A Freundlich‐type multi‐component approach for modeling the sorption of nickel and phosphate in soil

Abstract

In this study, the effect of phosphate on Ni sorption by Mahan soil was investigated. In batch experiments, an initial solution concentration of 1 mM phosphate increased Ni sorption by 15.1%, and initial concentrations of 1 mM Ni increased phosphate sorption by 12.8%. The effect of phosphate on Ni sorption, and vice versa, was dependent on initial concentrations of either solute, with greater effects being observed with greater initial concentrations. Sequential extractions suggest that the increased sorption of either species in the presence of the other is due to a combination of electrostatic interactions and the formation of ternary complexes. A novel Freundlich-type multi-component isotherm (FMC) was developed and described the sorption of Ni both in the absence and presence of phosphate with a single set of parameters. The effect of phosphate on the sorption kinetics of Ni was evaluated using the stirred-flow approach. The presence of phosphate increased the maximum sorbed concentration of Ni by 7.3% and increased the rate of Ni sorption. A novel Freundlich-type multicomponent kinetic model (FKM) was developed and described the stirred-flow data well. The FKM was able to describe the sorption-desorption of both Ni and phosphate applied individually as well as simultaneously. The FMC and FKM offer advantages over previous modeling approaches in that they require far fewer parameters than surface complexation models and have greater descriptive capabilities than traditional empirical models. However, both models are empirical, and their ability to describe the observed data should not be taken to imply specific molecular-level mechanisms.

Yesterday, Today, and Tomorrow. Evolution of a Sleeping Beauty: The Freundlich Isotherm

“…• 2015: Hamidouche et al 35 proved Brouers' result and have shown how the Freundlich formula can be derived from the hypergeometric function by approximation. • 2022: Padilla et al 36…”

“…An important specific type of multicomponent competitive system arises when a (divalent) metal cation Me and an (in)organic ligand L can be simultaneously fixed at the surface S of a soil sample (note that the ionic charges were omitted for the sake of simplicity). For such a case, commonly encountered at metalcontaminated sites, Padilla et al 36 developed a phenomenological Freundlich-type isotherm model based on the surfacecomplexation model (SCM). 41 Several surface interactions can thus be described as binary (S−Me and S−L) and ternary (S− Me−L (type-A complex) and S−L−Me (type-B Each binary complex can be described on the basis of a Freundlich-type relationship, such as, for the binary complexes:…”

“…where S i is the sorbed concentration at the solid surface (mmol/kg) for the species i, C i is the solution concentration (mmol/L), K i is the specific Freundlich-type constant, n and m are the respective Freundlich-type coefficients. 36 Then, the authors obtained the following expressions for the total surfacesorbed concentrations:…”

“…Each binary complex can be described on the basis of a Freundlich-type relationship, such as, for the binary complexes: S Me = K Me C Me n 0.25em 0.25em 0.25em 0.25em 0.25em 0.25em S normalL = K normalL C normalL m where S i is the sorbed concentration at the solid surface (mmol/kg) for the species i , C i is the solution concentration (mmol/L), K i is the specific Freundlich-type constant, n and m are the respective Freundlich-type coefficients . Then, the authors obtained the following expressions for the total surface-sorbed concentrations: S Me,T = ( K Me + K Me,B K L C L m ) C Me n S L,T = ( K L + K L,A K Me C Me n ) C normalL m where the notations K Me,B and K L,A are straightforward.…”

“…Then, the authors obtained the following expressions for the total surface-sorbed concentrations: S Me,T = ( K Me + K Me,B K L C L m ) C Me n S L,T = ( K L + K L,A K Me C Me n ) C normalL m where the notations K Me,B and K L,A are straightforward. These empirical relationships were tested with success in the Ni 2+ /PO 4 3– system and a sandy clay loam soil sample …”