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Table 1

Mathematical linear models used for kinetic, equilibrium and thermodynamic studies

Kinetic linear models 
 Pseudo-first order model (Ho & McKay 2004)  Qeq and Qt (mg g−1): quantities of adsorbate retained per gram of adsorbent in equilibrium and in time (t); K1 (min−1): the rate constant of pseudo-first order. 
 Pseudo-second order model (Ho & McKay 1999)  K2 (g mg−1 min−1): the rate constant of pseudo-second order. 
 Elovich model (Ho & McKay 2004)  A: the speed of initial chemisorption (mg g−1 h−1); B: number of suitable sites for adsorption, which is related to the extent of surface coverage and the activation energy of chemisorption (g mg−1). 
 Intraparticle diffusion model (Yang & Al-Duri 2005)  Kid: intraparticle diffusion constant (g mg−1 min−1/2); Ci: suggests the thickness of the boundary layer effect (mg g−1); t: time. 
Equilibrium linear models 
 Langmuir model (Langmuir 1916)  Ce or Ceq: concentration at equilibrium; Qe or qeq: amount adsorbed at equilibrium per unit of mass of the adsorbent; KL or qmb and Cm: reflect properly the nature of the adsorbent material and can be used to compare the performance of adsorption; Cm or qm: maximum capacity of adsorption; KL or qmb: adsorbent–adsorbate interaction forces. 
 
 Freundlich model (Freundlich 1906)  Ceq: concentration on balance; qeq: amount adsorbed at equilibrium per unit of mass of adsorbent; Kf and n: the two parameters of Freundlich. 
 Dubinin–Radushkevich model (Dubinin & Radushkevich 1947)  Qeq: amount of adsorbed ion per unit mass of the adsorbent (mol g−1); Qd: adsorption capacity (mol L−1); Bd: coefficient related to the energy of sorption (mol2 J−2); ɛ: potential of Polanyi. 
 R: universal gas constant (kJ mol−1 K−1); T: temperature (K); Ceq: liquid phase equilibrium concentration (mol L−1). 
Thermodynamic lineal models 
 Gibbs free energy parameter (Sari et al. 2007)  Kd: ratio of the quantity adsorbed per unit of adsorbent (Qeq) and solution concentration in equilibrium (Ceq); R: universal gas constant (8.314 J mol−1 K−1); T: temperature used in the experiment (K). The values of ΔH and ΔS were obtained from the graph of ln Kd as a function of 1/T. 
 Enthalpy and entropy parameters (Sari et al. 2007)  
Kinetic linear models 
 Pseudo-first order model (Ho & McKay 2004)  Qeq and Qt (mg g−1): quantities of adsorbate retained per gram of adsorbent in equilibrium and in time (t); K1 (min−1): the rate constant of pseudo-first order. 
 Pseudo-second order model (Ho & McKay 1999)  K2 (g mg−1 min−1): the rate constant of pseudo-second order. 
 Elovich model (Ho & McKay 2004)  A: the speed of initial chemisorption (mg g−1 h−1); B: number of suitable sites for adsorption, which is related to the extent of surface coverage and the activation energy of chemisorption (g mg−1). 
 Intraparticle diffusion model (Yang & Al-Duri 2005)  Kid: intraparticle diffusion constant (g mg−1 min−1/2); Ci: suggests the thickness of the boundary layer effect (mg g−1); t: time. 
Equilibrium linear models 
 Langmuir model (Langmuir 1916)  Ce or Ceq: concentration at equilibrium; Qe or qeq: amount adsorbed at equilibrium per unit of mass of the adsorbent; KL or qmb and Cm: reflect properly the nature of the adsorbent material and can be used to compare the performance of adsorption; Cm or qm: maximum capacity of adsorption; KL or qmb: adsorbent–adsorbate interaction forces. 
 
 Freundlich model (Freundlich 1906)  Ceq: concentration on balance; qeq: amount adsorbed at equilibrium per unit of mass of adsorbent; Kf and n: the two parameters of Freundlich. 
 Dubinin–Radushkevich model (Dubinin & Radushkevich 1947)  Qeq: amount of adsorbed ion per unit mass of the adsorbent (mol g−1); Qd: adsorption capacity (mol L−1); Bd: coefficient related to the energy of sorption (mol2 J−2); ɛ: potential of Polanyi. 
 R: universal gas constant (kJ mol−1 K−1); T: temperature (K); Ceq: liquid phase equilibrium concentration (mol L−1). 
Thermodynamic lineal models 
 Gibbs free energy parameter (Sari et al. 2007)  Kd: ratio of the quantity adsorbed per unit of adsorbent (Qeq) and solution concentration in equilibrium (Ceq); R: universal gas constant (8.314 J mol−1 K−1); T: temperature used in the experiment (K). The values of ΔH and ΔS were obtained from the graph of ln Kd as a function of 1/T. 
 Enthalpy and entropy parameters (Sari et al. 2007)  
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