Surfaces excess amount

An adsorption isotherm for a single gaseous adsorptive on a solid is the function which relates at constant temperature the amount of substance adsorbed at equilibrium to the pressure (or concentration) of the adsorptive in the gas phase. The surface excess amount rather than the amount adsorbed is the quantity accessible to experimental measurement, but, at lower pressures, the difference between the two quantities becomes negligible (see Appendix II, Part I, 1.1.11). 

The specific surface excess amount is what is typically measured in practical adsorption studies (see Section 6.4). This parameter is almost equal to the amount adsorbed, a, and is dependent on the equilibrium adsorption pressure, P, at constant adsorbent temperature, T. Accordingly, gas adsorption data is, in practice, expressed by the adsorption isotherm ... 

The surface excess amount, or Gibbs adsorption (see Section 6.2.3), of a component i, that is, /if, is defined as the excess of the quantity of this component actually present in the system, in excess of that present in an ideal reference system of the same volume as the real system, and in which the bulk concentrations in the two phases stay uniform up to the GDS. Nevertheless, the discussion of this topic is difficult on the other hand for the purposes of this book, it is enough to describe the practical methodology, in which the amount of solute adsorbed from the liquid phase is calculated by subtracting the remaining concentration after adsorption from the concentration at the beginning of the adsorption process. 

Figure 2.1. The Gibbs representation of the surface excess amount c, local concentration dn/dV of adsorbable gas z, distance from the surface.

In Figure 2.1b, the surface excess amount na is represented by hatched area d whereas the amount adsorbed n , which also includes term cg Va, is represented in Figure 2.1a by area (d + e). 

What is usually measured and recorded is the specific surface excess amount na/ms, where... 

For the sake of simplicity in some later sections of this book, we adopt the symbol n to denote the specific surface excess amount n°lm. Also, for convenience, this quantity will be often referred to as amount adsorbed. 

The surface excess chemical potential can be obtained by partial differentiation of G° (defined in Equation 2.28) with respect of the surface excess amount na, with the... 

Alternatively, the chemical potential of the adsorbed phase is equal to the transformed Gibbs energy divided by the surface excess amount, i.e. the transformed molar surface excess Gibbs energy ... 

We now return to the definition of the surface excess chemical potential fta given by Equation (2.19) where the partial differentiation of the surface excess Helmholtz energy, Fa, with respect to the surface excess amount, rf, is carried out so that the variables T and A remain constant. This partial derivative is generally referred to as a differential quantity (Hill, 1949 Everett, 1950). Also, for any surface excess thermodynamic quantity Xa, there is a corresponding differential surface excess quantity xa. (According to the mathematical convention, the upper point is used to indicate that we are taking the derivative.) So we may write ... 

The differential energy of adsorption can also be regarded as the change of internal energy of the complete adsorption system, produced by the adsorption of an infinitesimal surface excess amount dn°, when temperature, volume and surface area are held constant (and assuming the adsorbent to be inert and that its internal energy is not changed). Thus,... 

Thus in addition to the data required to determine the surface excess amount (cf. Section 3.3.1), one needs to know dQKV (the heat exchanged reversibly during each adsorption step) and Vc (the volume - dead space - of that part of the adsorption bulb which is located within the calorimetric detector (cf. Figure 3.15). Vc is evaluated by liquid weighing or by geometrical considerations and corrected for the sample volume. 

Scope and limitation of the normal surface excess amounts.142... 

The meaning of relative and reduced surface excess amounts.145... 

In Chapter 2 we have introduced a number of thermodynamic surface excess quantities (Equations (2.11)—(2.14)) in the case of a simple gas adsorption system involving a single adsorptive. These quantities were expressed as a function of the surface excess amount, na. In the case of the process of immersion of a solid in a pure liquid, the same surface excess quantities can still be defined and it is useful to express them as a function of the surface area. Thus ... 

Figure 5.11. Dependence of surface excess amount of component i on location of GDS. S, GDS of actual adsorbing surface ...

Another function invariant with respect to the position of the GDS and named the reduced surface excess amount was derived at by Defay (1941) in a similar way. Starting again from Equation (5.46), we can write the following two equations ... 

Here again the right-hand side does not depend on anything other than experimentally measurable quantities, and therefore we conclude that the right-hand side does not depend on the position of the GDS. This function is defined as the reduced surface excess amount of 2 ... 

The meaning of relative and reduced surface excess amounts Although the relative and the reduced surface excess amounts (or masses) do not depend on the position of the GDS, there is a special position of the GDS which cancels the last term of the defining equations ((5.48) and (5.55)) and gives a useful idea of the meaning of these two quantities. For Equation (5.48), this special position of the GDS is the one for which the surface excess amount n of component 1 is zero. We then get ... 

Adsorption isotherms expressed in reduced surface excess amounts... 

The principle of the null procedure (Nunn and Everett, 1983) is to restore, by injection of an appropriate dose of initial solution, the concentration prior to adsorption. This is done at each adsorption step. A refinement is to arrange that the sample cell is bypassed during the injection of a new dose of solution until the determination of a new amount concentration d2. The flow through is re-started and, as the concentration decreases, it is restored to its initial value d2 by addition of a volume A Va of a solution of amount concentration c2. The determination of the increase in reduced surface excess amount of 2 simply requires a knowledge of the void volume of the bypassed section and the concentration d 1 of the former adsorption equilibrium. Thus,... 

Both surface excess amounts must also remain unchanged this necessarily holds when using reduced surface excess amounts by the application of Equation (5.75), since nfn) = -nf"] (see Equation (5.10)) so that it is enough to maintain a constant nfn). This does not hold, however, when relative surface excess amounts or simple surface excess amounts are used. 

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