Table 2 The theoretical parameters of the studied the kinetic models, classic isotherm, and advanced isotherm models.
Model | Parameters | Cd (II) | Fe (II) | Pb (II) | Cr (VI) | Mn (II) |
|---|---|---|---|---|---|---|
Kinetic models | ||||||
Pseudo-first-order | K1 (min− 1) | 0.0096 | 0.0098 | 0.0119 | 0.0046 | 0.0117 |
Qe (Cal) (mg/g) | 72.6 | 79 | 88.9 | 49.1 | 53.4 | |
R2 | 0.93 | 0.93 | 0.95 | 0.96 | 0.98 | |
X2 | 2.21 | 2.03 | 1.46 | 0.12 | 0.23 | |
Pseudo-second-order | k2 (g mg− 1 min− 1) | 8.34 × 10− 5 | 8.01 × 10− 5 | 9.71 × 10− 5 | 1.66 × 10− 4 | 4.14 × 10− 5 |
Qe (Cal) (mg/g) | 95.5 | 103.3 | 111.8 | 66.5 | 74.3 | |
R2 | 0.90 | 0.90 | 0.90 | 0.94 | 0.94 | |
X2 | 2.95 | 2.87 | 2.87 | 0.76 | 0.91 | |
Classic isotherm models | ||||||
Langmuir | Qmax (mg/g) | 235.4 | 249.7 | 297.1 | 135.1 | 158.5 |
b(L/mg) | 3.9 × 10− 8 | 1.4 × 10− 7 | 7.9 × 10− 8 | 3.6 × 10− 8 | 1.5 × 10− 6 | |
RL | 0.99 | 0.99 | 0.99 | 0.99 | 0.99 | |
R2 | 0.98 | 0.99 | 0.99 | 0.99 | 0.99 | |
X2 | 1.47 | 0.16 | 0.67 | 0.24 | 0.19 | |
Freundlich | 1/n | 0.88 | 0.74 | 0.81 | 0.91 | 0.75 |
kF (mg/g) | 2.47 | 5.37 | 4.71 | 2.84 | 3.02 | |
R2 | 0.98 | 0.97 | 0.98 | 0.98 | 0.98 | |
X2 | 2.16 | 2.36 | 1.15 | 1.03 | 0.88 | |
D-R model | β (mol2/kJ2) | 0.0076 | 0.0065 | 0.0062 | 0.0079 | 0.0074 |
Qm (mg/g) | 250.3 | 264.3 | 326.8 | 142.0 | 166.7 | |
R2 | 0.98 | 0.99 | 0.90 | 0.99 | 0.99 | |
X2 | 1.44 | 1.01 | 4.12 | 0.38 | 0.17 | |
E (kJ/mol) | 8.1 | 8.7 | 8.9 | 7.95 | 8.2 | |
Advanced isotherm model | ||||||
Monolayer model of one energy site | R2 | 0.99 | 0.99 | 0.99 | 0.99 | 0.99 |
X2 | 1.47 | 0.15 | 0.67 | 0.23 | 0.09 | |
n | 4.67 | 4.45 | 10.58 | 4.44 | 3.56 | |
Nm (mg/g) | 51.2 | 56.7 | 29.12 | 29.87 | 43.46 | |
Qsat (mg/g) | 239.1 | 252.3 | 308.1 | 132.6 | 154.7 | |
C1/2 (mg/L) | 38.5 | 34.4 | 26.7 | 47.4 | 43.1 | |
ΔE (kJ/mol) | – 5.2 | – 7.6 | – 4.4 | – 5.9 | – 6.8 | |
