Molar excess surface concentration

Since Eq. (10) takes the difference between the two molar volumes into account, it is evident that means the excess amount in the adsorbed phase, which is the only directly measurable parameter. It is also evident that A means the excess surface concentration in relation to the gas (bulk) phase. The situation is quite analogous to adsorption from a two-component liquid mixture. To demonstrate the inconsistencies of limiting values [Eqs (17) and (18)] let us investigate the changes in n , n and (p - p") in the range of very high pressures (densities), that is, when p CO. After Menon [3,4] the excess character of n can also be defined by the densities of the gas phase (p, mol m ) and by that of the adsorbed phase (p ). The total amount of the adsorptive (n ) present in the sorbed phase is... 

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... 

In a two-phase system consisting of two or more components the composition of the discontinuity surface (see Chapter I) may significantly differ from that of a bulk of both phases in contact. Primarily the components that lower the system s free surface energy are expected to accumulate within the discontinuity surface this spontaneous concentration of substances is referred to as adsorption. The quantitative measure of the adsorption of the /-th component, T was introduced by Gibbs, and is also referred to as the adsorption, or the surface excess ofthe amount of substance. This measure has a meaning of the molar excess of a particular component per unit interfacial area ... 

There is large body of data on the surface and interfacial tensions of aqueous surfactant solutions. This data show that the structure of the surfactant molecule has a pronounced effect on its ability to reduce these tensions. As the length of the alkyl or fluorinated alkyl chain increases, the CMC decreases and the surface excess concentration increases, causing a drop in the interfacial tension at a fixed surfactant concentration. At low surfactant concentrations the reduction in surface tension (or increase in surface pressure O = yo - y) is linear with the molar bulk solute concentration c (in the case of the dilute solution)... 

Table III lists some common pesticides which have been widely reported to be extracted from water. The aqueous solubilities of pesticides vary within wide limits many, including chlorinated hydrocarbon insecticides, probably do not even occur as such in water but are always adsorbed to silt or other particles or dissolved in surface films (24). Overall concentrations, nevertheless, generally do not exceed the parts per trillion range—i.e., nanomolar (lO M). Reagents such as oxygen, hydroxide ion, and even metal ions normally are present in from perhaps 100- to 100,000-fold molar excess over the amounts of pesticides which are to be found in water (Table II).

For both types of catalysts, the reaction conditions considered in this review should be kept in mind (Table 1). Specifically, because oxygen is always present in large excess (from Table 1, the molar ratio of 0,/V0C is about 10 - 10 ), the catalyst surface concentration of oxygen is always relatively high. This also means that the oxygen concentration in the gas phase is essentially constant, and the overall rate will usually be a function of the VOC concentration only. 

The number of moles of solute present in the surface In excess of the number of moles of the same solute in the interior is taken to be the molar excess of solute. This molar excess of solute is the amount of solute adsorbed at the surface. If the concentration of the solute is small, a change in concentration will not affect the free energy of the solvent. In such a case, the... 

Surface activity in 1,4-polyisoprene-polyacetylene, AB, block copolymer solutions was to be expected from the amphiphilic properties of such a diblock system with one moiety so insoluble because of the strong polyacetylene-polyacetylene attractive interactions. The present experiments allow access, for the first time, to some of the thermodynamic parameters of these interactions and give a structural model for the surface excess above and below the critical micelle concentration. This has been identified as about 10" moles/L for the lelated polymer 1,4-polyisoprene-polyacetylene (MW 8000 520) in toluene at 20 C using the drop weight method to determine surface tension. From ca. 10" molar to molar the surface tension drops by about 3.5% to a constant value of ca. 28.4 dyne cm at concentrations above 10 3 molar (ca. 1% w/w). Referring to Figure 3 we see that it is above ca 1% that a broad peak develops in the solution/solvent reflectivity ratio for 0.15 < k / < 0.25. The area per... 

LDAO/SDS Interaction. Mixing of cationic and anionic surfactant solutions results In the formation of a mixed species that Is more surface active than the Individual species. The enhanced synergistic effect has been explained (2,3) by showing that a close-packed adsorption of electroneutral R R takes place (R" " and R represent the long chain cation and anion respectively). In the case of Ci2 and C14-DAO, a 1 1 LDAO/SDS molar ratio produces a minimum In surface tension and Is accompanied by an Increase In pH In the bulk solution the association seems to be of the type R R", and the absence of visible precipitate may be attributed to the solubilization of the R R" complex In the solution. In the region where LDAO Is In excess, the structure Is probably [cationic (LDAOH ) anionic (SDS)] nonlonlc (LDAO), while [cationic (LDAOH anionic (SDS)] anionic (SDS) Is formed when SDS Is In excess. Equal molar concentration results In cationic (LDAOH ) anionic (SDS) complex which should favor precipitation. However, at pH >9, there Is no Indication of precipitation (even when the total solute concentration Is 0.35 M). When the pH Is below 9, then precipitation will take place. 

The equation of state can be furnished if the partial molar fraction xf can be described in terms of the real surface excess The molar fraction is defined as the molar concentration of the component in the surface layer divided by the total molar concentration of all components in the layer. Since the molar concentrations can also be expressed in terms of the surface area, the molar fraction is equivalent to the partial coverage 9i of the component. Now we have x f = 6i = Ficoi. In terms of the surface coverage 9i and the bulk concentration Ci of the zth component, Eqs. 6 and 7 can be transformed to give... 

F surface excess molar concentration of any species in the interfacial region (Lorenlzian broadening parameter) y surface tension... 

The integral molar energy of adsorption is therefore obtained by integrating the differential energy of adsorption between the limits 0 and n°. It equals the mean of the differential energy of adsorption over the range of surface excess concentration from 0 to r. 

An adsorption step, during which an amount of liquid na is vaporized from the liquid phase (with a molar energy of vaporization Avap ) and adsorbed on the solid surface (with an integral molar adsorption energy A k, precisely defined for an adsorption process at constant volume (cf. Equation (2.59)), at temperature T and for the surface excess concentration r=n°/A. 

It thus becomes possible to assess the net molar integral energy of adsorption (u° - ux) from the difference between the energy of immersion of the outgassed adsorbent and that of the adsorbent with a pre-adsorbed surface excess concentration, as was originally pointed out by Hill (1949). 

In some instances (especially if the exact molar mass of one component is not known, which often happens with long chain molecules, like those of surfactants) it is more convenient to think in terms of mass. We then use mass fractions w1, or w 2 (instead of molar concentrations or molar fractions) and arrive at surface excess masses, either relative ... 

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