Table 3 Sorption kinetics models for MB uptake by AC(H).
From: Statistical modeling of mutagenic azo dye adsorption on bagasse activated carbon
Kinetic model | Linear form | Nonlinear form | Parameters | Refs. |
|---|---|---|---|---|
Pseudo-first order (PFO) | \(\ln \left( {q_{e} - q_{t} } \right) = \ln q_{e} - k_{1} t\) | \(q_{t} = q_{e} \left( {1 - exp - {\text{K}}_{1} t} \right)\) | qt (mg/g): removed amount of MB at time t qe (mg/g): equilibrium sorption uptake k1 (g/mg min): rate constant of the first-order adsorption | Lagergren and Svenska37 |
Pseudo-second order (PSO) | \(\frac{t}{{q_{t} }}\, = \,\frac{1}{{k_{2} \,q_{e}^{2} }} + \,\frac{t}{{q_{e} }}\) | \(q_{t} = \frac{{k_{2} t\left( {q_{e} } \right)^{2} }}{{1 + k_{2} q_{e} t}}\) | qt (mg/g): removed amount of MB at time t qe (mg/g): equilibrium sorption uptake k2 (g/mg min): rate constant of the second-order adsorption | Ho and McKay38 |
Intra-particle diffusion (IPD) | \(q_{t} \, = \,k_{p} \,t^{1/2} \, + \,C\) | – | qt (mg/g): removed amount of MB at time t Kp (mg/g min0.5): intra-particle diffusion rate constant C (mg/g): intercept of the line which reflects the thickness of the boundary layer kp = slope C = intercept | Weber and Morris80 |
