Table 1 The explored isothermal and kinetic models with the extracted parameters.
From: Carbon coated Fe0.65Ni0.30Mn0.05 magnetically separable adsorbent for phenanthrene removal
Model | Equation | Parameters | R2 | χ2 | Standard deviation (SD) | RSS |
|---|---|---|---|---|---|---|
Adsorption isotherms | ||||||
Sips | \(\:{q}_{e}=\frac{{q}_{s}{{(K}_{s}\:{C}_{e})}^{{B}_{s}}}{1+\:{{(K}_{s}\:{C}_{e})}^{{B}_{s}}}\) 3,36 | qs = 1.93 mg/g Ks = 12.94 L/g Bs = 6.90 | 0.997 | 10.7 × 10− 4 | 0.51 1.09 1.70 | 10.7 × 10− 4 |
Freundlich | \(\:{q}_{e}={K}_{F}\:{C}_{e}^{1/n_{F}}\) 3,36 | KF = 11235.61 L/g nF = 0.27 | 0.987 | 24.3 × 10− 4 | 8817.02 0.02 | 48.6 × 10− 4 |
Dubinin–Radushkevich | \(\:{q}_{e}={q}_{m,DR}\:{e}^{-{K}_{DR}{\epsilon\:}_{DR}^{2}},\:{\epsilon\:}_{DR}=RT\:\left(1+\frac{1}{{C}_{e}}\right)\:\)3,36 | qm, DR = 163.47 mg/g KDR = 1.27 × 10− 7 mol2/kJ2 | 0.989 | 19.4 × 10− 4 | 65.40 1.01 × 10− 8 | 38.7 × 10− 4 |
Temkin | \(\:{q}_{e}=\left(\:\frac{R\:T}{{b}_{TM}}\right)\:ln\left({K}_{TM}\:{C}_{e}\right)\)3,36 | bTM = 66.99 J/mol KTM =17.68 L/g | 0.998 | 3.6 × 10− 4 | 2.07 0.15 | 7.19 × 10− 4 |
Hill | \(\:{q}_{e}=\frac{{qs}_{H}\:{C}_{e}^{{n}_{H}}}{{K}_{D}+{C}_{e}^{{n}_{H}}}\) 3,36 | qsH = 1.93 mg/L KD = 2.12 × 10− 8 L/mg nH = 6.90 | 0.997 | 10.7 × 10− 8 | 0.54 1.32 × 10− 7 2.46 | 10.7 × 10− 4 |
Langmuir | \(\:{q}_{e=}{q}_{m\:}{K}_{L}\left(\frac{{C}_{e}}{1+{K}_{L}{C}_{e}}\right)\)26 | \(\:{q}_{m}\)= 1954.4 mg/g \(\:{K}_{L}\)= 0.00456 L/mg | 0.37 | 65.33 | 1.46 × 107 34.22 | 130.67 |
Kinetics models | ||||||
Pseudo-first-order | \(\:{q}_{t}={q}_{e}\left(1-{e}^{-{k}_{1}\:t}\right)\)3,36 | k1 = 0.065 min− 1 qe = 2.31 mg/g | 0.937 | 0.02785 | 0.01 0.05 | 0.33 |
Pseudo-second-order | \(\:{q}_{t}=\frac{{k}_{2}\:{q}_{e}^{2}\:t}{1+{k}_{2}\:{q}_{e}\:t}\)3,36 | k2 = 0.049 g/mg/min qe = 2.43 mg/g | 0.982 | 7.97 × 10− 3 | 0.007 0.03 | 0.0957 |
Elovich | \(\:{q}_{t}=1/{b}_{e}\text{ln}\left(1+{a}_{e}{b}_{e}t\right)\) 3,36 | ae = 201.34 mg/g/min be = 5.44 g/mg | 0.978 | 9.66 × 10− 3 | 270.01 0.66 | 0.11589 |
Weber Morris | \(\:{q}_{t}=k{t}^{1/2}+B\) 3,36 | K = 0.04256 mg/g.min B = 1.47316 mg/g | 0.41 | 0.01 0.24 | 3.11668 | |
Avrami | \(\:{q}_{t}={q}_{e}(1-{{e(}^{-{k}_{1}\:t})}^{n}\) 3,36 | qe=2.207 mg/g k = 8399 min− 1 n = 8399 | 0.85 | 0.07 0 0 | 0.77657 | |
