Equilibrium constant surface reaction

Activity ceofficients, surface and absorption effects, equilibrium constants of reactions... 

In these relations, Ki denotes the equilibrium constant of reaction step i. For the numerical evaluation of the model, it is assumed that the backward reaction of step lb has the same transition state as the transition state for the re-desorption of A2 in Model 1, and that the entropy of the molecular precursor on the surface is negligible. The results are shown in Figure 4.37. It is observed that the model predicts that catalysts of much larger reactivity (more negative AEt) will be optimal for reactions where the diatomic molecule is strongly bound to the surface before the dissociation. 

Kp Mi (iVa)l,( a)2 equilibrium constant for reaction (V). atomic weight of the adatom (X). total number of adsorbed atoms or molecules, respectively, per unit area of surface under stationary conditions. 

Reactions 17.5, 17.6, and 17.7 illustrate the gasification of char by reaction with various gases. The carbon-steam Reaction 17.5 is an endothermic reversible reaction. Steam undergoes a side reaction, Reaction 17.8, called the water-gas shift reaction. This reaction, which is very rapid, is catalyzed by various impurities and surfaces. The carbon-C02 reaction, Reaction 17.6, is favored at high temperatures and low pressures, whereas the carbon-H2 reaction, Reaction 17.7, is favored at low temperatures and high pressure. Since only three of Reactions 17.5-17.9 are independent, if the equilibrium constants for Reactions 17.6, 17.7, and 17.8 are known, the... 

The equilibrium constant of reaction (1), K = [Cu ][Cu ]/[Cu ], is of the order of 10 thus, only vanishingly small concentrations of aquo-copper(I) species can exist at equilibrium. However, in the absence of catalysts for the disproportionation—such as glass surfaces, mercury, red copper(I) oxide (7), or alkali (311)—equilibrium is only slowly attained. Metastable solutions of aquocopper(I) complexes may be generated by reducing copper(II) salts with europium(II) (113), chromium(II), vanadium(II) (113, 274), or tin(II) chloride in acid solution (264). The employment of chromium(II) as reducing agent is best (113), since in most other cases further reduction to copper metal is competitive with the initial reduction (274). 

For common adsorbates the equilibrium constants of reactions involving only solution species are available from literature for less common adsorbates they can be determined in separate experiments that do not involve the adsorbent. The equilibrium constants of (hypothetical) surface reactions are the adjustable parameters of the model, and they are determined from the adsorption data by means of appropriate fitting procedure. With simple models (e.g. the model leading to Langmuir equation which has two adjustable parameters) the analytical equations exist for least-square best-fit model parameters as the function of directly measured quantities, but more complicated models require numerical methods to calculate their parameters. 

In the above calculations the equilibrium constants of reactions (5.32) and (5.33) were treated as fully adjustable parameters. Although the fitting procedure for the data presented in Fig. 5.67 was successful in the mathematical sense, the physical sense of the best-fit ApK value (cf. Table 5.17) is problematic. The equilibrium constants characterizing consecutive steps of protonation/deprotonation of hydrocomplexes in solution usually differ by over ten orders of magnitude (cf. Section E). Probably the same applies to protonation of surface metal ions, thus, only high ApKa values (> 10) are physically realistic. 

One method is to allow unsymmetrical inert electrolyte binding, i.e. different equilibrium constants of reactions (5.46) and (5.47). This approach was used (among others) by Katz and Hayes [65], and many different sets of model parameters were found to simulate the surface charging of alumina equally well. With unsymmetrical inert electrolyte binding the PZC is a function of the ionic strength, and this is in conflict with the assumption that PZC = CIP (Chapter 3). 

Unsymmetrical inert electrolyte binding leads to semantic problems even at pristine conditions PZC becomes ionic strength dependent, the surface potential is not equal to zero at the PZC. etc., cf. Eqs. (3.2) and (3.3). Fortunately such problems are encountered in modeling exercises with unsymmetrical electrolyte binding, but not in reality. Anyway, this modification is not recommended. Ultimately a TLM with seven adjustable parameters (equilibrium constants of reactions (5.32), (5.33), (5.46), and (5.47) are unrelated) can be used to model raw titration data (the charging curves were not shifted to produce PZC = CIP) [66], but physical meaning of such model exercises is questionable. 

