Chemical equilibrium surface

Fig. 4.2. Potential singular point surfaces (dashed-dotted curve) for an ideal ternary system with single reaction A + B C. (a) Ellipse-type system (b) hyperbola-type system. RA = reactive azeotrope solid curve = chemical equilibrium surface.

If the liquid mixture is extremely non-ideal, liquid phase splitting will occur. Here, we first consider the hypothetical ternary system. The physical properties are adopted from Ung and Doherty [17] and Qi et al. [10]. The catalyst is assumed to have equal activity in the two liquid phases. The corresponding PSPS is depicted in Fig. 4.5, together with the liquid-liquid envelope and the chemical equilibrium surface. The PSPS passes through the vertices of pure A, B, C, and the stoichiometric pole Jt. The shape of the PSPS is affected significantly by the liquid phase non-idealities. As a result, there are three binary nonreactive azeotropes located on... 

Fig. 4.4. Bifurcation diagrams for reactive condenser (a) and for reactive reboiler (b), and feasibility diagram (c) for hyperbola-type system. Dashed curve = chemical equilibrium surface.

Figure 4.6 illustrates the PSPS and the chemical equilibrium surface. The PSPS has a hyperbola-type shape and passes through all pure component vertices and the stoichiometric pole n. It intersects the isobutene-MeOH edge and the MeOH-MTBE edge at two points, which are nonreactive binary azeotropes. From Fig. 4.6 one can also see that there exists no reactive azeotrope in this system. All the bifurcation branches and the pure component vertices, as discussed by Venimadhavan et al. [7], are located on the PSPS. 

Fig. 4.6. Potential singular point surface and chemical equilibrium surface for MTBE synthesis at 8.11 X 105 Pa.

Fig. 4.9. Potential singular point surface, liquid-liquid envelope and chemical equilibrium surface for methanol dehydration at two different pressures.

At Da —> °° (Fig. 4.29(c)), only pure water and pure THF remain stable nodes. The residue curves first are dominated by the reaction stoichiometry and approach the chemical equilibrium surface, and then converge to the water vertex or to the THF vertex. When starting from pure 1,4-BD, the undesired byproduct of water will be the final product in the distillation still. 

The question of whether it is possible to predict the concentration dependence of from information on Ky via equation (4.22) is discussed here using the esterification of 1-butanol with acetic acid at 80 °C as an example. The experimental data given in Fig. 4.9 show that is a strong function of the composition for that liquid-phase reaction. The numbers for are in the range 2-8 and systematically vary with composition. In the studied system, there is a liquid-liquid miscibility gap intersecting with the chemical equilibrium surface. No measurements with liquid-liquid phase split were carried out in the present work. 

For many laboratoiy studies, a suitable reactor is a cell with independent agitation of each phase and an undisturbed interface of known area, like the item shown in Fig. 23-29d, Whether a rate process is controlled by a mass-transfer rate or a chemical reaction rate sometimes can be identified by simple parameters. When agitation is sufficient to produce a homogeneous dispersion and the rate varies with further increases of agitation, mass-transfer rates are likely to be significant. The effect of change in temperature is a major criterion-, a rise of 10°C (18°F) normally raises the rate of a chemical reaction by a factor of 2 to 3, but the mass-transfer rate by much less. There may be instances, however, where the combined effect on chemical equilibrium, diffusivity, viscosity, and surface tension also may give a comparable enhancement. 

Our sun is, of course, a star. It is a relatively cool star and, as such, contains a number of diatomic molecules (see Figure 25-3). There are many stars, however, with still lower surface temperatures and these contain chemical species whose presence can be understood in terms of the temperatures and the usual chemical equilibrium principles. For example, as the star temperature drops, the spectral lines attributed to CN and CH become more prominent. At lower temperatures, TiO becomes an important species along with the hydrides MgH, SiH, and A1H, and oxides ZrO, ScO, YO, CrO, AlO, and BO. 

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. 

Under favorable environmental conditions, a chemical equilibrium is established between a corroded surface layer and its surroundings, which may lead to the preservation of the bulk of copper thus ancient objects made... 

When a solid acts as a catalyst for a reaction, reactant molecules are converted into product molecules at the fluid-solid interface. To use the catalyst efficiently, we must ensure that fresh reactant molecules are supplied and product molecules removed continuously. Otherwise, chemical equilibrium would be established in the fluid adjacent to the surface, and the desired reaction would proceed no further. Ordinarily, supply and removal of the species in question depend on two physical rate processes in series. These processes involve mass transfer between the bulk fluid and the external surface of the catalyst and transport from the external surface to the internal surfaces of the solid. The concept of effectiveness factors developed in Section 12.3 permits one to average the reaction rate over the pore structure to obtain an expression for the rate in terms of the reactant concentrations and temperatures prevailing at the exterior surface of the catalyst. In some instances, the external surface concentrations do not differ appreciably from those prevailing in the bulk fluid. In other cases, a significant concentration difference arises as a consequence of physical limitations on the rate at which reactant molecules can be transported from the bulk fluid to the exterior surface of the catalyst particle. Here, we discuss... 

Recently, Muha (83) has found that the concentration of cation radicals is a rather complex function of the half-wave potential the concentration goes through a maximum at a half-wave potential of about 0.7 V. The results were obtained for an amorphous silica-alumina catalyst where the steric problem would not be significant. To explain the observed dependence, the presence of dipositive ions and carbonium ions along with a distribution in the oxidizing strengths of the surface electrophilic sites must be taken into account. The interaction between the different species present is explained by assuming that a chemical equilibrium exists on the surface. 

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, Daughney CJ, Yee N, Davis TA (1997) A chemical equilibrium model for metal adsorption onto bacterial surfaces. Geochim Cosmochim Acta 61 3319-3328... 

Westall, J., 1980, Chemical equilibrium including adsorption on charged surfaces. In M. C. Kavanaugh and J. O. Leckie (eds.), Advances in Chemistry Series 189, American Chemical Society, Washington, DC, pp. 33 14. 

Here we are considering the dynamic equilibrium between molecular species in the gas phase and the adsorbed gas species on a surface. Let us consider the following quasi-chemical equilibrium between the species B in the gas, Bg, and the available sites at the surface of the adsorbate ... 

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. 

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],... 

The second integral in Equation 17 is the chemical contribution due to chemical reactions of the potential determining ions with the surface groups. This term may be recast as follows. Chemical equilibrium between potential determining ions bound on the surface and those in the solution adjacent to the surface during the changing process means that the chemical part of the chemical potentials are equal, i.e. 

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