Adsorption and Chromatography Equilibria

For gases, most adsorption isotherms follow an almost linear behavior at low partial pressures of the solute and the following form of Henry s law is obeyed  

At higher partial pressures, the behavior becones nonlinear, and more complex models are required to describe the observed equilibrium data. A frequently used model for monomolecular layer adsorption is the Langmuir isotherm equation. This equation is derived from simple mass-action kinetics. It assumes that the surface of the pores of the adsorbent is homogeneous and that the forces of interaction between the adsorbed molecules are negligible. Let/be the fraction of the surface covered by adsorbed molecules. Therefore, 1 -/ is the fraction of the bare surface. Then, the net rate of adsorption is the difference between the rate of adsorption on the bare surface and desorption from the covered surface  

Equation (9-34) is the Langmuir isotherm equation. At low partial pressures, if Kp 1, it reduces to the linear Henry s law form of equation (9-31), while at high partial pressures, if Kp 1, q = qm. 

The parameters K and qm are treated as empirical constants, obtained by fitting the nonlinear equation directly to experimental adsorption data or by first linearizing the Langmuir equation to the form 

Equation (9-35) represents a straight line when p/q is plotted against p the slope of the straight line is lqm and the intercept is MqJK. 

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