“…The amounts of CIP and AMP adsorbed in mg per g of MNCS-450, MNCS-650 and MNCS-850, ( q e ), were obtained via the mass balance equation:
where C i , C e , V and M are the initial concentration of solute ions (mg L −1 ), the equilibrium concentration of solute ions (mg L −1 ), the volume of aqueous solutions (L) and the mass of adsorbent (g), respectively. Also, the experimental data obtained from equilibrium, kinetic and thermodynamic studies were fit to two-parameter and three-parameter nonlinear equations by the Quasi-Newton least squares algorithm in the KyPlot software 2.0 model (KyensLab Inc., Tokyo, Japan) and Data Analysis and Graphing Software, OriginPro 9.1, Origin Lab Corporation, Northampton, Massachusetts, USA, as follows: q e = K F C 1/ n e Freundlich model (FM) 43
Langmuir model (LM) 44
Langmuir–Freundlich model (LFM) 45 q t = q e (1 − e − k 1 t )PFOM 46
PSOM 47
Mixed-1,2-order model (MOM) 48
Van’t Hoff model 49–51 K C = M w × 55.5 × 1000 × K L Δ G ° = Δ H ° − T Δ S °where K F = Freundlich constant (mg g −1 ) (L mg −1 ) 1/ n , n = an empirical constant that represents the adsorption affinity, K L = Langmuir adsorption constant (L mg −1 ), q max L = adsorption capacity for the complete monolayer adsorption of contaminants (mg g −1 ), q t = amounts of solute ions adsorbed at a time t (min) by MNCS-450, MNCS-650 and MNCS-850 (mg g −1 ), k 1 = pseudo-first-order rate constant (min −1 ), k 2 = pseudo-second-order rate constant (g mg −1 min −1 ), K C = the dimensionless thermodynamic equilibrium constant calculated using eqn (9), Δ S ° = entropy change (J mol −1 K −1 ), Δ H ° = enthalpy change (J mol −1 ), R = universal gas constant (8.314 J mol −1 K −1 ), T = absolute temperature (K), q max LF = Langmuir–Freundlich equilibrium adsorption capacity (mg g −1 ), n LF = Langmuir–Freundlich constant for adsorption affinity, K LF = Langmuir–Freundlich constant (mg g −1 ) (L mg −1 ) 1/ n , k 1,2 = mixed-1,2-order rate constant (min −1 ), η = mixed-1,2-order exponent (min −1 ), M w = the molecular weight of the adsorbate (349.406 and 331.346 for AMP and CIP, respectively) (g mol −1 ), and K C = dimensionless thermodynamic equilibrium constant, Δ G ° = Gibbs free energy (J mol −1 ).…”