Table 2 Modeled equations of adsorption kinetics with its parameters and coefficient of determination.

From: Equilibrium and kinetic modeling of Cr(VI) removal by novel tolerant bacteria species along with zero-valent iron nanoparticles

Model

Model equation

Corresponding parameters

R2

SSE

PFO

\({q}_{t}={q}_{e}(1-{\text{exp}}\left(-{k}_{1}t\right))\)

k1 = 0.0578 s−1, qe = 0.1007 mg/g

0.999053

6.02 × 10–6

PSO

\({q}_{t}={q}_{e}\left(1-\frac{1}{1+{q}_{e}{k}_{2}t}\right)\)

k2 = 0.6485 g/mg/s, qe = 0.1191 mg/g

0.999613

2.46 × 10–6

Vermeulen kinetic model

\(\frac{\overline{{\text{q}}}}{{{\text{q}} }_{{\text{e}}}}=\sqrt{1-{{\text{e}}}^{\left(\frac{-{\text{D}}{\uppi }^{2}{\text{t}}}{{{\text{R}}}^{2}}\right)}}\)

D = 0.0000314 cm2/s, qe = 0.1068 mg/g

0.999578

2.68 × 10–6

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