Treatment of adsorption data

Adsorption data are frequently presented as a plot of the amount of adsorbate taken up per unit weight or area of the adsorbent vs the equilibrium concentration remaining in the gaseous or solution phase (adsorption isotherm) pH, temperature and electrolyte concentration are held constant. Depending upon the purpose of the investigation, the extent of adsorption is expressed either as amount of adsorbate vs. surface area of adsorbent, as fraction adsorbed, or, in some cases, as a distribution coefficient, K.  

The adsorption data is often fitted to an adsorption isotherm equation. Two of the most widely used are the Langmuir and the Freundlich equations. These are useful for summarizing adsorption data and for comparison purposes. They may enable limited predictions of adsorption behaviour under conditions other than those of the actual experiment to be made, but they provide no information about the mechanism of adsorption nor the speciation of the surface complexes. More information is available from the various surface complexation models that have been developed in recent years. These models represent adsorption in terms of interaction of the adsorbate with the surface OH groups of the adsorbent oxide (see Chap. 10) and can describe the location of the adsorbed species in the electrical double layer. 

The Langmuir equation applies to a reaction of a surface Fe (= Fe) atom with an adsorbate molecule X, e. g.. 

Anion adsorption on iron oxides is frequently described by this equation whereas cation adsorption data is often fitted to the Freundlich equation, i.e. 

Although this equation is very convenient for representing data, it is purely empirical n is an adjustable parameter that characterizes the adsorption affinity. The effect of adsorbent concentration on the extent of adsorption has been treated by McKinley and Jenne (1991). 

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Table 22.2 Rate constants and correlation coefficients obtained from treatment of adsorption data according to the two kinetic models...

Table VI. Polanyi—Type Treatment of Adsorption Data...

It has long been known that the adsorption of a gas on a solid surface is always accompanied by the evolution of heat. Various attempts have been made to arrive at a satisfactory thermodynamic analysis of heat of adsorption data, and within the past few years broad agreement has been achieved in setting up a general system of adsorption thermodynamics. Here we are not concerned with the derivation of the various thermodynamic functions but only with the more relevant definitions and the principles involved in the thermodynamic analysis of adsorption data. For more detailed treatments, appropriate texts should be consulted. " ... 

We therefore felt it timely to attempt a critical exposition and assessment of the common methods for the evaluation of the surface area and pore size distribution of solids from adsorption measurements. Our main concern has therefore been with the use of adsorption data for these purposes rather than with adsorption per se and it is for this reason that our treatment of theoretical matters, whilst sufficiently detailed to bring out the nature of the assumptions underlying the various methods, is not exhaustive we have not set out to write a text-book or a treatise on adsorption, and our choice of material from the literature has been dictated solely by its seeming suitability for the explanation or illustration of the topic under discussion. 

This is the same case with which in Eqs. (2)-(4) we demonstrated the elimination of the time variable, and it may occur in practice when all the reactions of the system are taking place on the same number of identical active centers. Wei and Prater and their co-workers applied this method with success to the treatment of experimental data on the reversible isomerization reactions of n-butenes and xylenes on alumina or on silica-alumina, proceeding according to a triangular network (28, 31). The problems of more complicated catalytic kinetics were treated by Smith and Prater (32) who demonstrated the difficulties arising in an attempt at a complete solution of the kinetics of the cyclohexane-cyclohexene-benzene interconversion on Pt/Al203 catalyst, including adsorption-desorption steps. 

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... 

A distinctive feature of adsorption from solution is that it always involves a competition between the solvent and solute which has be taken into account in any complete treatment of the data. 

Thus treatment of the data with this alternative adsorption model yields a more negative enthalpy change by RT than the mobile model. 

Even the simplest reaction on a solid catalyst consists of a series of diffusional, adsorption, and surface reaction steps. In fact, it is a consecutive reaction, and useful formal treatment of rate data is possible only if one step is much slower than the other, that is if one step is ratedetermining (12). Now for the pmpose of structure-reactivity correlations, there would be little value if the rate were controlled by diffusion... 

Figure 11 shows a clear difference between the isotherms obtained experimentally by a traditional treatment of the data (with the adsorption cell volume estimated by helium expansion) and the new method. The lower adsorption cell volume obtained by the new method leads to greater excess amounts adsorbed. The difference is much greater for the isotherm at 273.15K than it is at 333.15K and in the region of high pressure. Surprisingly the two... 

The statistical thermodymamic Fowler-Guggenheim treatment of adsorption was applied, and the equilibrium constant of each reaction step in terms of partition functions was calculated, after the introduction of various additional assumptions. The experimental data of Ertl for a potassium-covered iron surface (at optimum potassium coverage) were used, but a much lower value for the nitrogen atom chemisorption energy than quoted by Ertl was adopted. This value and the sticking coefficient of nitrogen were recognized as the parameters on which the results depend most sensitively. 

