Adsorption isosteric heat (Qiso) can be determined both by differential calorimetry or by two isotherms (Clausius-Clapeyron). From Qiso the differential molar entropy of the adsorbed phase could be calculated by Sa= Sg -Qiso/T where Sg is the integral molar entropy of the gas. Finally, the specific heat could be obtained by Cp= T(dSa/dT), but the question is: the specific heat so calculated represents only the internal energy change due to adsorption, or also comprises the energy of thermal excitations of the atoms and molecules of the adsorbent?
The isosteric heat of adsorption is the difference between the enthalpy of the adsorbed state and the enthalpy of the fluid phase. By measuring the isosteric heat of adsorption at different temperatures you could determine experimentally the change in the specifc heat upon adsorption (cp = (dH/dT) at constant pressure).
You can then determine the specific heat of the adsorbed phase knowing (independently) the specific heat of the fluid phase (if you can assume that the specific heat of the adsorbent does not change due to presence of adsorbate - frozen phonon assumption). This specific heat of the adsorbed phase comprises all contributions (i.e. translational (if any), rotational and vibrational).
Thanks Eric. This is quite clear for Qiso determined by the two isotherms method because it seems that the adsorbent contribution to the heat effects are excluded; but it is not the same for the Qiso determined by differential scaning calorimetry; in such a case it is not too evident that the changes of the internal energy of the adsorbent are registered together with the adsorption heat. This question is very important for the energy applications of the zeolites, because it is necessary to know whether the heat capacity of the adsorbent is also to be considered in the heat balance, or only the heat capacity from Qiso.
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