Table 2.

Kinetics and mechanism modeling of adsorption^40–51.

Kinetic and mechanism models	Linear expression	Parameters nomenclature and description
Pseudo first order (PFO)	$log\left(q_e,-,q_t\right)={\mathit{logq}}_e-\frac{K_{1}t}{2.303}$ (15) $h_1=k_1{q}_e$ (16)	qe is the quantity of adsorbate at equilibrium per unit weight of the adsorbent (mg/g), qt is the amount of adsorbed at any time (mg/g) and k1 is the pseudo first-order rate constant (min−1) and h1 initial pseudo first-order rate constant (mg/g/min). qe and k1 were determined respectively from intercept and slope of the linear plot of loqe-qt vs t
Pseudo second-order (PSO)	$\frac{t}{q_t}=\frac{1}{k_2{q}_e^2}+\frac{t}{q_e}$(17) $h_2=k_2{q}_e^2$ (18)	k2 is the pseudo second-order rate constant (min−1) h2 is initial pseudo second-order adsorption rate constant (mg/g/min). qe and k2 were determined respectively from slope and intercept of the linear plot of t/qt vs t
Elovich	$q_t=\frac{1}{\beta }ln\left(\alpha ,\beta \right)+\frac{1}{\beta }ln\left(t\right)$(19)	qt is the amount of adsorbate per unit mass of adsorbent at time (t), and α and β are the constants slope and intercept of the determined from the linear plot of qt versus ln(t). ∝ is the initial adsorption rate (mg/g-min); β is the desorption constant (g/mg) during any one experiment. The slope is $1/\beta$ while the intercept is $1/\beta ln(\alpha \beta )$
Fractional power (power function)	$log(q_t)=\mathit{log}(k)+v\mathit{log}(t)$(20)	qt is the amount of adsorbate per unit mass of adsorbent, k is a constant, t is time, and v is a positive constant (< 1). The parameters v and k are obtainable from slope and intercept of a linear plot of log (qt) versus log (t)
Intraparticle diffusion (IPD)	$q_t=k_{\mathit{id}}{t}^{0.5}+C$(21)	kid is the intraparticle diffusion rate constant (mg.g−1min0.5) and C is the thickness of the adsorbent determined from slope and intercept of linear plot of qt vs t0.5
Liquid film diffusion (LFD)	$\mathit{ln}\left(1,-,F\right)=-K_{\mathit{LFD}}t$+C (22) $F=\frac{\left[q_t^n\right]}{\left[q_e^n\right]}$ (23)	F is fractional attainment to equilibrium and KLFD is the rate coefficient for particle-diffusion controlled process corresponding to the particle size of the adsorbent. -KLFD was determined from the linear plot of ln(1 − F) vs t