Experimentally, the investigation of adsorption from solution is much simpler than that of gas adsorption. A known mass of solid adsorbent is shaken with a known volume of solution at a given temperature until there is no further change in the concentration of the solution. This concentration can be determined by various methods involving chemical or radiochemical analysis, colorimetry, refractive index, etc. The experimental data are usually expressed in terms of the apparent (or composite) adsorption isotherm in which the amount of solute adsorbed at a given temperature per unit mass of adsorbent, as calculated from the decrease (or increase) of solution concentration, is plotted against the equihbrium concentration. The theoretical treatment of adsorption is, however. 

The following several sections deal with various theories or models for adsorption. It turns out that not only is the adsorption isotherm the most convenient form in which to obtain and plot experimental data, but it is also the form in which theoretical treatments are most easily developed. One of the first demands of a theory for adsorption then, is that it give an experimentally correct adsorption isotherm. Later, it is shown that this test is insufficient and that a more sensitive test of the various models requires a consideration of how the energy and entropy of adsorption vary with the amount adsorbed. Nowadays, a further expectation is that the model not violate the molecular picture revealed by surface diffraction, microscopy, and spectroscopy data, see Chapter VIII and Section XVIII-2 Steele [8] discusses this picture with particular reference to physical adsorption. 

At the point where capillary condensation commences in the finest mesopores, the walls of the whole mesopore system are already coated with an adsorbed film of area A, say. The quantity A comprises the area of the core walls and is less than the specific surface A (unless the pores happen to be parallel-sided slits). When capillary condensation takes place within a pore, the film-gas interface in that pore is destroyed, and when the pore system is completely filled with capillary condensate (e.g. at F in Fig. 3.1) the whole of the film-gas interface will have disappeared. It should therefore be possible to determine the area by suitable treatment of the adsorption data for the region of the isotherm where capillary condensation is occurring. 

Contemporary development of chromatography theory has tended to concentrate on dispersion in electro-chromatography and the treatment of column overload in preparative columns. Under overload conditions, the adsorption isotherm of the solute with respect to the stationary phase can be grossly nonlinear. One of the prime contributors in this research has been Guiochon and his co-workers, [27-30]. The form of the isotherm must be experimentally determined and, from the equilibrium data, and by the use of appropriate computer programs, it has been shown possible to calculate the theoretical profile of an overloaded peak. 

Adsorption — An important physico-chemical phenomenon used in treatment of hazardous wastes or in predicting the behavior of hazardous materials in natural systems is adsorption. Adsorption is the concentration or accumulation of substances at a surface or interface between media. Hazardous materials are often removed from water or air by adsorption onto activated carbon. Adsorption of organic hazardous materials onto soils or sediments is an important factor affecting their mobility in the environment. Adsorption may be predicted by use of a number of equations most commonly relating the concentration of a chemical at the surface or interface to the concentration in air or in solution, at equilibrium. These equations may be solved graphically using laboratory data to plot "isotherms." The most common application of adsorption is for the removal of organic compounds from water by activated carbon. 

The quantitative solution of the problem, i.e. simultaneous determination of both the sequence of surface chemical steps and the ratios of the rate constants of adsorption-desorption processes to the rate constants of surface reactions from experimental kinetic data, is extraordinarily difficult. The attempt made by Smith and Prater 82) in a study of cyclohexane-cyclohexene-benzene interconversion, using elegant mathematic procedures based on the previous theoretical treatment 28), has met with only partial success. Nevertheless, their work is an example of how a sophisticated approach to the quantitative solution of a coupled heterogeneous catalytic system should be employed if the system is studied as a whole. 

It is noteworthy that even a separate treatment of the initial data on branched reactions (1) and (2) (hydrogenation of crotonaldehyde to butyr-aldehyde and to crotyl alcohol) results in practically the same values of the adsorption coefficient of crotonaldehyde (17 and 19 atm-1)- This indicates that the adsorbed form of crotonaldehyde is the same in both reactions. From the kinetic viewpoint it means that the ratio of the initial rates of both branched reactions of crotonaldehyde is constant, as follows from Eq. (31) simplified for the initial rate, and that the selectivity of the formation of butyraldehyde and crotyl alcohol is therefore independent of the initial partial pressure of crotonaldehyde. This may be the consequence of a very similar chemical nature of both reaction branches. 

Application of equation 10 to the experimental D vs. [HSOIJ] data determined at 25°C and both 1 and 2 M acidity yielded straight line plots with slopes indistinguishable from zero and reproduced the Bi values determined in a non-linear regression fit of the data. This result implies no adsorption of PuSO by the resin and justifies use of the simpler data treatment represented by equation 2. A similar analysis of the Th(IV)-HSOiJ system done by Zielen (9) likewise produced results consistent with no adsorption of ThS0 + by Dowex AG50X12 resin. 

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