Adsorption defined

Similarly, we can derive the differential (or isosteric) enthalpy of adsorption (defined by Equation (2.51)) ... 

Otlier heats of adsorption, defined differently, are also in use. However, tlie isosteric heat is the most common, and is tlie one needed for energy balances on adsorption columns. 

Adsorption defines the accumulation of a substance, or material, at tlie interface between a solid surface and a bathing solution (Sparks, 2002). Within the adsorption framework, the individual components are referred to as the adsorbate, the accumulating material at the interface, and the adsorbent, or solid surface (Sparks, 2002). If adsorption occurs and results in the formation of a stable molecular phase at the interface, this entity can be described as a surface complex. Two general surface complexes exist and are described by the configuration geometry of the adsorbate at the adsorbent surface. These are the iiuier-and outer-sphere surface complexes, defined by the presence, or absence, of the hydration sphere of the adsorbate molecule upon interaction. When at least one water molecule of the hydration sphere is retained upon adsorption, the surface complex is referred to as an outer-sphere complex (Sposito, 1984) when an ion or molecule is bound directly to the adsorbent without the presence of the hydration sphere, an inner-sphere complex is formed. 

Adsorption coefficient for NO adsorption, defined by eqn 3. Adsorption coefficient for NO2 adsorption. 

Rate constant for oxidation of NO to NO2, defined by eqn 16. Rate constant for dissociation ofN02 to NO, defined by eqn 17. Rate constant for NOx reduction by CsHg, defined by eqn 7. Rate constant for oxygen adsorption, defined by eqn 1. 

The Frumkin isotherm arises from the assumption that the electrochemical free energy of adsorption, defined in (13.5.3), is linearly related to Fi. ... 

Volatilization defines the partitioning of a chemical between water and air. Adsorption defines the partitioning of a chemical between water and soil. In the process of adsorption, which is also referred to variously as sorption or retention, molecules move back and forth between being dissolved in water and being attached to the surfaces of soil or sediment particles with which the water is in contact. How a chemical distributes itself between being adsorbed to soil and dissolved in water is described by the adsorption coefficient, or the soihwater partition coefficient. The ratio of the concentrations of adsorbed to dissolved chemical at equilibrium under standard conditions is ... 

A gas can adsorb on a solid surface either physically (physisorption) or chemically (chemisorption), the latter involving actual bonding at the surface between the gas molecule and the metal as explained in Section 1.2. While the magnitude of the heat of adsorption (defined below) is often used to differentiate physisorption from chemisorption, the most useful way of distinguishing them is the way in which gas molecules cover the surface only a monolayer of adsorbed gas molecules... 

A somewhat subtle point of difficulty is the following. Adsorption isotherms are quite often entirely reversible in that adsorption and desorption curves are identical. On the other hand, the solid will not generally be an equilibrium crystal and, in fact, will often have quite a heterogeneous surface. The quantities ys and ysv are therefore not very well defined as separate quantities. It seems preferable to regard t, which is well defined in the case of reversible adsorption, as simply the change in interfacial free energy and to leave its further identification to treatments accepted as modelistic. 

There are numerous references in the literature to irreversible adsorption from solution. Irreversible adsorption is defined as the lack of desotption from an adsoibed layer equilibrated with pure solvent. Often there is no evidence of strong surface-adsorbate bond formation, either in terms of the chemistry of the system or from direct calorimetric measurements of the heat of adsorption. It is also typical that if a better solvent is used, or a strongly competitive adsorbate, then desorption is rapid and complete. Adsorption irreversibility occurs quite frequently in polymers [4] and proteins [121-123] but has also been observed in small molecules and surfactants [124-128]. Each of these cases has a different explanation and discussion. 

It is important to note that the experimentally defined or apparent adsorption no AN 2/, while it gives F, does not give the amount of component 2 in the adsorbed layer Only in dilute solution where N 2 0 and = 1 is this true. The adsorption isotherm, F plotted against N2, is thus a composite isotherm or, as it is sometimes called, the isotherm of composition change. 

The case of a vapor adsorbing on its own liquid surface should certainly correspond to mobile adsorption. Here, 6 is unity and P = the vapor pressure. The energy of adsorption is now that of condensation Qu, and it will be convenient to define the Langmuir constant for this case as thus, from Eq. xvn-39. 

There are alternative ways of defining the various thermodynamic quantities. One may, for example, treat the adsorbed film as a phase having volume, so that P, V terms enter into the definitions. A systematic treatment of this type has been given by Honig [116], who also points out some additional types of heat of adsorption. 

