A Method of Correlation of High-Temperature, High-Pressure Gas-Solid Adsorption Data
Authors: McCain William D. 
Published: December 2007

The literature does not give an adequate method of correlation of gas-solid adsorption data obtained at high temperatures and high pressures. The two most commonly used correlation methods, proposed by Freundlich and Langmuir, have been shown to be unsatisfactory at high temperatures and high pressures. The correlation method proposed by pressures. The correlation method proposed by Lewis et al. is satisfactory; however, it cannot be used at pressures above the critical pressure of the adsorbate. In order to correlate gas-solid adsorption data previously reported by the authors, a correlation procedure based on the potential theory of Polanyi was developed. potential theory of Polanyi was developed. The development of this method and an example of its application will be given.

THE POTENTIAL THEORY OF ADSORPTION
Brunauer pointed out that the equation most suitable for describing adsorption above the critical temperature is the potential theory of Polanyi. Polanyi developed the following equation Polanyi. Polanyi developed the following equation which gives the energy change involved in transferring molecules from the gas phase to the adsorbed phase.
(1)
where Delta is a free energy change, eta is the amount adsorbed, R the gas constant, T the absolute temperature, p' the vapor pressure of the adsorbed phase, and p the adsorption pressure. Polanyi phase, and p the adsorption pressure. Polanyi further concluded that p' could be replaced with Ps, the vapor pressure of the adsorbate at adsorption temperature. He successfully tested the theory over a wide range.
Dubinin and Radushkevich suggested that the free energy change for an adsorbent would be a constant, independent of the adsorbate gas, when the volume of gas adsorbed is constant. Thus, for two different gases, 1 and 2,
(2)
for equal quantities of gas adsorbed
(3)
where V M is the molal volume of the adsorbed phase at adsorption temperature. Dubinin divided Eqs. 2 and 3 to obtain:
(4)
Lewis et al. found that Dubinin's equation was not satisfactory at higher pressures. They therefore modified the equation by replacing pressure with fugacity f, and by assuming that V M could be replaced with V M, the molal volume of the saturated liquid at adsorption pressure. Thus,
(5)
This correlation method worked quite well at pressures below the critical pressure of the pressures below the critical pressure of the adsorbent.
Since Relationship 5 is valid only for equal values of eta V Ms, it follows that graph of (eta V Ms) plotted against (T/V Ms, 1n s/f) should give a single plotted against (T/V Ms, 1n s/f) should give a single line independent of the temperature. Lewis et at also showed that this line is independent of the particular gas as long as the gases selected are particular gas as long as the gases selected are reasonably similar in properties.
The problem in application of this correlation is in the determination of the molal volume of the adsorbed phase. Lewis et al. applied the correlation by assuming that the molal volume of the adsorbed phase could be represented by the molal volume of phase could be represented by the molal volume of the saturated liquid at adsorption pressure. This correlation worked quite well over the pressure range they investigated. However, this assumption is only useful at pressures below the critical pressure of the gas. pressure of the gas. SPEJ
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