Composite adsorption isotherms corrected for solution-adsorbate molar volume differences

Abstract

The components of a binary solution do not necessarily “see” the same volume of the pores of an adsorbent. If this difference in behavior is not taken into account, the calculated composite adsorption isotherms can be in error by several percent, even in normal cases. Three reasons pure liquid or solution species can have a molar volume in the bulk phase different from that in the adsorbate phase are discussed. The pore volume of silica gel, measured assuming that the gel does not swell, depends upon the liquid used to measure it; for one batch of gel, values are reported using water and 19 organic liquids. Equations are derived that show: (1) how composite isotherms can be calculated, taking into account this volume effect and using the pore volume data; and (2) the extent of the error if the pore volume difference is not noted. The method is applied to the composite isotherms of three representative pairs of liquids, and the effect of various assumptions on the calculation of these isotherms is shown. For spherical solute species, such as solvated ions, size comparisons can be made using the volume effect even if the solvent species is not spherical, providing ion reaction with the surface is prevented. The method used in earlier work to obtain the relative sizes of hydrated ions is shown to be in fair agreement with a thermodynamic analysis of the volume effect developed by Giddings et al. for use in other solution-gel systems.