Table 1 Kinetic and isotherm modelling approaches were employed for the interpretation of the experimental dataset.
From: Kinetic and isothermal insights on phenol removal via biochar from vicia Faba stems
Equation | Parameters |
|---|---|
Kinetic models | |
\(\begin{array}{l}\text{Pseudo-first-order (PFO):}\:\\{q}_{t}={q}_{e}\left(1-{e}^{-{K}_{1}t}\right)\end{array}\) | k1 (min⁻¹) denotes the rate coefficient associated with the pseudo-first-order model. |
\(\begin{array}{l}\text{Pseudo-second-order (PSO):}\\{q}_{t}=\frac{{q}_{e}^{2\:}{K}_{2}t}{1+{q}_{2}{K}_{2\:}t}\end{array}\) | k2 (g·mg⁻¹·min⁻¹) represents the rate constant associated with the pseudo-second-order model. |
Isotherm models | |
Langmuir: \(\:qe=\frac{{Q}_{m}{K}_{L{C}_{e}}}{1+{K}_{L}{C}_{e}}\) | The maximum adsorption capacity of the material, as predicted by the Langmuir model, is indicated by Qmax (mg·g⁻¹). The constant KL (L·mg⁻¹) reflects the Langmuir adsorption equilibrium parameter. |
Freundlich: \(\:qe={K}_{F}{C}_{e}^{1/n}\) | KF(mg/g)/(mg/L)1/n, and the dimensionless factor n characterize the adsorption capacity and heterogeneity, respectively. |
Temkin: \(\:{q}_{e}=RT/bln(A\times\:{C}_{e})\) | A is the equilibrium binding constant, b denotes the heat of adsorption measured in joules.The universal gas constant R, used in the Temkin formulation, is taken as 8.314 J·mol⁻¹·K⁻¹. |
