Table 7 Non-linear and linearized equations for Langmuir, Freundlich, Temkin, and Sips isotherm models and related constants and correlation coefficients for As(III) removal efficiency on the ZnO/Hal.

Langmuir isotherm (type II)

\({q}_{e}=\frac{{q}_{m}{K}_{l}Ce}{1+{K}_{l}{C}_{e}}\)

\(\frac{1}{{q}_{e}}=\left(\frac{1}{{K}_{l}{q}_{m}}\right)\frac{1}{{C}_{e}}+\frac{1}{{q}_{m}}\)

q_m: maximum adsorption capacity

2.83

42.07

k_l: Langmuir isotherm constant

0.51

0.029

R²: correlation coefficient

0.99

0.98

Freundlich isotherm

\({q}_{e}={K}_{f}{C}_{e}^\frac{1}{n}\)

\(\mathrm{log}\left({q}_{e}\right)=\mathrm{log}\left({K}_{f}\right)+\frac{1}{n}\mathrm{log}({C}_{e})\)

K_f: Freundlich isotherm constant

1.44

1.76

1/n: Adsorption intensity

0.79

0.72

R²: correlation coefficient

0.99

0.97

Temkin isotherm

\({q}_{e}=\frac{RT}{b}\mathrm{ln}\left({{K}_{T}C}_{e}\right)\)

\({q}_{e}=\frac{RT}{b}\mathrm{ln}\left({C}_{e}\right)+\frac{RT}{b}\mathrm{ln}\left({K}_{T}\right)\)

K_T: Temkin isotherm equilibrium constant

0.86

0.56

b: Temkin isotherm constant

481.3

402

R²: adsorption intensity

0.92

0.93

Sips isotherm

\({q}_{e}=\frac{{q}_{m}{{(K}_{Si}Ce)}^{n}}{1+{{(K}_{Si}Ce)}^{n}}\)

\(\mathrm{ln}(\frac{{q}_{e}}{{q}_{m}-{q}_{e}})=\frac{1}{n}\mathrm{ln}\left({C}_{e}\right)+\mathrm{ln}\left({K}_{Si}\right)\)

q_m: maximum adsorption capacity

15.79

42.5

K_si: Sips isotherm constant

0.167

0.028

R²: correlation coefficient

0.97

0.98

1/n: Sips exponent

1.39

0.99