  The Freundlich isotherm has been used widely to describe sorption of solutes
to soils for many decades. The Freundlich parameters are often estimated using
unweighted least squares (ULS) analysis after log-log transformation.
Estimating the accuracy of these parameters (characterized by their coefficient
of variation, CV) is an essential element of the use of these parameters.
Accurate CVs can be derived with weighted least squares (WLS), but only if
proper weights are assigned to the residuals in the fitting procedure. This
work presents the derivation of an analytical approximation of these weights
which were found to decrease with increasing concentration, increasing
Freundlich exponent, and increasing CVs of the initial and equilibrium
concentrations. Monte-Carlo simulations for a wide range of Freundlich systems
based on known values of the CVs of the initial and equilibrium concentrations
confirmed the accuracy of this analytical approximation. Unfortunately, in
practice, the CVs of the initial and equilibrium concentrations are unknown a
priori. Simulations showed that the accuracy of the estimated CVs of the
Freundlich parameters was distinctly lower if the CVs of the initial and
equilibrium concentrations were estimated from the isotherm data. However, this
accuracy was still considerably better than when using ULS. It is recommended
to use this analytical approximation whenever these CVs are relevant for the
further use and interpretation of the estimated Freundlich parameters.
