Langmuir Isosteric heat

Inserted in Eq. (3), this gives the Langmuir isotherm P = Zi ,exp( u ABr)= - exp(-KoABr,, from which we get the isosteric heat of adsorption... 

At A <5C 2RT the two terms become the same. In intermediate ranges, although invariably smaller than the Langmuir term, the second term may be important enough not be to neglected. In that case, even if divided by T, it remains dependent on the temperature. This means that the distribution of the adsorbed gas over the various subsurfaces at a certain over-all 6 depends on the temperature. This makes the procedure for obtaining isosteric heats virtually meaningless. 

Pan, H., Ritter, J.A., andBalbuena, P.B. (1999). Binary isosteric heats of adsorption predicted from density functional theory. Langmuir, 15, 4570-78. 

Abstract Infrared spectroscopic methodsfor the measurement of adsorption and adsorption kinetics of some aromatics (benzene, ethylbenzene, p-xylene), pyridine, and paraffins in solid microporous materials such as zeolites (MOR, ZSM-5, silicalite-1) are described as well as the evaluation of the spectroscopically obtained data. The adsorption isotherms are of the Langmuir-Freundlich type. Isosteric heats of adsorption, transport diffusivities, and activation energies of diffusion as deduced from the spectroscopic measurements are compared with literature data as far as available, and they are found to be in reasonable agreement with results provided by independent techniques. Special attention is paid to sorption and sorption kinetics of binary mixtures, especially the problems of co- and counter-diffusion. ... 

ABSTRACT. An isosteric sorption system has been used to study the sorption of methane, ethane, ethene, propane, N2 and CO2 and some of their binary mixtures in silicalite-1. Isotherms of some of these sorbates have been determined at equilibrium pressures up to 20 atmospheres. Isosteric heats of sorption have been obtained from the slopes of the isosteres. Separation factors calculated from the Henry s Law constants determined from the initial slopes of the single conq>onent isotherms are found to be in good agreement with experim tal separation factors. The Langmuir-Freundlich equation has be used to lit the single component data and the Ideal Adsorbed Solution theory has be used to predict a binary sorption isotherm from the respective single component data. Comparison of the sorption behaviour of the hydrocarbons in silicalite-1 and NaY zeolites has been made. 

Thus, the isosteric heat is a constant, the same conclusion we obtained earlier for the Langmuir isotherm. This means that the mobility of the adsorbed molecules does not affect the way solid atoms and adsorbate molecule interact vertically with each other. 

Here b is the adsorption affinity constant at infinite temperature, bo is that at some reference temperature Tq, Uq is the parameter n at the same reference temperature and a is a constant parameter. The temperature dependence of the affinity constant b is taken from the that of the Langmuir equation. Unlike Q in the Langmuir equation, where it is the isosteric heat, invariant with the surface loading, the parameter Q in the Sips equation is only the measure of the adsorption heat. We shall discuss its physical meaning in Section 3.2.2.2.I. The temperature-dependent form of the exponent n is empirical and such form in eq. (3.2-18c) is chosen because of its simplicity. The saturation capacity can be either taken as constant or it can take the following temperature dependence ... 

The isosteric heat for the Langmuir isotherm equation (6.2-la) can be calculated from the van t Hoff equation ... 

The above equation shows the variation of the isosteric heat with loading as the pressure P is related to loading via the Langmuir equation (6.2-1). 

Bxample 8.4 >l Isosteric heat of local Langmuir and uniform energy distribution... 

We will illustrate in this example the evaluation of the isosteric heat when the local adsorption isotherm takes the form of the Langmuir equation and the energy distribution is uniform. The local Langmuir equation and the distribution are ... 

Substituting the local Langmuir adsorption equation and the above distribution into isosteric heat equation (6.4-2), we obtain the following isosteric heat equation ... 

We have seen the example of isosteric heat (eq. 6.4-2) for the case of local Langmuir equation and an uniform distribution. For other choices of local adsorption isotherm and energy distribution, eq. (6.4-2) must be done numerically. 

The experimental permeation results could be consistently described using Eqs. (9.43b) and (9.47) for Langmuir and Henry sorption respectively as shown by de Lange in a full analysis of sorption, permeation and separation results of five different gases [63]. This description requires knowledge of adsorption isotherms which could be measured only on unsupported membranes. To use these data for calculation of the permeation of supported membranes requires the assumption of equal pore characteristics in both cases. As discussed by de Lange et al. this is probably not correct in the case of silica layers. Based on sorption data a microporosity of about 30% and a pore size distribution with a peak at 0.5 nm is found. Analysis of permeation data point to a pore diameter of = 0.4 nm and a considerably smaller porosity. Table 9.7 summarises the sorption data. H2 and CH4 have relatively low (isosteric) adsorption heats (cf ) while CO2 and isobutane strongly adsorb. 

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