A unified sorption variable for environmental applications of the Freundlich equation

The Freundlich equation (x/m = K-f C-e(1/n)) has been used widely in sorpti on studies in chemistry and environmental research. Two problems arise in c omparing sorbate-sorbent systems if C-e not equal 1 or if 1/n values differ . First, it is often not possible to compare k(f) values from the literatur e if they w ere derived from different units of x/m and C-c. Second, the ex ponent 1/n. determines the interpretation of K-f. Consequently, comparing v alues of K-f or Koe-f is problematic. We propose a way to characterize sorp tion dynamics in systems that follow the Freundlich isotherm that avoids pr oblems caused by comparing K-f values. We show that: (i) The units of K-f a re: 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 amon g samples whenever the Un parameters are different; (ii) For K-f values tha t are associated with different units, the units-conversion factor for K-f; is also a function of Un. It has the form of: A(1-1/n), where A is the unit s-conversion factor if 1/n = 1; (iii) We propose a new variable, K-u, to un ify the units of K-f and to conduct sensitivity analyses of K-f and 1/n. Nu merically K-u is the slope, (x/m)/C-e, of the sorption isotherm at any valu e of C-e or x/m and has units of L kg(-1).