Adsorption rate, definition

The estimation of results of the given comparison requires, however, great care. The choice of conditions for the measurements of adsorption rate to be compared with the rate of exchange in case of solid oxides offers difficulties which almost definitely could not be overcome. 

The peaks of Fig. 2 are well separated and definite while the small peaks are not masked by the large peak. This out-of-phase component, I, exhibits the character of an adsorption-rate spectrum. In addition, the rate constants can be approximated directly, as can the magnitudes of the respective adsorptions, from the positions where local maxima appear on the ciuwe of I versus logarithm of frequency, the points where [Pg.252]

Both problems, changes of the equilibrium adsorption with micellar concentration and the influence of micelles on the adsorption rate, are the subjects of this review. Various definitions of the CMC are represented at the outset. Nowadays the thermodynamics of micellisation is the most developed part of modem theories of micellar systems. Two main approaches ("quasichemical and "pseudophase") are discussed in the second section of this chapter. In section 3 the thermodynamic equations for the Gibbs adsorption of surfactants in the micellar region are considered together with corresponding experimental data. The subsequent sections are devoted to non-equilibrium micellar systems. First, section 4 delineates briefly the theory of... 

Second, there is a surface concentration of the ligands or capturing sites immobilized on a functionalized surface, with a concentration of [FJo. Finally, there is a surface concentration of the adsorbed targets (products of the reaction), with a concentration of [F]. The units of [F] and [F]q are in mol/m, whereas [S] is expressed in units of mol/m. In case of adsorption, the definitions of the reaction rates are somewhat modified from the usual rate constant definitions mentioned above, primarily because of the fact that the immobilization of the substrate S not only depends on the volume concentration at the wall but also depends on the available sites for adsorption. Accordingly, one can write —d[S]/dt = a([F]o - [F])[S]w and -d[F]/dt = ka[F], where and k are the adsorption and dissociation rates, respectively. The concentration of F is increased by the former and is decreased by the latter, and the net rate of change is given by their balance, i.e.,... 

If, for the purpose of comparison of substrate reactivities, we use the method of competitive reactions we are faced with the problem of whether the reactivities in a certain series of reactants (i.e. selectivities) should be characterized by the ratio of their rates measured separately [relations (12) and (13)], or whether they should be expressed by the rates measured during simultaneous transformation of two compounds which thus compete in adsorption for the free surface of the catalyst [relations (14) and (15)]. How these two definitions of reactivity may differ from one another will be shown later by the example of competitive hydrogenation of alkylphenols (Section IV.E, p. 42). This may also be demonstrated by the classical example of hydrogenation of aromatic hydrocarbons on Raney nickel (48). In this case, the constants obtained by separate measurements of reaction rates for individual compounds lead to the reactivity order which is different from the order found on the basis of factor S, determined by the method of competitive reactions (Table II). Other examples of the change of reactivity, which may even result in the selective reaction of a strongly adsorbed reactant in competitive reactions (49, 50) have already been discussed (see p. 12). 

Electrochemical reactions can be broken down into two groups outer-sphere electron-transfer reactions and inner-sphere electron transfer reactions. Outer-sphere reactions are reactions that only involve electron transfer. There is no adsorption and no breaking or forming of chemical bonds. Because of their simplicity, numerous studies have been performed, many entirely theoretical.18-25 By definition, though, electrode reactions are not outer-sphere reactions. However, if charge transfer is rate limiting for an electrode reaction, it typically takes a form similar to that of an outer-sphere reaction, which is described later in this section. 

The results of adsorption and desorption of CO mentioned above suggest that for the reaction at low temperature, the sites for relatively weakly chemisorbed CO are covered by the deposited carbon and the reaction occurs between molecularly adsorbed CO and oxygen on the carbon-free sites which are the sites for relatively strongly chemisorbed CO. Therefore, the definition of the turnover rate at 445 K remains as given in Equation 1. For the reaction at 518 K, however, this definition becomes inappropriate for the smaller particles. Indeed, to obtain the total number of Pd sites available for reaction, we now need to take into consideration the number Trp of CO molecules under the desorption peak. Furthermore, let us assume that disproportionation of CO takes place through reaction between two CO molecules adsorbed on two adjacent sites, and let us also assume that the coverage is unity for the CO molecules responsible for the LT desorption peak, since this was found to be approximately correct on 1.5 nm Pd on 1012 a-A O (1). Then, the number Np of palladium sites available for reaction at 518 K is given by HT/0 + NC0 LT s nce t ie co molecules under the LT desorption peak count only half of the available sites. Consequently, the turnover rate at 518 K should be defined as ... 

The residuals discussed thus far have been associated with some dependent variable, such as the reaction rate r. It is particularly advantageous in pinpointing the type of defect present in an inadequate model to expand this definition to include parametric residuals. The parametric residual, then, is simply the difference between a value of a given parameter estimated from the data and that predicted from a model. For example, the dots in Fig. 17 represent the logarithm of the alcohol adsorption constants measured in alcohol dehydrogenation experiments from isothermal data at each of several temperature levels (FI). The solid line represents the expectation that these... 

