On the Determination of the Constant Parameters of the “Two‐surface” Langmuir Equation

The constant parameters k 1 , k 2 (in ml/μg P) and b 1 , b 2 (in μg P/g soil) of the two‐surface Langmuir Equation for phosphate adsorption were determined by three methods for ten high pH montmorillonitic soils. The techniques included a graphical approach in which a curve is resolved into two straight line components (“Hofstee” method) and two methods utilizing the regression characteristics of the experimental adsorption data. The first regression method obtains estimates of k 1 , k 2 , b 1 and b 2 indirectly through various relationships resulting from the mathematical representation of the sorption isotherm as a “Stieltjes” transform (“Sposito” method). The second regression method obtains the parameters directly, assuming that k 1 ≫ k 2 and b 1 ≪ b 2 (“Approximation” method). Statistical analyses showed that each method yielded significantly different k 1 and k 2 constants compared to the other two. With regard to b 1 and b 2 , the “Approximation” method produced significantly higher b 1 and lower b 2 values in all samples, though no difference was found among the three methods for the theoretical adsorption maximum (b T =b 1 +b 2 ). The relationship between k 1 and k 2 as well as b 1 and b 2 , as expressed by their ratios, changed significantly from one method to another. This indicates the need for a more precise arithmetic definition of the condition k 1 ≫ k 2 and b 1 ≪ b 2 which is necessary for the “Approximation” method, accepted so far to be valid for k 1 ∼ 100 k 2 and b 1 ∼ 0,3 b 2 respectively.