{'fraction_non_alphanumeric': 0.019340159271899887, 'fraction_numerical': 0.005688282138794084, 'mean_word_length': 5.23758865248227, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Langmuir Equation Modifications to Describe Phosphorus Sorption in Soils of Ontario, Canada

Abstract Various Langmuir equation modifications have been developed to describe phosphorus (P) sorption reactions in soils for either agronomic or environmental purposes. Comparisons of estimated sorption parameters or goodness of fit for these different models, however, are rarely reported. This study was conducted to address this limitation. Phosphorus sorption studies were conducted on 60 representative agricultural soils in Ontario, Canada. We used five Langmuir equation modifications based on four different methods of estimating initial sorbed P (Q0) in the soil either by mathematical means or by using Olsen-extractable P (Olsen P) as a direct measure of Q0. Based on the residual root mean square error, the goodness of fit was improved for most soils with equations where Q0 was estimated from the P sorption data compared with the use of Olsen P as a measure of Q0. No significant changes in P sorption maximum (Qmax) were found between the four equation modifications, with Q0 estimated from the sorption data, whereas Qmax values obtained from the equation with Q0 estimated by Olsen P were significantly different for some soils. Significant changes in P sorption strength (k), Q0, and equilibrium P concentration in the solution at zero net sorption (Ce) were observed between the tested equations. For each P sorption parameter, significant linear relationships were found between the five Langmuir equations. If Q0 and Ce values remain to be determined as well as Qmax and k, the modified Langmuir equation that includes the linear estimate of the Ce parameter may be preferred provided that equilibrium P concentrations are sufficiently low.