Heat of Adsorption at Low Coverage

At low coverage any effects of interaction between neighboring adsorbed molecules can be neglected. Under these conditions there is a simple relationship between the average potential energy ( ) and the heat of sorption which may be derived as follows  

Internal energy for 1 mole of sorbate in the vapor phase = 

Ug - Uj is the difference in kinetic energy between a sorbate molecule in the gaseous and adsorbed states and as such depends on the nature of the adsorbed phase. Using the principle of equipartition of energy 

The value of in these equations should really be the average value of (f , calculated by integration over all possible positions of the sorbate molecule, weighted according to a Boltzmann factor. In practice, except at very high temperatures the molecules are for the most part located close to the potential minima so it is a good approximation to take  

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For decationated mordenites, an increase in the ammonia adsorption temperature caused a significant increase in the differential heat of adsorption at low coverages, the largest increase of the initial heat being from 130 to 170 kJ mol" , corresponding to Lewis acid sites on a 90% decationated mordenite that was dehydroxylated at 923 K (88-90). The effect of increasing the... 

Bhatia [39] studied the transport of adsorbates in microporous random networks in the presence of an arbitrary nonlinear local isotherm. The transport model was developed by means of a correlated random walk theory, assuming pore mouth equilibrium at an intersection in the network and a local chemical potential gradient driving force. The author tested this model with experimental data of CO2 adsorption on Carbolac measured by Carman and Raal [40]. He concluded that the experimental data are best predicted when adsorbate mobility, based on the chemical potential gradient, is taken to have an activation energy equal to the isosteric heat of adsorption at low coverage, obtained from the Henry s law region. He also concluded that the choice of the local isotherm... 

There is a recent report, also from Vilches group [60], of specific heat and adsorption isotherm data for He on HiPco SWNTs. The general features of the isotherms measured on the HiPco samples were similar to those on the arc-discharge nanotubes. However, the values of the isosteric heat of adsorption at low coverages were considerably higher on the HiPco tubes. 

The isosteric heat of adsorption at low coverage on porous glass is definitely higher (17 kcal-mole- ) for the untreated surface in comparison to the methylated or sintered one (10-12 kcal mole- ) (3S). These values are approximately the same as found for CgHg on silica gel (39). 

Aranovich (1989) used a lattice model to provide a thermodynamics foundation for his model. The differential heat of adsorption at low coverage for his multimolecular isotherm equation as well as other properties are considered in Aranovich (1990, 1992). 

The differential heat profiles are characterised by a plateau of nearly constant heat of adsorption at low coverage (15-20 /xmol g m ) followed by an abrupt decrease as the surface saturation limit is reached. In the low coverage plateau region the... 

Another important property of the basal planes is their affinity for polycyclic aromatics. This was found by pulse adsorption of dilute solutions of anthracene and pyrene in cyclohexane which produced very high molar heats of adsorption at low surface coverages. Later work by the author indicated that in spite of the strong initial adsorption, the polycyclic compounds do not form closely packed layers on the basal planes but are localised on certain more active parts of the graphene surface without the formation of plateaux in their adsorption isotherms [40]. 

In Faujasites. Bezus et al. (49) reported in 1978 statistical calculations on the low-coverage adsorption thermodynamics of methane in NaX zeolite (Si/Al = 1.48). As for single-atom adsorbates described earlier, the agreement between their calculated values and a range of experimental values was excellent. Allowing for different orientations of the molecule, they calculated a value of 17.9 kJ/mol for the isosteric heat of adsorption at 323 K. Experimental values available for comparison at that time (134-136) ranged from 17.6 to 18.8 kJ/mol. Treating the methane molecule as a hard-sphere particle, with a radius of 2 A, resulted in a far lower heat of adsorption (12.6 kJ/mol). Further calculations (99) yielded heats of adsorption of 19.8 and 18.1 kJ/mol for methane in NaX and NaY zeolites, respectively. 

At very low pressures (P/Po < 0.1) the adsorption isotherm rises steeply. Adsorbing molecules find many free binding sites. These very few molecules on the surface have a chance to bind to strong binding sites at grain boundaries. This can also be seen from the differential heats of adsorption at coverages below 0.3 //, mol/m2 the heat of adsorption is maximal. 

The values are presented in figure 3 (left part) as a function of the amount adsorbed. The heat of adsorption at very low coverage (75 kJ/mol) is well above the heat of liquefaction of bulk water (44 kJ/mol) which means that the surface is hydrophilic, as previously deduced from the shape of adsorption isotherm at low pressure. We also report the result obtained by Markova, et. al. [27] on vycor. The agreement is quite good, taking into account the fact that our sample has pores slightly smaller than real vycor which errhances the strength of the interaction. 

The adsorption isotherm calculated is of type IV in lUPAC classification, showing a rapid increase at low pressure as expected for hydrophilic surfaces. The steep rise in adsorption arround P/P°=0.7 is due to capillary condensation in the mesoporous solid. The result is comparable to two available experimental adsorption isotherm of water measured by very different techniques (gravimetry and calorimetry). This result, and the good agreement of the simulated isosteric heat of adsorption at very low coverage (75 kJ/mol) with experimental data, show that the model presented is able to describe quantitatively the hydrophilicity of the vycor surface with no adjustable parameters. 

The initial entropy of cumene adsorption on a commercial aluminosilicate was measured to be about —750JmoP K , whereas the gas-phase entropy of cumene at 298 K is 389 J moP K (709). This seemingly inconsistent result appears to be caused by the dissociative adsorption of cumene at low coverages on this catalyst. In this case, the measured heat corresponds to a combination of heats of adsorption and reaction. Higher coverages produced lower, nearly constant heats and entropies of adsorption. These entropies correspond to the loss of between two and three degrees of translational freedom. The adsorption of benzene on these samples did not show abnormally... 

Direct calorimetric measurements have confirmed that the heat of adsorption of oxygen (po, = 2 torr) on NiO(200°) increases when the temperature is increased from 30 to 200° (initial heat for a low coverage at 30°, 60 kcal/mole at 70°, 74 kcal/mole at 115°, 85 kcal/mole at 160°, 99 kcal/mole at 200°, 116 kcal/mole). The differential heats of adsorption at 200° for an increasing coverage are reported in Fig. 5. 

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