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A Unified Sorption Variable for Environmental Applications of the Freundlich Equation

Dep. of Renewable Resources, 4-42 Earth Sciences Bldg., Univ. of Alberta, Edmonton, AB T6G 2E3, Canada;
Dep. of Plant and Soil Sciences, Univ. of Massachusetts, Amherst, MA 01003.

^* Corresponding author (bill.mcgill{at}ualberta.ca).

ABSTRACT

The Freundlich equation (x/m = K_f C^1/n_e) has been used widely in sorption studies in chemistry and environmental research. Two problems arise in comparing sorbate-sorbent systems if C_e 1 or if 1/n values differ. First, it is often not possible to compare K_f values from the literature if they were derived from different units of x/m and C_e. Second, the exponent 1/n, determines the interpretation of K_f. Consequently, comparing values of K_f or K_oc—f is problematic. We propose a way to characterize sorption dynamics in systems that follow the Freundlich isotherm that avoids problems caused by comparing K_f values. We show that: (i) The units of K_f are: mmol^1-1/n kg^–1 L^1/n, or mg^1-1/n kg^–1 L^1/n, etc. depending on the units of x/m and C_c. Therefore, K_f parameters cannot be compared among samples whenever the 1/n parameters are different; (ii) For K_f values that are associated with different units, the units-conversion factor for K_f is also a function of 1/n. It has the form of: A^1-1/n, where A is the units-conversion factor if 1/n = 1; (iii) We propose a new variable, K_u, to unify the units of K_f and to conduct sensitivity analyses of K_f and 1/n. Numerically K_u is the slope, (x/m)/C_e, of the sorption isotherm at any value of C_e or x/m and has units of L kg^–1.

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