Entropy Langmuir equation

The recent investigation by Damkohler and Edse (5) virtually consists of the calculation of the entropy of CO adsorbed on copper oxide. They calculated the theoretical value of the constant bo in the Langmuir equation... 

Vj, is the specific pore volume of the material typical values are 200-400 cm /kg for zeolites and up to 1000 cm /kg for activated carbon, n is the actual number of molecules contained in the micropores the excess adsorption subtracts from n the number of molecules which would have been present in the micropores at the bulk density in the absence of adsorption. The (oversimplified) case when absolute adsorption is described by the Langmuir equation and the gas obeys the perfect gas law p - PjRT) has been worked out in detail for the isotherms and thermodynmnic functions (enthalpy, entropy, etc.) [2j. 

The Szyszkowski equation has proved useful for describing the relatively simple adsorptions under consideration. However, its foundation is at issue because the Langmuir equation was not derived for mobile but for localized adsorbates the translational entropy is not properly accounted for. We return to this issue below, in the mean time accepting [4.3.13] as a useful empirical expression. 

As stated earlier, the retardation term owing to the product adsorption or the constant K in the Langmuir-type equation, v = k/(l + /<[P]) (Equation 13.4), where P is the condensable product), is related to its adsorption equilibrium driven by the concentration term in solutions. Under boiling conditions, the reaction products are desorbed not only to the solution bulk but also into the bubble formed at the catalyst surface. Because the molecular translational entropy is far larger in the gas phase than in the liquid phase, the... 

If much less than 10% of the surface is covered, then the conventional Langmuir-Hinshelwood TST equation, given by Eq. (10) and the C expression for Step 7 of Table I, applies for both one- and two-reactant cases. Step 7 is second order in the intermediate coverage range, where Eq. (34) can best be used, the reaction is first order and at high coverage the reaction is zero order even when bimolecular. For a zero-order reaction. Step 5 of Table I applies. (The assumption that the entropy of activation is zero for Step 5 is not necessarily correct when the surface reaction is bimolecular.)... 

The next set of examples show an entropy of adsorption roughly equal to the entropy change on losing the degree of translational freedom normal to the surface, i.e., in the adsorbed state the molecules are equivalent to a two-dimensional gas or vapor. The data for a variety of different adsorbates and adsorbents is given in Table V. The isotherms obtained by Armbruster (20) for the adsorption of CO and N2 on silver were not S-shaped, and they could be fitted to equations of the Langmuir type. The amount of adsorbate required to saturate the surface was given for each substance at both temperatures. Armbruster calculated the heats of adsorption by the method of Brunauer, Emmett and Teller (22) and there is some doubt about the validity of such heats. 

This equation has a formal analogy to (17). Instead of the Langmuir configurational entropy —2RT In [(1 — 8)/8], we now find the term... 

These considerations have their consequences regarding the interpretation of experimental data should it be done in terms of isotherms or in equations of state Preferably both should be considered, but when specific features are under study a choice may have to be made. For instance, surface heterogeneity shows up very strongly in the shapes of the Isotherms (sec. 1.7) but very little in the equation of state in the model case of local Langmuir isotherms without lateral interaction heterogeneity is not seen at all in the equation of state (because the energy is not considered and the entropy not affected) whereas the isotherm shape is dramatically Influenced. On the other hand, for homogeneous model surfaces equations of state may be more suited to observe subtle distinctions in lateral mobility or lateral interaction. 

The Langmuir adsorption isotherm is represented hy P — K C/(Cm — U), where K is a function of T only, and Cm represents the maximum concentration of adsorbed species that can be accommodated as a monolayer on the surface. Derive the corresponding two-dimensional equation of state. Determine the molar enthalpy and entropy of the adsorbate, using the perfect gas approximation for the gaseous phase. 

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