Surface equilibrium constants determination

Extensive tabulations on experimentally determined surface equilibrium constants (Schindler and Stumm, 1987 Dzombak and Morel, 1990) reflecting the acid-base characteristic of surface hydroxyl groups and the stability of surface metal com-... 

The results found in the adsorption studies are given in Table II. From these results the surface equilibrium constants for the reactions given in Table III were determined using the SURFEQL program. In these calculations it is assumed that the Ca2+, Mg2+, Cl, SO,2, phosphate and silicate surface species are those found previously to occur on the a-FeOOH surface (33, 34). The phthalate and salicylate complexes =FeA and sFeAH (where A7 is phthalate or salicylate) were considered in these calculations. 

For practical heterogeneous catalyst kinetics this principle has the following consequence. Usually, the assumption of a homogeneous surface is not valid. It would be more realistic to assume the existence of a certain distribution in the activity of the sites. From the above, certain sites will, however, contribute most to the reaction, since these sites activate the reactants most optimally. This might result in an apparently uniform reaction behaviour, and can explain why Langmuir adsorption often provides a good basis for the reaction rate description. This also implies that adsorption equilibrium constants determined from adsorption experiments can only be used in kinetic expressions when coverage dependence is explicitly included otherwise they have to be extracted from the rate data. 

Using the data presented here we have no basis for distinguishing between these alternative reactions. The possible reactions for the interactions of the ions with the goethite surface as well as the corresponding estimate of the intrinsic equilibrium constants determined by the double extrapolation method are summarized in Table I. The intrinsic acidity constants,... 

The charges assigned to the surface species in reaction 44 indicate relative values. Surface equilibrium constants need to be established in order to estimate the species distribution as a function of [H" ] and other potential-determining species. An aqueous suspension of CaC03 crystals in the presence of CO2 iPcoi - constant) at the point of zero charge (pHpzc) at equilibrium—in line... 

The next step in describing the importance of surface adsorption in this model involves the exchange affinity of the surface sites for metal ions as well as protons. In other words, metals in solution compete with protons for the oxide surface sites. Equations for this process are exactly analogous to those for similar solution reactions. Again it was demonstrated (see, for example, Schindler and Stumm, 1987) that the equilibrium constants determined for the competition between protons and metals for the metal oxide surface are linearly... 

Adsorption of anions or neutral molecules on oxides is controlled by the same parameters (pH, concentration, temperature) as those involved in complexatiqn of cations in solution. The pH of the suspension imposes both the level of protonation of the anion and the surface charge of the oxide. As in the case of cation complexation in solution (see Chapter 5), there is an optimum pH range for anion adsorption. Adsorption is characterized by complexation equilibrium constants, determined using an approach similar to the calculation of complexation constants in solution from acid-base titration of suspensions [48-51]. 

Another important area of analytical chemistry, which receives some attention in this text, is the development of new methods for characterizing physical and chemical properties. Determinations of chemical structure, equilibrium constants, particle size, and surface structure are examples of a characterization analysis. 

A dye used in the coloration of materials, such as fibers, must be present as the monomer if it is to adsorb to the material s surface. This experiment describes how spectrophotometry can be used to determine the equilibrium constant between a monomer and a dimer for the dye pinacyanol iodide in water. 

The critical hydrogen content for the ductility loss increased with increasing hydrogen solubility in the alloy. The fracture surfaces were not characteristic of those found under conditions of SCC. In terms of hydrogen and deuterium solubility in a similar series of bcc alloys, the equilibrium constants were determined at infinite dilution as a function of temperature The free energy function was expressed in terms of the bound-proton model. 

The acid-base equilibrium constant for the Me residue can be determined by spectroscopic pH titration. An example for the titration is shown in Fig. 2. The electrostatic potential

difference between the apparent pK on the charged surface (pKobs) and that on an intrinsic neutral surface (pK1) by... 

The direction chosen for the equilibrium reaction Is determined by convenience. A scientist interested in producing ammonia from N2 and H2 would use f. On the other hand, someone studying the decomposition of ammonia on a metal surface would use eq,r Either choice works as long as the products of the net reaction appear in the numerator of the equilibrium constant expression and the reactants appear in the denominator. Example applies this reasoning to the iodine-triiodide reaction. 

