Adsorption, coefficient enthalpy

True activation energies are obtained when the reaction order is zero and probably also when the rate coefficient, k, and adsorption coefficient, Ka, have been separated by treatment of rate data by means of eqn. (3). In the case of the first-order rate equation, the apparent activation energy, calculated from k values [eqn. (5)] by means of the Arrhenius equation, is the difference between the true activation energy and the adsorption enthalpy of the reactant A... 

The proposed mechanism of the effect of water can be supported by two other findings (i) the calculations of Maatman et al. [410] revealed that the active sites could be identified with surface silanol groups [Sect. 4.1.2.(a)] and(ii) independent studies of other authors [424—426] showed that silica gel could actually adsorb two layers of water the first layer is strongly chemisorbed whereas the second is less strongly adsorbed and retains much of the character of free water. The standard enthalpy and entropy changes on adsorption determined from kinetic adsorption coefficients, Kr and Kr, for the first and second layer, respectively [411], are consistent with this observation. 

Relative Adsorption Coefficients (zr), Free Energies (A F°), Enthalpies (—AH °), and Entropies (AS°) of Adsorptive Exchange Rate Constants (K), Activation Energies (e), and the h Parameters in Catalytic Dehydrogenation. AF°, AH°, and t cal./mole AS° e.u. Ai Rate of Reactant Supply, andmo Reaction Rate ml. Substance Vapor/min., K-ml./(ml. min.). All Valuesfor N.T.P. Original Data Are Reduced to the Same Units. 

The adsorption coefficients of benzene on the ZSM-5 extrudates were determined by the first moment of the pulse experiments [10]. As indicated in Fig.2, benzene exhibited a strong adsorption with a high adsorption enthalpy of 130 kJ/mol. This strong adsorption behaviour at zero occupancy is well known from literature [11] and heats of adsorption close to 100 kJ/mol are reported for laboratory ZSM-5 crystals. 

The Arrhenius and Van t Hoff plots for the rate and adsorption coefficients are shown in Fig. 11.9.1.A-3. The pre-exponential factors, activation energies, and enthalpy changes are given in Table 11.9.1.A-2. 

It is not necessary to limit the model to idealized sites Everett [5] has extended the treatment by incorporating surface activity coefficients as corrections to N and N2. The adsorption enthalpy can be calculated from the temperature dependence of the adsorption isotherm [6]. If the solution is taken to be ideal, then... 

Despite the importance of mixtures containing steam as a component there is a shortage of thermodynamic data for such systems. At low densities the solubility of water in compressed gases has been used (J, 2 to obtain cross term second virial coefficients Bj2- At high densities the phase boundaries of several water + hydrocarbon systems have been determined (3,4). Data which would be of greatest value, pVT measurements, do not exist. Adsorption on the walls of a pVT apparatus causes such large errors that it has been a difficult task to determine the equation of state of pure steam, particularly at low densities. Flow calorimetric measurements, which are free from adsorption errors, offer an alternative route to thermodynamic information. Flow calorimetric measurements of the isothermal enthalpy-pressure coefficient pressure yield the quantity 4>c = B - TdB/dT where B is the second virial coefficient. From values of obtain values of B without recourse to pVT measurements. 

As appears from the examination of the equations (giving the best fit to the rate data) in Table 21, no relation between the form of the kinetic equation and the type of catalyst can be found. It seems likely that the equations are really semi-empirical expressions and it is risky to draw any conclusion about the actual reaction mechanism from the kinetic model. In spite of the formalism of the reported studies, two observations should be mentioned. Maatman et al. [410] calculated from the rate coefficients for the esterification of acetic acid with 1-propanol on silica gel, the site density of the catalyst using a method reported previously [418]. They found a relatively high site density, which justifies the identification of active sites of silica gel with the surface silanol groups made by Fricke and Alpeter [411]. The same authors [411] also estimated the values of the standard enthalpy and entropy changes on adsorption of propanol from kinetic data from the relatively low values they presume that propanol is weakly adsorbed on the surface, retaining much of the character of the liquid alcohol. 

