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. 2019 Aug 5;12(15):2486. doi: 10.3390/ma12152486

Table 3.

Kinetic equations of biosorption.

Model	Equation	Linearized Formula
Pseudo-first-order	$d q_{t} / d t = k_{1} (q_{e} - q_{t})$	$\ln (q_{e} - q_{t}) = \ln q_{e} - k_{1} t$
Pseudo-second-order	$d q_{t} / d t = k_{2} (q_{e} - q_{t}) ²$	$\frac{t}{q_{t}} = \frac{1}{k_{2} q_{e}^{2}} + \frac{t}{q_{e}}$