The rate of the ammonia production can now be predicted if we can estimate all of the participating equilibrium constants and k. Where possible, one should take experimental values for the different constants. For instance, it is possible to measure the uptake of atomic nitrogen on the Fe or Ru surface and thereby determine... 

To parameterize a Langmuir model, you determine from experimental measurements not only the equilibrium constant K, but the surface s sorption capacity (or exchange capacity). The latter value is a measure of the number of sorbing sites and is commonly reported in moles or electrical equivalents, per gram of dry sediment. Multiplying the sorption capacity in moles by the mass of sediment in a system gives the mole number of sorbing sites, which is... 

Surface plasmon resonance studies were employed to measure the equilibrium constants and association and dissociation rate constants of bisnaphthalimide derivatives (20, 21) with hairpin DNA immobilized on the metal surface.123 The equilibrium constants were higher and the dynamics slower for compounds 20 and 21 when compared to the equilibrium constants and dynamics of the model monomer (19). The values for ka and kd were determined from the change in the surface plasmon resonance signal when, respectively, the ligand solution was flowed over the... 

As seen in equations (32)-(34), the forward adsorptive flux depends upon the concentration of free cell surface carriers. Unfortunately, there is only limited information in the literature on determinations of carrier concentrations for the uptake of trace metals. In principle, graphical and numerical methods can be used to determine carrier numbers and the equilibrium constant, As, corresponding to the formation of M — Rcen following measurement of [M] and (M —Rceii. For example, a (Scatchard) plot of (M — RCeii /[M] versus (M — RCeii should yield a straight line with a slope equal to the reciprocal of the dissociation constant and abscissa-intercept equal to the total carrier numbers (e.g. [186]). 

Since k2/k 2 corresponds to the equilibrium constant of the redox reaction (redox potential), Eq. (9.12) suggests that the dissolution reaction may depend both on the tendency to bind the reductant to the Fe(III)(hydr)oxide surface and (even if the electron transfer is not overall rate determining), on the redox equilibrium (see Fig. 9.4b). 

Co/pH and V o/pH results are sensitive to different aspects of the surface chemistry of oxides. Surface charge data allow the determination of the parameters which describe counterion complexation. Surface potential data allow the determination of the ratio /3 —< slaDL- Given assumptions about the magnitude of the site density Ns and the Stern capacitance C t, this quantity can be combined with the pHp2C to yield values of Ka and Ka2. Surface charge/pH data contain direct information about the counterion adsorption capacitances in their slope. To find the equilibrium constants for adsorption, a plot such as those in Figures 7 and 8 can be used, provided that Ka and Kai are independently known from V o/pH curves. 

To calculate the concentration terms in Equations 22 and 23, the intrinsic equilibrium constants Rint and K nt, 3, and the equilibrium concentrations of surface species have to be obtained. These values were determined by solving a set of simultaneous equations, i.e., Equations 4-14, 20 and 21. In a series of calculations, the values, K nton = 80, Nation = 50, and C2 = 20 yF/cm2, which have been reported by Davis et al. (5), were used. 

The kinetic studies of the hydrogenolysis of DPM indicate that both the DPM and hydrogen are adsorbed on the same kind of active sites on the catalyst. Also, the rate-determining step of the hydrogenolysis is a surface reaction between adsorbed DPM and dissociatively adsorbed hydrogen. When the rate equation for DPM is applied to asym DAMs, their reactivities can be satisfactorily explained, and it is suggested that the product selectivity is proportional to the ratio of the adsorption equilibrium constants of the two aryl groups. 

Day, Y.S., Baird, C.L., Rich, R.L, Myszka, D.G. Direct comparison of binding equilibrium, thermodynamic, and rate constants determined by surface- and solution-based biophysical methods. Protein Sci. 

In order to better understand the detailed dynamics of this system, an investigation of the unimolecular dissociation of the proton-bound methoxide dimer was undertaken. The data are readily obtained from high-pressure mass spectrometric determinations of the temperature dependence of the association equilibrium constant, coupled with measurements of the temperature dependence of the bimolecular rate constant for formation of the association adduct. These latter measurements have been shown previously to be an excellent method for elucidating the details of potential energy surfaces that have intermediate barriers near the energy of separated reactants. The interpretation of the bimolecular rate data in terms of reaction scheme (3) is most revealing. Application of the steady-state approximation to the chemically activated intermediate, [(CH30)2lT"], shows that. 

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