Alternatively, an integral distribution function F may be defined as giving the fraction of surface for which the adsorption energy is greater than or equal to a given Q,... 

Sing (see Ref. 207 and earlier papers) developed a modification of the de Boer r-plot idea. The latter rests on the observation of a characteristic isotherm (Section XVII-9), that is, on the conclusion that the adsorption isotherm is independent of the adsorbent in the multilayer region. Sing recognized that there were differences for different adsorbents, and used an appropriate standard isotherm for each system, the standard isotherm being for a nonporous adsorbent of composition similar to that of the porous one being studied. He then defined a quantity = n/nx)s where nx is the amount adsorbed by the nonporous reference material at the selected P/P. The values are used to correct pore radii for multilayer adsorption in much the same manner as with de Boer. Lecloux and Pirard [208] have discussed further the use of standard isotherms. 

An adsorption system follows Eq. XVII-79 in the form lnv = B-(l/n)lnln(P /P) with n - 2.75 and B = 3.2. Assuming now that you are presented with data that fall on the curve defined by this equation, calculate the corresponding BET vm and c values. 

The saturation coverage during chemisorption on a clean transition-metal surface is controlled by the fonnation of a chemical bond at a specific site [5] and not necessarily by the area of the molecule. In addition, in this case, the heat of chemisorption of the first monolayer is substantially higher than for the second and subsequent layers where adsorption is via weaker van der Waals interactions. Chemisorption is often usefLil for measuring the area of a specific component of a multi-component surface, for example, the area of small metal particles adsorbed onto a high-surface-area support [6], but not for measuring the total area of the sample. Surface areas measured using this method are specific to the molecule that chemisorbs on the surface. Carbon monoxide titration is therefore often used to define the number of sites available on a supported metal catalyst. In order to measure the total surface area, adsorbates must be selected that interact relatively weakly with the substrate so that the area occupied by each adsorbent is dominated by intennolecular interactions and the area occupied by each molecule is approximately defined by van der Waals radii. This... 

Detailed derivations of the isothemi can be found in many textbooks and exploit either statistical themio-dynaniic methods [1] or independently consider the kinetics of adsorption and desorption in each layer and set these equal to define the equilibrium coverage as a function of pressure [14]. The most conmion fomi of BET isothemi is written as a linear equation and given by ... 

Similarly, one may define the molar integral enthalpy of adsorption, SJt as... 

To characterize the state of the adsorbed phase, it is useful to evaluate its molar entropy, s , defined as the mean molar value for all the molecules adsorbed over the complete range of surface coverage up to the given amount adsorbed. The molar integral entropy of adsorption. As, is then defined as... 

Similarly, the differential molar enthalpy of adsorption, Ji is defined as... 

The term heat of adsorption has been defined in a number of different ways. Unfortunately, the initial and final states of the adsorption system and the conditions under which the exchange of heat takes place have not always been adequately defined. As in all applications of thermodynamics, it is essential that the experimental data refer to a system which has reached equilibrium. 

The state of the surface is now best considered in terms of distribution of site energies, each of the minima of the kind indicated in Fig. 1.7 being regarded as an adsorption site. The distribution function is defined as the number of sites for which the interaction potential lies between and (rpo + d o)> various forms of this function have been proposed from time to time. One might expect the form ofto fio derivable from measurements of the change in the heat of adsorption with the amount adsorbed. In practice the situation is complicated by the interaction of the adsorbed molecules with each other to an extent depending on their mean distance of separation, and also by the fact that the exact proportion of the different crystal faces exposed is usually unknown. It is rarely possible, therefore, to formulate the distribution function for a given solid except very approximately. 

The physical adsorption of gases by non-porous solids, in the vast majority of cases, gives rise to a Type II isotherm. From the Type II isotherm of a given gas on a particular solid it is possible in principle to derive a value of the monolayer capacity of the solid, which in turn can be used to calculate the specific surface of the solid. The monolayer capacity is defined as the amount of adsorbate which can be accommodated in a completely filled, single molecular layer—a monolayer—on the surface of unit mass (1 g) of the solid. It is related to the specific surface area A, the surface area of 1 g of the solid, by the simple equation... 

The most direct test is to compare the BET area with the geometrical area of the solid. Unfortunately, comparisons of this kind are relatively rare on account of experimental difficulties. The choices are to work with, say, single crystals having a well defined surface, when techniques of quite extraordinary sensitivity will be needed for measurement of the adsorption or, to obtain a larger surface area by use of thin sheets, narrow rods or small spheres, and run the risk that the surface will not be truly smooth so that the actual area will exceed the geometrical area. 

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