Simultaneous reactions, equilibrium

The presence of water in synthesis gas mixtures along with light components, such as carbon monoxide or hydrogen, has the effect that phase separations may persist even under extreme conditions of temperature and pressure. The need exists to demonstrate that these phase separations, perhaps with simultaneous reaction equilibrium, can be described by models capable of some accuracy. 

Complex Clieinical-Reaction Equilibria When the composition of an equilibrium mixture is determined by a number of simultaneous reactions, calculations based on equilibrium constants become complex and tedious. A more direct procedure (and one suitable for general computer solution) is based on minimization of the total Gibbs energy G in accord with Eq. (4-271). The treatment here is... 

As shown in Fig. 33, the decreasing mechanism of this fluctuation is summarized as follows At a place on the electrode surface where metal dissolution happens to occur, the surface concentration of the metal ions simultaneously increases. Then the dissolved part continues to grow. Consequently, as the concentration gradient of the diffusion layer takes a negative value, the electrochemical potential component contributed by the concentration gradient increases. Here it should be noted that the electrochemical potential is composed of two components one comes from the concentration gradient and the other from the surface concentration. Then from the reaction equilibrium at the electrode surface, the electrochemical potential must be kept constant, so that the surface concentration component acts to compensate for the increment of the concen-... 

Thus, there is no great difficulty in accounting for each of the ions in Table IV the problem which remains is that of characterizing the rates and equilibrium constants of the various simultaneous reactions. 

The concentration of PB in the reaction products (Table 1) is too high to be accounted for by dehydrogenation of PCHE, especially in the absence of H2S, since at thermodynamic equilibrium the PCH/PB ratio sho lld be greater than 50 (15) under our experimental conditions. Furthermore, no toluene was observed in the simultaneous reaction of methylcyclohexene and DHQ under the same reaction conditions. Therefore, there must be another reaction path to accoimt for the formation of PB in the HDN products of DHQ. This second reaction path can only be the reaction of DHQ->THQl- OPA-> HC. It has been demonstrated that a relatively high concentration of PB is present in the HDN of OPA due to the direct hydrogenolysis of the C(sp-)-N bond of OPA (16). 

ILLUSTRATION 2.2 DETERMINATION OF EQUILIBRIUM COMPOSITIONS IN THE PRESENCE OF SIMULTANEOUS REACTIONS [ADAPTED FROM STRICKLAND-CONSTABLE (2)]... 

In Unit 3, you learned that the rate of any reaction depends on the concentration of the reacting chemicals. As a reaction proceeds, the concentrations of the product chemicals increases, and the reverse reaction may re-form reactants. Under certain conditions, the rate of the reverse reaction increases as the rate of the forward reaction decreases. Eventually, the rate of the forward reaction equals the rate of the reverse reaction. Equilibrium occurs when opposing changes, such as those just described, are occurring simultaneously at the same rate. 

Therefore, we need to find approximate methods for simultaneous reaction systems that will permit finding analytical solutions for reactants and products in simple and usable form. We use two approximations that were developed by chemists to simplify simultaneous reaction systems (1) the equilibrium step approximation and (2) the pseudo-steady-state approximation... 

Consider two electrode reactions O/R and OVR with transfer of n and ri electrons, respectively, taking place at a given electrode surface simultaneously with equilibrium potentials E f and E2. Inspection of Fig. 13(a), shows that, at open circuit, the mixed potential, EM, adopts an intermediate value E < EM equilibrium potential of the faster component reaction. 

The above arguments for a single chemical reaction are readily extended to the case of several simultaneous reactions in the same system. In the equilibrium state, for several reactions, I, II,. . . , n the affinities of all reactions are zero ... 

It is important to note that catalysts for alkoxysilane hydrolysis are usually catalysts for condensation. In typical silane surface treatment applications, alkoxysilane reaction products are removed from equilibrium by phase separation and deposition of condensation products. The overall complexity of hydrolysis and condensation has not allowed simultaneous determination of the kinetics of silanol formation and reaction. Equilibrium data for silanol formation and condensation, until now, have not been reported. 

If a fast reaction system is considered, the RSP can be satisfactory described assuming a reaction equilibrium. Here, a proper modeling approach is based on the nonreactive equilibrium-stage model, extended by simultaneously using the chemical equilibrium relationship. 

