Table 3. Adsorption Kinetic Rate Constants of Pseudo-first-order, Pseudo-second-order and Elovich Models in Single- and Bisolute Systemsa.
| metal | kinetic model | parameter | sample |
|||
|---|---|---|---|---|---|---|
| AC | BB | MB | PSB | |||
| Cd | PFO | K1 (1/min) | 0.006 (0.005) | 0.005 (0.006) | 0.005 (0.004) | 0.004 (0.003) |
| Qe (mg/g) | 0.462 (0.458) | 0.390 (0.376) | 0.330 (0.312) | 0.265 (0.251) | ||
| R2 | 0.898 (0.877) | 0.909 (0.876) | 0.959 (0.879) | 0.884 (0.994) | ||
| RMSE | 0.027 (0.027) | 0.023 (0.020) | 0.012 (0.012) | 0.005 (0.003) | ||
| PSO | K2 (g/mg min) | 0.075 (0.065) | 0.077 (0.086) | 0.051 (0.050) | 0.018 (0.017) | |
| Qe (mg/g) | 0.472 (0.490) | 0.399 (0.385) | 0.345 (0.326) | 0.295 (0.285) | ||
| h | 0.017 (0.014) | 0.012 (0.013) | 0.006 (0.005) | 0.002 (0.001) | ||
| R2 | 0.999 (0.999) | 0.999 (0.998) | 0.999 (0.999) | 0.985 (0.985) | ||
| RMSE | 0.003 (0.002) | 0.001 (0.002) | 0.001 (0.003) | 0.004 (0.004) | ||
| Elovich | α (mg/g·min) | 0.055 (0.046) | 0.040 (0.037) | 0.017 (0.015) | 0.006 (0.005) | |
| β (g/mg) | 13.7 (13.5) | 15.8 (16.1) | 16.9 (17.5) | 20.7 (21.3) | ||
| R2 | 0.9453 (0.9516) | 0.9428 (0.9373) | 0.9760 (0.9661) | 0.9446 (0.9391) | ||
| RMSE | 0.009 (0.009) | 0.008 (0.008) | 0.005 (0.005) | 0.006 (0.006) | ||
| Pb | PFO | K1 (1/min) | 0.007 (0.006) | 0.005 (0.005) | 0.005 (0.005) | 0.003 (0.004) |
| Qe (mg/g) | 0.484 (0.481) | 0.459 (0.446) | 0.364 (0.359) | 0.294 (0.279) | ||
| R2 | 0.889 (0.886) | 0.873 (0.927) | 0.897 (0.985) | 0.977 (0.980) | ||
| RMSE | 0.034 (0.033) | 0.022 (0.015) | 0.013 (0.011) | 0.009 (0.007) | ||
| PSO | K2 (g/mg min) | 0.126 (0.106) | 0.053 (0.036) | 0.043 (0.038) | 0.031 (0.031) | |
| Qe (mg/g) | 0.490 (0.488) | 0.473 (0.468) | 0.381 (0.379) | 0.311 (0.297) | ||
| h | 0.030 (0.025) | 0.012 (0.008) | 0.006 (0.005) | 0.003 (0.003) | ||
| R2 | 0.999 (0.999) | 0.999 (0.999) | 0.998 (0.999) | 0.996 (0.996) | ||
| RMSE | 0.005 (0.004) | 0.004 (0.004) | 0.005 (0.004) | 0.004 (0.004) | ||
| Elovich | α (mg/g·min) | 0.140 (0.104) | 0.032 (0.022) | 0.020 (0.017) | 0.010 (0.009) | |
| β (g/mg) | 14.9 (14.3) | 12.5 (12.2) | 15.6 (15.5) | 19.1 (19.8) | ||
| R2 | 0.8913 (0.9000) | 0.9490 (0.9730) | 0.9814 (0.9865) | 0.9847 (0.9792) | ||
| RMSE | 0.012 (0.012) | 0.010 (0.007) | 0.005 (0.004) | 0.003 (0.004) | ||
a
Note: Data are shown in the single-solute system followed by the bisolute system in parentheses. RMSE: root-mean-square error.