The equilibrium constant of reaction (5.62) is the stability constant of the surface species of interest, and values of this equilibrium constant are reported in Chapter 4, For monodentate surface complexes (one surface site on l.h.s. of reaction (5.62)) ... 

This leads to unique definition of the stability constants of monodentate surface complexes involved in the specific adsorption of cations. Thus, reaction (5.65) rather than reactions (5.66)-(5.68) should be chosen as a standard definition, according to the above standards. The exact definition of the stability constant of the =TiOCd species in the present example depends on the electrostatic position of Cd in the surface complex. It should be also emphasized that even with fixed electrostatic position of Cd, the numerical value of the equilibrium constant of reaction (5.65) depends on the choice of the model of primary surface charging. The details on the models of primary surface charging are not given in the tables in Chapter 4, and the reader is referred to the original publications. 

Babic et al. [2] report a CIP of charging curves (25°C, 0.001-0.1 mol dm KNO3) at pH 7, for self synthesized active carbon obtained from carbonized viscose rayon cloth. Seco et al. [3] titrated commercial activated carbon at four different ionic strengths and attempted to determine the equilibrium constants of reactions (5.32) and (5.33) from these titrations. Only results obtained at extreme pH values (<3 or > 11) were used, thus the apparent surface charge densities were obtained as differences of two large and almost equal numbers. On the other hand, at pH 4-10 the titration curve of carbon suspension and the blank curve were practically identical. 

Figure 4.5. A schematic diagram of interactions in an aqueous metal-ligand-surface system. The parameters K refer to equilibrium constants for reactions in the direction of the arrows.

During adsorption and desorption from the semiconductor surface, the ions gain or lose energy while crossing the Helmholtz layer due to the Helmholtz voltage. This leads to the following equilibrium constants for reactions (2.43) and (2.44) ... 

The usual atmospheric O2 defines the oxidizing boundary of water stability, and we may use 0.21 bar (or log fo = —0.68 ) since oxygen makes up 21% of the atmosphere by volume. Combining with the equilibrium constant of reaction [14] in Table 3, this corresponds to log/bj = 41.21. The reducing bovmdary occurs at 1 bar H2(g) since the pressure of hydrogen gas in surface environments cannot exceed the atmospheric pressure, and this sets the upper bovmdary at log fw = 0. 

Equilibrium constants for Reaction (5.26) are shown in Appendix 2. The equilibrium constant at 700 C is 3.3 10, which means that even a small amount of hydrogen will inhibit the conversion of hydrogen sulphide. Therefore, sulphur removal following this reaction pattern requires a total oxidation of the catalyst. If some part of the nickel surface is still exposed to the gas, hydrogen formed by Equation (5.14) will cause hydrogen sulphide to be retained at the surface by the chemisorption reaction [377] [389]. 

This reaction is of significance mainly in the case of alloys containing relatively large amounts of chromium. Corrosion proceeds by the selective oxidation of Cr at the hotter loop surfaces and reduction and deposition of chromium at the cooler loop surfaces. In some solvents (Li,Na,K,U/P for example) the equilibrium constant for reaction (5.9) with Cr changes sufficiently as a function of temperature to cause formation of dendritic chromium crystals in the cold zone. Por Li,Be,U/P mixtures the temperature dependence of the mass transfer reaction is small, and the equilibrium is satisfied at reactor temperature conditions without the formation of crystalline chromium. Of course, in the case of a coolant salt with no fuel component, reaction (5.9) would not be a factor. 

Let Ci = concentration of species i, Kj = equilibrium constant for Reaction j, Cy = concentration of vacant sites and Ct = total concentration of sites. Further, let I denote the intermediate SiH2,1-S denote the SiH2—S surface complex, A denote SiHt, and H denote H2. 

A quite analogous treatment may be applied to the kinetics of heterogeneously catalyzed reactions. Consider a surface S that contains so active sites to which reactant A, a gaseous or solute species, may bind reversibly with an equilibrium constant KA ... 

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