Table 6 The kinetic equations used for analysis of kinetic data

PFO

ln(q _e  − q _t ) = ln q _e  − K₁t

ln(q _e  − q _t ) vs. Time

PSO

$\frac{\mathit{t}}{{\mathit{q}}_{\mathit{t}}}=\frac{1}{\left({\mathit{K}}_2^2{\mathit{q}}_{\mathit{e}}^2\right)}+\frac{\mathit{t}}{{\mathit{q}}_{\mathit{e}}}$

$\frac{\mathit{t}}{{\mathit{q}}_{\mathit{t}}}\mathit{vs}.\mathit{Time}$

Elovich

${\mathit{q}}_{\mathit{t}}=\left(\frac{1}{\mathit{\beta }}\right)ln\left(\mathit{\alpha \beta }\right)+\left(\frac{1}{\mathit{\beta }}\right)ln\mathit{t}$

q _t vs. Time

BVM

ln[1 − (U)T] = K _B t

ln[1 − (U)T] vs. Time