Table 1.

Adsorption isotherms, kinetics, and thermodynamics.

Isotherms, kinetics, and thermodynamics	Equation	References	Parameters
Langmuir	$\frac{1}{q_e}=\frac{1}{q_m}+\frac{1}{q_m{\times K}_L}\times {{(C}_e)}^{-1}$	37	qm = maximum adsorption on MPPs (mg/g), KL = Langmuir constant (L/mg)
Freundlich	${\mathrm{Log}q}_e=\frac{1}{n}\mathrm{Log}{C}_e+{\mathrm{Log}K}_f$	38	qe = chemicals absorbed per unit adsorbent at equilibrium (mg/g) Ce = equilibrium adsorbate concentration (mg/L) Kf and n = Freundlich adsorption isotherm constants
Pseudo-first-order	$\ln \left(q_e,-,q_t\right)=\ln q_e-K_{1}t$	39	qe = chemicals adsorbed at equilibrium (mg/g) qt = chemicals absorbed at time t (mg/g) K1 = pseudo-first-order constant rate (min−1)
Pseudo-second-order	$\frac{t}{q_t}=\frac{1}{K_2{q}_e^2}+\frac{t}{q_e}$	40	K2 = pseudo-second-order constant rate (g mg−1 min−1)
Thermodynamics	$\mathrm{\Delta }{G}^{\circ }=-\mathrm{R}\times \mathrm{T}\times \ln {(K}_L)$ $K_L=\frac{q_e}{C_e}$ $\ln {(K}_L)=\frac{-\mathrm{\Delta }{H}^{\circ }}{\mathrm{RT}}+\frac{\mathrm{\Delta }{S}^{\circ }}{\mathrm{R}}$ $\mathrm{\Delta }{G}^{\circ }={\mathrm{\Delta }H}^{\circ }-\mathrm{T}\times {\mathrm{\Delta }S}^{\circ }$	41	ΔG° = Gibbs free energy, ΔS° = standard entropy ΔH°= standard enthalpy T = temperature (K) R = the universal gas constant (8.314 J/mol K)