Table 2. Parameters for Pseudo-First-Order and Pseudo-Second-Order As Well As Weber–Morris Modelsa.
dye/substrate | pseudo-first-order modelb |
pseudo-second-order modelc |
Weber–Morris
modeld |
|||||||
---|---|---|---|---|---|---|---|---|---|---|
qmax, exp (mg g–1) | qmax,cal (mg g–1) | k1 (min–1) | R2 | qmax,cal (mg g–1) | k2 (g mg–1 min–1) | R2 | C (mg g–1) | kip (mg g–1 min–1/2) | R2 | |
EY/calc. fib. | 0.3424 | 0.2467 | 0.007 | 0.88 | 0.3265 | 0.089 | 0.95 | 0.1138 | 0.0074 | 0.66 |
EY/arag. tab. | 0.2801 | 0.3433 | 0.002 | 0.49 | 0.2726 | 0.3128 | 0.91 | 0.1363 | 0.0051 | 0.43 |
BM/calc. fib. | 0.0552 | 0.0269 | 0.083 | 0.72 | 0.05331 | 1.6211 | 0.96 | 0.026 | 0.001 | 0.44 |
BM/arag. tab. | 0.0764 | 0.0532 | 0.0086 | 0.92 | 0.07584 | 0.5815 | 0.93 | 0.024 | 0.001 | 0.26 |
The reaction conditions were based on 0.01 mM EY, 0.07 mM BM, and pH 7.2.
The pseudo-first-order model is given by ln (qmax – qt) = ln qmax – k1t, where qmax and qt are the amounts of adsorbed dye (EY or BM) at equilibrium and at time t (mg g–1), respectively. k1 is the equilibrium rate constant of pseudo-first-order kinetics (min–1).
The pseudo-second-order model is determined by 1/qt = 1/k2qmax2 1/t + 1/qmax, where k2 is the equilibrium rate constant of the pseudo-second-order kinetics (g mg–1 min–1).
The Weber–Morris model is expressed by qt = kipt1/2 + C, where kip is the intraparticle diffusion rate constant (mg g–1 min–1/2) and C (mg g–1) is a constant that reflects the thickness of the boundary layer.