By J. J. Kipling
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Additional info for Adsorption from Solutions of Non-Electrolytes
02 0-4 0-6 0-8 Mole fraction of benzene in liquid phase FIG. 4. 6). ) 0-2 0-4 0-6 08 Mole fraction of benzene in liquid phase 10 FIG. 5. Individual isotherms for adsorption by charcoal from mixtures of benzene and ethyl alcohol, calculated on the basis of the Freundlich equation (dotted lines) and the "Langmuir" equation (full lines): A, ethyl alcohol; B, benzene. 7). The constants in each case were evaluated by successive approximations. The corresponding pairs of individual isotherms, however, are quite different from each other (Fig.
The Langmuir equation at least has a more satisfactory theoretical basis in describing adsorption of gases. The equation for the composite isotherm would then be : n0Ax _ kiK^ix(V-x) _ k2X2*(1 -_*) ,* 7) m l + klx l + k2(l — x)' 4. ADSORPTION FROM COMPLETELY MISCIBLE LIQUIDS S^ 37 ^^\. 20 X χ s X Ν X \ χ ΝX \ χ \ χ ^. 0·4 0 -0-4 1 1 ! -χ—>*Δ 02 0-4 0-6 0-8 Mole fraction of benzene in liquid phase FIG. 4. 6). ) 0-2 0-4 0-6 08 Mole fraction of benzene in liquid phase 10 FIG. 5. Individual isotherms for adsorption by charcoal from mixtures of benzene and ethyl alcohol, calculated on the basis of the Freundlich equation (dotted lines) and the "Langmuir" equation (full lines): A, ethyl alcohol; B, benzene.
At that time it had no theoretical foundation, the lack of which hampered the development of a theory for either kind of adsorption. A justification for its application to adsorption from solution was subsequently given by Henry (see Chapter 11), but it has generally been overlooked that this is based on an approximation which is valid only for dilute solutions. The Freundlich equation proved to be applicable to the adsorption of gases over only limited ranges of pressure. It was replaced by the Langmuir equation and others which had a theoretical basis in the kinetic theory of gases.