Prediction Of Henry’s Law Constants
PREDICTION OF HENRY’S LAW CONSTANTS
BAISING ON THE CORRESPONDING STATES THEOREM
V.V. Kutarov, B.M. Kats
Physical Research Institute, I.I. Mechnikov National University of Odessa,
Pastera st. 27, 65026 Odessa, Ukraine; e-mail kats@tm.Odessa.ua
In the classical approximation the obvious statistic expressions for calculation and prediction of the Henry coefficient depend on the adsorbate molecule structure. Such expressions were obtained under investigation of adsorption of monoatomic, diatomic and some simplest polyatomic molecules, as well as for molecules possessing different levels of inner rotation freedom.
It is known in many cases the molecules properties in the adsorption layer can be described by the Lennard – Johnes potential
, (1)
where (r) is the potential energy of two molecule interaction on the distance r between their centers, and is the minimum value of this energy on the distance r between the centers of two molecules. In this case the two-parameter corresponding states theorem can be used
, (2)
where is the reserved value of the Henry coefficient , is the adsorbent surface, is the equilibrium distance, corresponding to the minimum value of the interaction potential, and . It is assumed that the exiting adsorbent action changes the form of the potential curve similarly to all molecules.
The functional dependence (2) perfectly describes the molecule behavior of inert gases, hydrogen, methane and a number of other simple substances in the adsorption layer. Alongside it was shown that the functional dependence of the reversed Henry coefficient doesn\’t depend on the form of the chosen potential i.e. here we may use potentials of (6,exp), (6,8 exp) types and a number of others. However it is known that the two parameter theorem is not
held for the arbitrary configuration molecules as the molecule symmetry type is the dominating factor influencing the interaction potential curve form.
The aim of the given work is the application of the corresponding states theorem for Henry coefficient prediction under the adsorption of the arbitrary configuration molecules. This application is based on the known statements of the thermodynamic theory of excitements.
Thus in analogy with the Trappeniers and Prigogine theorems, the two-parameter corresponding states theorem for the Henry coefficient in general can be written as follows
, (3)
where the values "0" are referred to the comparison substance. The structural parameter definition based on the molecular-statistic calculations is difficult enough and can be done separately for molecules of different configurations (Trappeniers; Prigogine).
It was suggested that the two-parameter theorem (3) of the corresponding states for the Henry coefficient prediction should be broadened to the four-parameter theorem. In general case the corresponding states theorem for the arbitrary configuration molecules with quantum amendments should be represented in the following way:
(4)
where ω is the Pitzer acentricity factor and
, (5)
where h is the Plank constant and m is the molecular mass. The index "0" as the formula relates to the comparison substance.
The obtained four-parameter theorem was used for the analyzing of the experimental data of 16 organic and non-organic substance adsorption on the active carbons of different types. It was shown that under the chosen method of accounting the form and position change of the potential curve minimum, the corresponding state theorem in application to the Henry coefficient is true for the molecules of arbitrary configuration and conditions requiring introduction of quantum amendments. All the suggested amendments to the known two-parameter theorem of the corresponding states are strictly based and can be easily defined a priori.
The authors are grateful to A. Mersmann and S. Maurer (Technische Universitaet Muenchen, Germany) for fruitful discussion of this article.
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