Table 2 The coefficient isotherm parameters for MB dye sorption by rC/AC3.7-EDTA.

Langmuir isotherm model

\(\frac{{C_{e} }}{{q_{e} }} = \frac{1}{{K_{a} Q_{m} }} + \frac{1}{{Q_{m} }} \times C_{e}\)   (6)

Q_m

K_a × 10³

R²

^58,59

0.5

60.61

242.29

0.99

1.0

32.89

347.03

1.00

1.5

30.58

671.46

0.99

2.0

25.71

3382.61

1.00

2.5

35.71

666.67

0.99

Freundlich isotherm model

\({\text{Log}}q_{{\text{e}}} = \log K_{{\text{f}}} + 1/{\text{n}}\;\log C_{{\text{e}}}\)   (7)

1/n

K_f

R²

⁶⁰

0.5

0.12

4.32

0.99

1.0

0.18

3.19

0.93

1.5

0.22

3.11

0.94

2.0

0.22

2.77

0.97

2.5

0.2

3.24

0.97

Temkin isotherm model

\(q_{{\text{e}}} = \beta \ln A + \beta \ln C_{{\text{e}}}\)   (8)

1/n_H

K_H

R²

⁶¹

0.5

0.173

2.30*10⁸

0.97

1.0

0.241

5.06*10⁴

0.99

1.5

0.203

4.58*10⁵

1

2.0

0.143

8.47*10⁸

0.97

2.5

0.250

7.6*10⁴

0.99

Halsey isotherm model

\({\text{Ln}}\left( {q_{e} } \right) = \left[ {\left( \frac{1}{nH} \right)\ln K_{{\text{H}}} } \right] + \left( \frac{1}{nH} \right)\ln C_{{\text{e}}}\)     (9)

Dose (g/L)

A_T

B_T

b_T

R²

⁶²

0.5

956.17

4.32

573.9

1.000

1.0

12.73

4.97

498.92

0.990

1.5

1.08

10.20

242.97

1.000

2.0

4.20

18.12

136.73

0.990

2.5

21.41

5.62

441.19

0.990

Generalized isotherm model

\({\text{Ln}}\left( {\frac{Qm}{{qe}} - 1} \right) = \ln {\text{K}}_{{\text{G}}} - {\text{N}}_{{\text{G}}} \ln C_{{\text{e}}}\)   (10)

N_b

K_G

R²

^63,64

0.5

0.21

149.42

0.970

1.0

0.27

890.64

0.990

1.5

0.29

727.78

1.000

2.0

0.24

690.88

1.000

2.5

0.27

533.09

0.990