36.2.1 |
Gibb’s Adsorption Isotherm
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This isotherm normally considers the case when adsorbents are liquids and adsorbates are soluble or partially soluble in it e.g., surfactants / water or organic liquid / water system.
Considering a system having a plane interface between them, the Gibb’s free energy of a system containing two components could be written as follows: |
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Where  and  are the number of moles and  and  are the chemical potentials of the two components respectively. While dealing with the adsorption of one of the components on the surface of another, an additional term of surface energy has to be introduced, and hence, equation (36.2.1) modifies to |
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where  is the surface energy per unit area and  is the surface area. It is now clear that equation (36.2.1) is for bulk while equation (36.2.2) will be applicable for the surface of the absorbent liquid. The complete differential of (36.2.2) may be written as |
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We find that the total free energy G of the whole system depends on independent variables , namely , T,P,n1,n2 and , thus, |
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and complete differential of G will be, |
