Chemical equilibrium approach

Fowle and Fein (1999) measured the sorption of Cd, Cu, and Pb by B. subtilis and B. licheniformis using the batch technique with single or mixed metals and one or both bacterial species. The sorption parameters estimated from the model were in excellent agreement with those measured experimentally, indicating that chemical equilibrium modeling of aqueous metal sorption by bacterial surfaces could accurately predict the distribution of metals in complex multicomponent systems. Fein and Delea (1999) also tested the applicability of a chemical equilibrium approach to describing aqueous and surface complexation reactions in a Cd-EDTA-Z . subtilis system. The experimental values were consistent with those derived from chemical modeling. 

Fein JB, Delea D (1999) Experimental study of the effect of EDTA on Cd adsorption by Bacillus subtilis-. a test of the chemical equilibrium approach. Chem Geol 161 375-383... 

Chemical Equilibrium The chemical equilibrium approach is more complex computationally than applying the assumption of an infinitely fast reaction. The equilibrium composition of a multicomponent system is estimated by minimizing the Gibbs free energy of the system. For a gas-phase system with K chemical species, the total Gibbs free energy may be written as... 

The chemical equilibrium assumption often results in modeling predictions similar to those obtained assuming infinitely fast reaction, at least for overall aspects of practical systems such as combustion. However, the increased computational complexity of the chemical equilibrium approach is often justified, since the restrictions that the equilibrium constraint places on the reaction system are accounted for. The fractional conversion of reactants to products at chemical equilibrium typically depends strongly on temperature. For an exothermic reaction system, complete conversion to products is favored thermodynamically at low temperatures, while at high temperatures the equilibrium may shift toward reactants. The restrictions that equilibrium place on the reaction system are obviously not accounted for by the fast chemistry approximation. 

Tnterest in the fate of chemical substances in the aquatic environment has stimulated research in many areas, including the adsorption of materials on hydrolyzable metal oxide surfaces. Quantitative interpretation of adsorption on these surfaces is complicated because the electrostatic energy of adsorption is variable, and often a large number of chemical species are present in solution and adsorbed to the surface. In this chapter a chemical equilibrium approach is used to interpret adsorption on charged surfaces. 

The approach outlined here will describe a viewpoint which leads to the standard calculational rules used in various applications to systems in themiodynamic (themial, mechanical and chemical) equilibrium. Some applications to ideal and weakly interacting systems will be made, to illustrate how one needs to think in applying statistical considerations to physical problems. 

The situation becomes more complicated when the reaction is IdneticaUy controlled and does not come to complete-chemical equilibrium under the conditions of temperature, hquid holdup, and rate of vaporization in the column reactor. Venimadhavan et al. [AIChE J., 40, 1814 (1994)] and Rev [Jnd. Eng. Chem. Res., 33, 2174 (1994)] show that the existence and location of reactive azeotropes is a function of approach to equilibrium as well as the evaporation rate. 

We also give calculations of the performance of some of these various gas turbine plants. Comparison between such calculations is often difficult, even spot calculations at a single condition with state points specified in the cycle, because of the thermodynamic assumptions that have to be made (e.g. how closely conditions in a chemical reformer approach equilibrium). Performance calculations by different inventors/authors are also dependent upon assumed levels of component performance such as turbomachinery polytropic efficiency, required turbine cooling air flows and heat exchanger effectiveness if these are not identical in the cases compared then such comparisons of overall performance become invalid. However, we attempt to provide some performance calculations where appropriate in the rest of the chapter. 

One difficulty Haber faced is that the reactions used to produce compounds from nitrogen do not go to completion, but appear to stop after only some of the reactants have been used up. At this point the mixture of reactants and products has reached chemical equilibrium, the stage in a chemical reaction when there is no further tendency for the composition of the reaction mixture—the concentrations or partial pressures of the reactants and products—to change. To achieve the greatest conversion of nitrogen into its compounds, Haber had to understand how a reaction approaches and eventually reaches equilibrium and then use that... 

Data were gathered during activities described in the six lessons of 100 minutes. In Activities 1-5 (in consecutive lessons) stndents worked in gronps (4-6 students), while in Activity 6 (some weeks later) stndents worked individnally. This teaching approach was adopted to promote stndents nnderstanding of how a chemical equilibrium process occurs by supporting the nse of empirical observation and... 

Even if a system is not in chemical equilibrium it is possible to calculate the rate at which it is approaching equilibrium if we have sufficiently detailed knowledge of the energies involved in the transition state (so that it is possible to calculate the partition functions - the crucial step). However, computational chemistry has advanced to a level that good estimates of reaction rates can almost be obtained routinely. We will discuss examples in Chapter 6. 

