 13-31 represent actual trays. 

In the preceding sections we have shown that at sufficiently high concentrations or for molecules sufficiently complex, unimolecular reactions may proceed in such a manner that the disturbance of the equilibrium distribution of reactive molecules does not significantly affect the rate of reaction. Under such conditions it is permissible to approximate the rate of a unimolecular reaction by its high-pressure rate. But such a pseudoequilibrium invites still another approach to the formulation of the theory of reactions. This approach, known as the transition-state method, was first outlined by Marcellin, was developed further by Rodebush " and Rice and Gershinowitz, and was put in its present form by Eyring and Evans and Polanyi. - ... 

Both diffusion and conduction are nonequilibrium (irreversible) processes and are therefore not amenable to the methods of equilibrium thermodynamics or equilibrium statistical mechanics. In these latter disciplines, the concepts of time and change are absent. It is possible, however, to imagine a situation where the two processes oppose and balance each other and a pseudoequilibrium obtains. This is done as follows (Fig. 4.62). 

When part of a bitumen solution is precipitated, for example, by a nonpolar solvent, eventually an equilibrium or pseudoequilibrium will be... 

If the unidirectional rates of step 1 become large enough, the step is in pseudoequilibrium and we can measure only the ratio of the A s, and... 

Also, the pseudoequilibrium line, which allows for tray... 

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