A statistical study of seven curves for describing the sorption of phosphate by soil

summary Seven mathematical models, which have been advanced for describing phosphate sorption by soils, are studied here with respect to their statistical behaviour in estimation. These seven non‐linear regression models include the Langmuir equation and two extensions of it, the Freundlich equation and two extensions of it, and Gunary's equation. Measures of non‐linear behaviour, such as the Bates & Watts (1980) curvature measure of intrinsic non‐linearity and the Lowry & Morton (1983) asymmetry measure of non‐linearity, were calculated for each model in combination with each of six data sets. It was found that the Freundlich equation and the extension of it proposed by Sibbesen behaved best, with Gunary's equation also having acceptable statistical properties, whereas the Langmuir equation and its extensions behaved worse, exhibiting properties which indicate that the estimators of their parameters would be severely biased and non‐normal in distribution. It is believed that similar conclusions may apply to other processes involving surface adsorption.