Use of equilibrium and initial metal concentrations in determining Freundlich isotherms for soils and sediments

Batch equilibrium test results of Pb and Cd retention by kaolinite, humic acid and mackinawite and mixtures of these soil/sediment materials are modeled using Freundlich isotherms with the retained metal plotted as a function of the equilibrium metal concentration, Ce and as a function of the initial metal concentration, Ci. When Ci rather than Ce is used, smaller values of KF and larger values of 1 / n are obtained and this means the isotherm is more linear. There is no significant difference in goodness of fit for the two types of isotherms based on the coefficient of determination, r2 and a normalized deviation, Δq. Advantages in using Ci are that no data points need to be excluded when metal is completely retained by the adsorbent and it is easier to compare the same range of metal concentrations on one graph. A unified sorption variable Ku is evaluated for each isotherm. Since Ku represents the changing slope of the Freundlich isotherm, the value of Ci or Ce needs to be specified with the value of Ku. A dimensionless form of Ku was developed so as to permit more universal application of this parameter and Ku could potentially be used in transport prediction models. r2 and Δq together were better able to quantify goodness of fit of the data with the Freundlich isotherm than either of the two parameters separately.