Intrinsic surface reaction constants

By substituting expressions for the apparent acidity constants the two intrinsic surface acidity constants K J[ K for surface reactions are defined as... 

Typical values of pK[nt and pfor a humic acid are 2.67 and 4.46. The introduction of the electrostatic factor into the equilibrium constant is analogous to the coulombic term used in the definition of the intrinsic surface complexation constants. In addition another binding site (WAH) is recognised which is thought to behave as a weak acidic phenolic functional group. Although this site does not contribute to the titratable acidity and, therefore, no pK is needed for proton dissociation, it is involved in metal complexation reactions. The total number of the three monoprotic sites is estimated from titratable acidity and then paired to represent the humic substance as a discrete non-interacting mixture of three dipro-tic acids, which act as the metal complexation sites. The three sites are... 

Figure 10,26 Correlation plot for some metal cations, of their first hydrolysis constants ( /fii) versus intrinsic surface complex constants i Ku) for their adsorption by Si02(am) assuming the constant capacitance model. The equation of the solid line is log = 0.09 -( 0.62 log A. Hydrolysis and adsorption reactions are written A,i -t- H2O = +...

Hou, W.G. and Song, S.E., Intrinsic surface reaction equihbrium constants of structurally charged amphoteric hydrotalcite-like compounds, J. Colloid Interf. Sci., 269, 381, 2004. 

Here kgr is the surface reaction rate constant, Rr is the adsorption equilibrium constant for product R, Pr is the partial pressure of R and Kp is the reaction equilibrium constant. At low loading the reaction rate simply becomes proportional to the product of the intrinsic rate constant and the Henry coefficient. 

It is interesting to note that the chlorinated ethylenes do not appear to follow this trend of increasing rates with increasing chlorination. (Lowry and Reinhard 1999 Schreier 1996) This may be due in part to the extremely fast rates of these reactions, which increase the relative importance of mass transfer limitations. For very fast reactions, mass transfer of compounds to the catalyst surface, rather than the intrinsic catalytic reaction rate, may determine the rate of disappearance of hydrocarbons and the resulting apparent rate constants. 

This effect will be particularly emphasized at small values of the Thiele modulus where the intrinsic rate of reaction and the effective rate of diffusion assume the same order of magnitude. At large values of , the effectiveness factor again becomes inversely proportional to the Thiele modulus, as observed under isothermal conditions (Section 6.2.3.1). Then the reaction takes place only within a thin shell close to the external pellet surface. Here, controlled by the Arrhenius and Prater numbers, the temperature may be distinctly higher than at the external pellet surface, but constant further towards the pellet center. 

As seen from Equations 1.54-1.56, the intrinsic stability constants of surface reactions are dependent on two factors a chemical and an electric contribution. The chemical contribution is taken into consideration by the mass balance the electric contribution is treated by the charge balance. There are several surface complexation models that mainly differ in the description of the electric double layer that is used to calculate the surface potential, which is done by different double-layer models. These models have been mentioned previously in this chapter. Since, however, the terminology usually used in electrochemistry, colloid chemistry and, especially, in the discussions of surface complexation models is different, they are repeated again ... 

The rate constant decreases from the intrinsic value (kf ) at low degrees of polymerization to an asymptotic value at high degrees of polymerization. The decrease in rate is greater for higher values of the initial intrinsic surface reactivity (oCq), and for sufficiently high values the reaction may be diffusion controlled from the start. 

Data obtained in fixed-bed reactors and in continuous high-velocity coil-t ype reactors (fluid catalyst) indicate that the catalytic cracking of gas oils is approximately a first-order reaction, but that the apparent order approaches two because of the effect of nonhomogeneity of the feed and because of the increasing dilution of reactant with cracked products as conversion increases at constant total pressure (73). The extent of reaction is determined by the intrinsic activity of the catalyst surface, reaction time at the surface, temperature, and susceptibility of the feed to cracking. Superficial contact time in the reactor is of little consequence. The effective time of reaction is the time spent by oil on the active surface of the catalyst. For a given extent of adsorption, the reaction time should be inversely proportional to weight space velocity and should also be a function of the reactant partial pressure. Results of experiments with... 

From the measured intrinsic relative reaction rates VdieneA butenes. the rate constant ratio kadsorption coefficients shows that under reactive mixture, butadiene will be the main product on the Pd surface while both butadiene and butene will compete on the Pt surface. These observations explain the high selectivity of Pd as compared to Pt. 

There are two approaches to the equilibrium constants of surface reactions. Originally, the so-called intrinsic approach was developed [28]. For example, binding of a proton to a surface site was separated into two steps. In the first step the proton was transferred from the bulk of solution (aq) to the space in the vicinity of the surface site (int). This equilibrium was treated by Boltzmann statistics, so that the distribution was affected by the electrostatic potential of that space (( jnt). The second process was chemical binding with the surface site represented by so-called intrinsic equilibrium constant (Ki t) ... 

The chemical model is defined in a separate file that must be written by the user. It creates the input file for PRISM and a template for the speciation code, assuring a model description consistent for all parts of the modelling. The input file has a well defined, line-oriented structure. Detailed chemical data for each compartment includes the selected SCM with its intrinsic surface parameter, also pH, Eh and the concentrations for all components. Default reaction constants (for complexation, precipitation/dissolution, sorption) can be modified, and reactions can also be suppressed totally. 

Samples from the site contained considerable amounts of freshly precipitated iron hydroxides. Their transformation into thermodynamically more stable minerals such as goethite or hematite has a very slow kinetics, thus ferrihydrite was chosen as the major adsorbing surface. The Diffuse Double Layer model (Dzombak and Morel, 1990) was selected to describe surface complexation. The respective intrinsic surface parameters and the reaction constants for the ions competing with uranium(VI) for sorption sites were taken from a database mainly based on Dzombak and Morel, 1990, with the urani-um(Vl) sorption parameters as determined by Dicke and Smith, 1996. The results, based on runs with 1000 varied parameter sets, are summarized in Table 5.2. 

The charge regulation model can be used successfully for interpretating pH poten-tiometric titration data, thus enabling the determination of intrinsic equilibrium constants of surface reactions and the prediction of surface composition under various conditions. The following example demonstrates this. 

Edwards [25] investigated the hydrolysis of aspirin in aqueous solution at 17A° and demonstrated that the aspirin is hydrolyzed by general acid-base catalysis and water molecules for ionic and nonionic aspirin, comprising six simultaneous reactions involving H O, O H, and H2O for ionic and nonionic aspirin. The intrinsic hydrolysis rate constant in the heated mixture was comparable with the hydrolysis rate constants of the two-element reactions of nonionic aspirin and H2O or ionic aspirin and H2O in aqueous solution. As aspirin molecules would be adsorbed onto the pore surface of PCC in the molecular state, as a possible mechanism of aspirin hydrolysis in the mixture with PCC it was suggested that the aspirin is dispersed monomolecularly in the heated mixture and reacts with water molecules rather than by acid-base catalysis. 

Since the particle Reynolds numbers in laboratory PBRs are very low, as stated in Section 2.2.2.2, the range of flow rates to be covered for producing adequate increases in transport coefficients has to be rather wide. It is important to determine the minimum gas flow rate after which the exit conversions Xa or the global rates ( Ra)p remain constant (Figure 2.6). All subsequent kinetic experiments must be conducted at flow rates equal to or above this minimum. When the overall process is surface reaction controlled, that is, if intrinsic kinetics is being observed, neither Xa nor -Ra)p will change with increasing linear velocity of the fluid. 

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