Table 2.

Biosorption equilibrium and kinetic models

Models		Nonlinear equation
Nonlinear isotherm model	Langmuir	${\mathrm{q}}_{\mathrm{e}}=\frac{{\mathrm{Q}}_{\mathrm{o}}{\mathrm{K}}_{\mathrm{L}}{\mathrm{C}}_{\mathrm{e}}}{1+{\mathrm{K}}_{\mathrm{L}}{\mathrm{C}}_{\mathrm{e}}}$
	Freundlich	${\mathrm{logq}}_{\mathrm{e}}={\mathrm{logK}}_{\mathrm{F}}+\frac{1}{\mathrm{n}}{\mathrm{logC}}_{\mathrm{e}}$
Kinetic model	Pseudo-first order	$\log \left({\mathrm{q}}_{\mathrm{e}},-,{\mathrm{q}}_{\mathrm{t}}\right)={\mathrm{logq}}_{\mathrm{e}}-\frac{{\mathrm{K}}_1}{2.303}\mathrm{t}$
	Pseudo-second order	$\frac{\mathrm{t}}{{\mathrm{q}}_{\mathrm{t}}}=\frac{1}{{\mathrm{K}}_2{\mathrm{q}}_{\mathrm{e}}^2}+\frac{1}{{\mathrm{q}}_{\mathrm{e}}}\mathrm{t}$