Several kinetic models have appeared to describe phosphorus reactions in soils. Enfield (1978) classified models for estimating phosphorus concentrations in percolate waters derived from soil that had been treated with wastewater into three categories (1) empirical models that are not based on known theory (2) two-phase kinetic models that assume a solution phase and some adsorbed phase and (3) multiphase models, which include solution, adsorbed, or precipitated phases. Mansell and Selim (1981) classified models as shown in Table 9.2. The reader is urged to consult this reference for a complete discussion of the phosphorus kinetic models. For the purpose of this discussion, attention will be given to models that assume reversible phosphorus removal from solution, which can occur simultaneously by equilibrium and nonequilibrium reactions, and mechanistic multiphase models for reactions and transport of phosphorus applied to soils. 

Mathematical models that assume reversible phosphorus removal from solution to occur simultaneously by equilibrium and nonequilibrium reactions Transport models that assume two types of phosphorus sorption sites... 

During adsorption on a solid, surfactants differ from other adsorbates because of the polar-apolar structure of their molecule. Their adsorption from an aqueous medium on a surface of an distorted crystalline lattice is a result of a reaction equilibrium between binding forces of all species participating at this process. Because of the heterogeneity of such forces acting on the mineral-water interface it is necessary to consider several simultaneous, subsequent reactions. 

With simultaneous phase and reaction equilibrium the system has only two dynamic degrees of freedom (five solutes - three chemical equilibria) and therefore corresponds again to a nonreactive system with two solutes. If the dimers are taken as reference components the following definition of the transformed concentration variables is found from Eq. (6)... 

Schultes presented an absorption model for packed columns including simulations [81], while Eden [18] developed a non-equilibrium stage model describing the absorption of electrolytes in co-current and countercurrent scrubbers. The simultaneous view of phase and reaction equilibrium and the existence of solids in the liquid phase were emphasized in these reports. 

When liquid and gas phases are both present in an equilibrium mixture of reacting species, Eq. (11.30), a criterion of vapor/liquid equilibrium, must be satisfied along with the equation of chemical-reaction equilibrium. There is considerable choice in the method of treatment of such cases. For example, consider a reaction of gas A and water B to form an aqueous solution C. The reaction may be assumed to occur entirely in the gas phase with simultaneous transfer of material between phases to maintain phase equilibrium. In this case, the equilibrium constant is evaluated from AG° data based on standard states for the species as gases, i.e., the ideal-gas states at 1 bar and the reaction temperature. On the other hand, the reaction may be assumed to occur in the liquid phase, in which case AG° is based on standard states for the species as liquids. Alternatively, the reaction may be written... 

In an electrochemical reaction (O + ne o R), both forward and backward reactions can occur simultaneously. At equilibrium, no net current flows out of or draws into the system, and the current density of the forward reaction equals the current density of the backward reaction. This current density is called the exchange current density, as described above in Equations 1.34 to 1.37. The exchange current density is a kinetic parameter that depends on the reaction and on the electrode surface upon which the electrochemical reaction occurs. 

Type 2. What is the pH of a 0.01 M solution of NaA (pXa of HA = 5.0) The salt NaA completely dissociates in H20 to give Na+ and A". This is a type 2 problem because only the base form (A-) is initially present. HA is a weak acid, the A" will tend to combine with any available H+ to form HA. The only H+ available, however, comes from H20 dissociation, and H20 is such a weak acid that only a limited amount of H+ will become available. The two reactions below will proceed simultaneously until equilibrium is obtained. 

What we mean in this report by equilibrium and disequilibrium requires a brief discussion of definitions. Natural physicochemical systems contain gases, liquids and solids with interfaces forming the boundary between phases and with some solubility of the components from one phase in another depending on the chemical potential of each component. When equilibrium is reached by a heterogeneous system, the rate of transfer of any component between phases is equal in both directions across every interface. This definition demands that all solution reactions in the liquid phase be simultaneously in equilibrium with both gas and solid phases which make contact with that liquid. Homogeneous solution phase reactions, however, are commonly much faster than gas phase or solid phase reactions and faster than gas-liquid, gas-solid and... 

Figure 1. Log rate of calcite dissolution as a function of hulk fluid pH and Pco in the pH-stat experiments of Plummer et al. (1). All data are far from equilibrium and are described in the text by three simultaneous reactions (1)...

The screen for each chemical kinetic calculation simultaneously displays a variety of characterizations in multiple windows and allows analysis of time/temperature-dependent species and reaction information including species concentrations, species steady-state analysis, individual reaction rates, net production/destruction rates, reaction equilibrium analysis and the temperature/time history of the system. The interactive user-sorting of the species and reaction information from the numerical simulations is mouse/cursor driven. An additional feature also allows interactive analysis and identification of dependent and independent species and reaction pathways, on-line reaction network analysis and pathway/flowchart construe-... 

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