Asymmetric diarylmethanes, hydrogenolytic behaviors, 29 229-270, 247-252 catalytic hydrogenolysis, 29 243-258 kinetics and scheme, 29 252-258 M0O3-AI2O3 catalyst, 29 259-269 relative reactivity, 29 255-257 schematic model, 29 254 Asymmetric hydrogenations, 42 490-491 Asymmetric synthesis, 25 82, 83 examples of, 25 82 Asymmetry factor, 42 123-124 Atom-by-species matrix, 32 302-303, 318-319 Atomic absorption, 27 317 Atomic catalytic activities of sites, 34 183 Atomic displacements, induced by adsorption, 21 212, 213 Atomic rate or reaction definition, 36 72-73 structure sensitivity and, 36 86-87 Atomic species, see also specific elements adsorbed... 

For the electron transfer of hydrated redox particles (the outer-sphere electron transfer), the electrode acts merely as a source or sink of electrons transferring across the compact double layer so that the nature of the electrode hardly affects the reaction kinetics this lack of influence by the electrode has been observed for the ferric-ferrous redox reaction. On the other hand, the electron transfer of adsorbed redox particles (the inner-sphere electron transfer) is affected by the state of adsorption so that the nature of the electrode exerts a definite influence on the reaction kinetics, as has been observed with the hydrogen electrode reaction where the reaction rate depends on the property of electrode. 

A similar system, (CH3)2C=CH X, was studied by Endrysova and Kraus (55) in the gas phase in order to eliminate the possible leveling influence of a solvent. The rate data were separated in the contribution of the rate constant and of the adsorption coefficient, but both parameters showed no influence of the X substituents (series 61). A definitive answer to the problem has been published by Kieboom and van Bekum (59), who measured the hydrogenation rate of substituted 2-phenyl-3-methyl-2-butenes and substituted 3,4-dihydro-1,2-dimethylnaphtalenes on palladium in basic, neutral, and acidic media (series 62 and 63). These compounds enabled them to correlate the rate data by means of the Hammett equation and thus eliminate the troublesome steric effects. Using a series of substituents with large differences in polarity, they found relatively small electronic effects on both the rate constant and adsorption coefficient. 

Adsorption kinetics involve a time-dependent process that describes the rate of adsorption of chemical contaminants on the solid phase. The standard chemical meaning of kinetics usually covers the study of the rate of reactions and molecular processes when transport is not a limiting factor however, this definition is not... 

If the definition of TOW established by ISO is used (TOW-ISO), a linear relationship between time and TOW is obtained, in spite of the different possible changes in corrosion rate caused by changes in the nature of TOW. It has to be remarked that it is not the same effect on corrosion rate caused by a heavy rain than dew, fog or water adsorption, so for the same interval of relative humidity (80-100%), notable changes in nature of TOW-ISO and consequently in corrosion rate could take place. 

The estimation of the surface area of finely divided solid particles from solution adsorption studies is subject to many of the same considerations as in the case of gas adsorption, but with the added complication that larger molecules are involved whose surface orientation and pore penetrability may be uncertain. A first condition is that a definite adsorption model is obeyed, which in practice means that area determination data are valid within the simple Langmuir Equation 5.23 relation. The constant rate is found, for example, from a plot of the data, according to Equation 5.23, and the specific surface area then follows from Equations 5.21 and 5.22. The surface area of the adsorbent is generally found easily in the literature. 

Chronopotentiometry, galvanostatic transients, 1411 as analytical technique, 1411 activation overpotential, 1411 Clavilier, and single crystals, 1095 Cluster formation energy of, 1304 and Frumkin isotherm, 1197 Cobalt-nickel plating, 1375 Cold combustion, definition, 1041 Cole-Cole plot, impedance, 1129, 1135 Colloidal particles, 880, 882 and differential capacity, 880 Complex impedance, 1135 Computer simulation, 1160 of adsorption processes, 965 and overall reaction, 1259 and rate determining step, 1260... 

In line with the Gibbs adsorption equation (equation 3.33 in chapter 3), the presence of thermodynamically unfavourable interactions causes an increase in protein surface activity at the planar oil-water interface (or air-water interface). As illustrated in Figure 7.5 for the case of legumin adsorption at the n-decane-water interface (Antipova et al., 1997), there is observed to be an increase in the rate of protein adsorption, and also in the value of the steady-state interfacial pressure n. (For the definition of this latter quantity, the reader is referred to the footnote on p. 96.)... 

At 315°C. the rate constant ki has a value of 7.0 X 1016 molecules/sec.-cm.2-atm. From the definition of kh this represents the rate of adsorption of methylcyclohexane per cm.2 of bare platinum surface at a methylcyclohexane partial pressure of 1 atm. From kinetic theory and statistical mechanics, one can calculate the number of molecules striking a unit area of surface per unit time with activation energy Ea. This is given by... 

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