Molar surface excess quantities

By adopting the usual conventions of chemical thermodynamics, we are able to derive from the surface excess chemical potential pa a number of useful surface excess quantities. Our purpose here is to draw attention to the difference between the molar and the differential surface excess quantities. 

The differential quantities of adsorption , are the differences between the differential surface excess quantities and the same molar quantity, as in Equation (2.46) or... 

The difference between a molar surface excess thermodynamic quantity xar r and the corresponding molar quantity x p for the gaseous adsorptive at the same equilibrium T and p is usually called the integral molar quantity of adsorption, and is denoted Aads r,r ... 

Similarly, for other surface excess thermodynamic quantities, the corresponding molar quantities are as follows ... 

We may derive the relation between these integral molar quantities of adsorption from Equations (2.20) using the expression of surface excess chemical potential p° given by Equation (2.41) and assuming the gas to be ideal ... 

In the field of adsorption from solution, many discussions and reviews were published about the measurement of the adsorbed amount and the presentation of the corresponding data [14, 45—47]. Adsorption isotherms are the first step of any adsorption study. They are generally determined from the variation of macroscopic quantities which are rigorously measurable far away from the surface (e.g., the concentration of one species, the pressure, and the molar fraction). It is then only possible to compare two states with or without adsorption. The adsorption data are derived from the difference between these two states, which means that only excess quantities are measurable. Adsorption results in the formation of a concentration profile near an interface. Simple representations are often used for this profile, but the real profile is an oscillating function of the distance from the surface [15, 16]. Without adsorption, the concentration should be constant up to the soHd surface. Adsorption modifies the concentration profile of each component as well as the total concentration profile. It must be noted also that when the liquid is a pure component its concentration profile, i.e., its density, is also modified. Experimentally, the concentration can be measured at a large distance from the surface. The surface excess of component i is the... 

Thus we now learn that we cannot measure the absolute surface excess of K, but only its excess relative to water. For example, a zero relative excess does not imply a lack of adsorption of K", but only that and H2O are adsorbed to the same degree. That is, and H2O are adsorbed in the same mole ratio that they have in the bulk electrolyte. A positive relative excess means that is adsorbed to a greater degree than water, not in absolute molar quantities, but with respect to the amounts available in the bulk electrolyte. 

The quantity n° is the total amount of components 1 and 2 (n° = i + 2. in moles) offered per gram of adsorbent, and Axi indicates the change of the molar fraction of component 1 by adsorption. The specific reduced surface excess = /( i) represents the composite isotherm from which the true... 

In a simple example where a small metal particle M and a species X react to a compound MX, the excess surface energy of both reactants and products must be taken into account. Thus, the molar free energy of formation of a particle MX may be described in a simplified manner on the basis of the Gibbs concept in which excess quantities are addressed ... 

Furthermore, an extensive study of the dynamic and structural properties of water/alcohol systems by Onori and Santucci [73] based on adiabatic compressibility and surface tension measurements, infrared and near-infrared absorption spectra, and the dielectric relaxation method showed that two characteristic Umiting molar fraction values can be designated for a specific alcohol. The adiabatic compressibility is a quantity that refers to the volume unit of solution irrespective of the number of molecules therefore, the excess quantity (Ps which is... 

The expansibilities, compressibilities, and surface tensions of the mixtures are intensive properties, so they should be expressed not in terms of excess quantities but just as deviations from the linear dependence on the (mole fraction) composition. Data for the isobaric expansibilities and the adiabatic compressibilities of binary mixtures of water with many cosolvents on the list are available in [56]. The isobaric compressibilities can then be calculated from such data by Equation 3.3, using also the molar volumes of the mixtures, V = x V- + XcK -i- V. ... 

Add a quantity of NHS-salicylic acid methyl ester reagent dissolved in coupling buffer to the slide surface to provide at least a 2-fold molar excess of crosslinker over the quantity of amines present on the surface. The surface of the slide may be coated with a minimum solution volume of the crosslinker by layering the solution over the surface. Slide masks or gaskets may be used to isolate only certain regions for modification. Alternatively, the slide may be immersed in the crosslinker solution. The NHS-salicylic acid methyl ester may be first dissolved in DMF as a concentrated stock solution and then an aliquot... 

The surface pressure—area and surface dipole moment-area data for both components and a 1 to 1 molar ratio of all but the last mixture were obtained for at least two temperatures in the range 0° to 40 °C. From such data excess thermodynamic quantities were calculated. For reasons... 

This quantity provides information about the excess of component-adsorbent interactions averaged over all surface domains from which the solvent has been displaced by the adsorbing solute species. In consequence, it is not easy to monitor subtle changes in the adsorption mechanism based on usually small variations of the Adpih values with increasing quantity of adsorption. Compared to the differential molar enthalpy of displacement, the enthalpy Adpih is less sensitive to the energetic heterogeneity of the solid surface. 

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