The Relationship between the Brunauer-Emmett-Teller Adsorption Isotherm and the New Isotherm of Jura and Harkins

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Abstract
Values for the surface pressure and area of molecules adsorbed on solid surfaces can be calculated from the adsorption equation of Brunauer‐Emmett‐Teller. Over a wide pressure range these calculated values are in approximate agreement with the two‐dimensional equation of state for vapor‐condensed films. Since the adsorption equation of Jura and Harkins was derived from this same equation of state, it is concluded that for a great many experimental isotherms, the mathematical agreement between the two adsorption equations is so good that extremely accurate experimental work would be necessary to determine which equation was more nearly correct. The Brunauer‐Emmett‐Teller equation gives calculated curves on Gregg‐type plots that agree qualitatively with those reported by Gregg for multi‐layer adsorptions. Surface‐area values obtained from these curves by Gregg's X‐point method are generally considerably higher than those that would be obtained by the method of Brunauer‐Emmett‐Teller. The limiting area occupied by a molecule (i.e., in a mono‐molecular layer) as calculated by the method of Harkins and Jura appears to decrease with decreasing energies of adsorption (i.e., decreasing values of c in the Brunauer‐Emmett‐Teller isotherm). It is suggested that this decrease is artificial, rather than real, and results from the assumption that the constant a in the two‐dimensional equation of state does not vary with changes in the nature of the solid adsorbent. It is not possible at the present time to suggest that one of the isotherms is to be preferred to the other on theoretical grounds. In general, preference should be given to the one which fits experimental data over the broader pressure range.