Molar area

Now, nfV /T is just the surface area, and, moreover, V /t and Vi/t have the dimensions of molar area, (/"the surface region is considered to be just one molecule thick, V /t and V /t becomes A and A2, the actual molar areas, so that Eq. III-115 takes on the form... 

A n +A2it2, where A and A2 are the molar areas. A particular gaseous film has... 

Fig. 17. An homologous series of alkane probes is generally used because good values for their adsorbed molar areas are available [87]. The linearity of the plot (the alkane line ) lends credence to the procedure.

Fig. 17. A schematic of the alkane line obtained by inverse gas chromatography (IGC) measurements. The relative retention volume of carrier gas required to elute a series of alkane probe gases is plotted against the molar area of the probe times the. square root of its surface tension. The slope of the plot is yielding the dispersion component of the surface energy of...

Since surface pressure is a free energy term, the energies and entropies of first-order phase transitions in the monolayer state may be calculated from the temperature dependence of the ir-A curve using the two-dimensional analog of the Clausius-Clapeyron equation (59), where AH is the molar enthalpy change at temperature T and AA is the net change in molar area ... 

This means that the partial molar area may directly be determined from the change in molecular area, when an amphiphilic molecule is introduced into a host liquid crystalline pattern. Of course, this area is the change of area per molecule at the introduction of one molecule of the substance in question and may be influenced by the interaction between the host molecules and the guest molecules. Since this interaction is an essential part of the present problem, it appears obvious that the method exactly meets the requirements. 

We commence with the adsorption of nonionic surfactants, which does not require the consideration of the effect of the electrical double layer on adsorption. The equilibrium distribution of the surfactant molecules and the solvent between the bulk solution (b) and at the surface (s) is determined by the respective chemical potentials. The chemical potential /zf of each component i in the surface layer can be expressed in terms of partial molar fraction, xf, partial molar area a>i, and surface tension y by the Butler equation as [14]... 

The average To of the partial molar area for all components or all possible states at the interface is often used in conjunction with the Lucassen-Reynders dividing surface, which can be equivalently described as... 

The average partial molar area is determined by Eq. 12 as l + niFi/Fcr- ... 

Later, Alexander and Barnes ( ) showed that the constant conditions of equation 7 are not those required for the partial molar area. This is given by ... 

It should be noted that in both of these approaches it is necessary to make an assumption about the partial molar area of monolayer (equation 8 or 11). 

Here Tos(T,P)= Ios are the standard chemical potentials dependent on temperature T and pressure P, x3 = nii / Zm are the molar fraction of the i-th component, m the number of moles, fj the activity coefficients, and L2 the molar area. The superscript s refers to the surface (interface). Assuming that the value is independent of y, and integrating Eq. (1) one obtains the expression ... 

These treatments suppose the surface molar areas of A and B atoms to be equal. However, for alloys with A 0, the low molar volume much greater than that of A (up to 100%). Typical examples are the Cu-Pb, Cu-Bi and Al-Pb systems, for which the experimental decreases in rxLV caused by adding small quantities of B are significantly more than those predicted by the regular solution model. These differences have been attributed to the fact that not all the sites of the quasicrystalline lattice on which A and B atoms are distributed are equivalent (Goumiri et al. 1979). 

An analogous equation may be written for a two-dimensionalphase. The only difference is that pressure and molar volume are not in this case appropriate variables. Pressure is replaced by the spreading pressure FI, and the molar volume by the molar area a ... 

This equation is written on the basis of a unit mass, usually a gram or a kdogram, of solid adsorbent. Thus n is the specific amount adsorbed, i.e., the number of moles of adsorbate per unit mass of adsorbent. Moreover, area A is defined as the specific surface area, i.e., the area per unit mass of adsorbent, a qrrantity characteristic of a particular adsorbent. The molar area, a = A/ , is the surface area per mole of adsorbate. 

Molar area, adsorbed phase Parameter, cubic equations of state Partial parameter, cubic equations of state Second virial coefficient, density expansion... 

In words, Idy/dp] equals the increase in volume if the area is increased at fixed p,T and composition. This increase obviously stems from the fact that the molar volume in the interfacial layer is larger than that in the bulk phase(s). So, the r.h.s, of [2.9.17) can be interpreted as a molar volume per molar area. 

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