In this example the exit gas stream composition from a converter will be determined for a given inlet gas composition and steam ratio by assuming that in the outlet stream the gases reach chemical equilibrium. In practice the reaction is carried out over a catalyst, and the assumption that the outlet composition approaches the equilibrium composition is valid. Equilibrium constants for the reaction are readily available in the literature. 

If the electrolyte components can react chemically, it often occurs that, in the absence of current flow, they are in chemical equilibrium, while their formation or consumption during the electrode process results in a chemical reaction leading to renewal of equilibrium. Electroactive substances mostly enter the charge transfer reaction when they approach the electrode to a distance roughly equal to that of the outer Helmholtz plane (Section 5.3.1). It is, however, sometimes necessary that they first be adsorbed. Similarly, adsorption of the products of the electrode reaction affects the electrode reaction and often retards it. Sometimes, the electroinactive components of the solution are also adsorbed, leading to a change in the structure of the electrical double layer which makes the approach of the electroactive substances to the electrode easier or more difficult. Electroactive substances can also be formed through surface reactions of the adsorbed substances. Crystallization processes can also play a role in processes connected with the formation of the solid phase, e.g. in the cathodic deposition of metals. 

In its simplest form a partitioning model evaluates the distribution of a chemical between environmental compartments based on the thermodynamics of the system. The chemical will interact with its environment and tend to reach an equilibrium state among compartments. Hamaker(l) first used such an approach in attempting to calculate the percent of a chemical in the soil air in an air, water, solids soil system. The relationships between compartments were chemical equilibrium constants between the water and soil (soil partition coefficient) and between the water and air (Henry s Law constant). This model, as is true with all models of this type, assumes that all compartments are well mixed, at equilibrium, and are homogeneous. At this level the rates of movement between compartments and degradation rates within compartments are not considered. 

In a similar approach McCall et al.(5) have defined a model ecosystem which represents a unit world, however, this development incorporates standard chemical equilibrium expressions into a... 

The method of using fugacity calculations will be discussed later in this symposium, therefore a detailed description will not be given in this paper. The description of equilibrium models using chemical equilibrium expressions will be discussed with the recognition that the two approaches are very much the same. 

The estimation of the number of Frenkel defects in a crystal can proceed along lines parallel to those for Schottky defects by estimating the configurational entropy (Supplementary Material S4). This approach confirms that Frenkel defects are thermodynamically stable intrinsic defects that cannot be removed by thermal treatment. Because of this, the defect population can be treated as a chemical equilibrium. For a crystal of composition MX, the appropriate chemical equilibrium for Frenkel defects on the cation sublattice is... 

As previously mentioned, the simple equilibrium approach requires that the relevant volatile compounds exist in a nondissociated molecular form in the water phase. For several substances, this is not the case. Hydrogen sulfide is, as an odorous compound, an important example, with sulfide chemical species related according to the following equilibrium ... 

The FM approach to modeling turbulent reacting flows had as its initial focus the description of turbulent combustion processes (e.g., Chung 1969 Chung 1970 Flagan and Appleton 1974 Bilger 1989). In many of the early applications, the details of the chemical reactions were effectively ignored because the reactions could be assumed to be in local chemical equilibrium.26 Thus, unlike the early emphasis on slow and finite-rate reactions... 

Predictions of high explosive detonation based on the new approach yield excellent results. A similar theory for ionic species model43 compares very well with MD simulations. Nevertheless, high explosive chemical equilibrium calculations that include ionization are beyond the current abilities of the Cheetah code, because of the presence of multiple minima in the free energy surface. Such calculations will require additional algorithmic developments. In addition, the possibility of partial ionization, suggested by first principles simulations of water discussed below, also needs to be added to the Cheetah code framework. 

Because of the lack of high-pressure experimental reaction rate data for HMX and other explosives with which to compare, we produce in Figure 15 a comparison of dominant species formation for decomposing HMX that have been obtained from entirely different theoretical approaches. The concentration of species at chemical equilibrium can be estimated through thermodynamic calculations with the Cheetah thermochemical code.32,109... 

Most industrial catalysts are heterogeneous catalysts consisting of solid active components dispersed on the internal surface of an inorganic porous support. The active phases may consist of metals or oxides, and the support (also denoted the carrier) is typically composed of small oxidic structures with a surface area ranging from a few to several hundred m2/g. Catalysts for fixed bed reactors are typically produced as shaped pellets of mm to cm size or as monoliths with mm large gas channels. A catalyst may be useful for its activity referring to the rate at which it causes the reaction to approach chemical equilibrium, and for its selectivity which is a measure of the extent to which it accelerates the reaction to form the desired product when multiple products are possible [1],... 

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