Differential) enthalpy of adsorption on uncovered surface — q° Transfer coefficient a... 

The acidic sites on iron oxides are believed to be FeOH sites (32), much like the well-known SiOH sites on silica. Heats of adsorption on iron oxide of bases of known Cg and Eg, having appreciably different ratios of Cg to Eg ("hardness" or "softness"), allow estimation of the and for the acidic sites of iron oxide. Our initial studies were done by measuring adsorption isotherms at two or more temperatures (Figure 7) and from the temperature coefficient of the equilibrium constant K the enthalpy of adsorption was calculated. In Figure 7 the adsorption data is plotted as a Langmuir isotherm ... 

Here A//adS is the enthalpy of adsorption, T is the temperature, and AAads is the entropy change associated with the adsorption of the protein onto the surface. Protein adsorption will take place if AGads < 0. Considering a complex system, where proteins are dissolved in an aqueous environment, and are brought into contact with an artificial interface, there are a vast number of parameters that impact AGads due to their small size (i.e., large diffusion coefficient), water molecules are the first to reach the surface when a solid substrate is placed in an aqueous biological environment. Hence, a hydrate layer is formed. With some delay, proteins diffuse to the interface and competition for a suitable spot for adsorption starts. This competition... 

The necessity of having two independent terms to describe the specific (or polar) interactions is relevant to the fact that most organic probes are amphoteric and may as well act as electron donors or electron acceptors, as seen in Table 9. In Table 9, it should be noted that LFERs for a general set of electron acceptors (or donors) which is the specific component of adsorption enthalpy may be closely related to LSERs of Kamlet-Taft, resulting in that the correlation coefficients are largely constant and the standard deviations are low, as below [119]... 

Here the pre-exponential factor, K, is equal to the ratio of the adsorption and desorption coefficients, a//. Alternatively, b may be regarded as a function of the enthalpy and entropy of adsorption (Everett, 1950 Barrer, 1978, p. 117). 

Adsorption enthalpies are also very similar but quite different pre-exponential factors are obtained. This indicates that the same sites are involved for the adsorption of NO but their number has increased. The increase of the number of active sites can be confirmed by TPD experiments obtaining that the total amount of CO and CO2 increased considerably after treatment of the raw sample (Table 2). On the other hand, the amount of different type of surface groups varies in a low extent after treatment of the raw sample, except for the carbonyls that increases in concentration by approximately a factor of three. So, these structures could be the responsible of the enhancement of the NO conversion once determined that diffusion coefficients are similar for both samples. 

Table 2 Constants ofEq. (3) for differential enthalpy (isosteric heat) of adsorption of gases in NaX zeolite at 298.15 K. Virial coefficients Z),- in units ofkJ kg mol< >...

Equation (5) is an equation-of-state for the adsorption of a pure gas as a function of temperature and pressure. The constants of this equation are the Henry constant, the saturation capacity, and the virial coefficients at a reference temperature. The temperature variable is incorporated in Equation (5) by the virial coefficients for the differential enthalpy. This equation-of-state for adsorption of single gases provides an accurate basis for predicting the thermodynamic properties and phase equilibria for adsorption from gaseous mixtures. 

The key step in the derivation by Reuter et al. of their lattice model is the use of detailed balance to determine the sticking coefficients for each species on each type of site.31 The total adsorption rate at a particular site can be expressed as Tad = SI(p, T), where S is the local sticking coefficient and I(p,T) is the impingement rate of the species of interest from a gas phase with partial pressure p and temperature T. At steady state, the total adsorption and desorption rates must satisfy the detailed balance condition TdesjTad = exp[(Fb—/j,(T, p))/kT, where Fb is the free energy of the adsorbed species and fi(T, p) is the chemical potential of the gas phase species. The adsorption free energy is well approximated by the adsorption enthalpy, which is simply the adsorption energy calculated by a DFT calculation. This approach provides a direct link between the adsorption and desorption rates and the pressure and temperature of the bulk gas phase. 

---