Table 3 The modal parameters for pb(II) adsorbed on three carbonisation materials (n = 3).

Pseudo-first order

Q_e (mg g^− 1)

11.64

14.30

14.67

K₁ (min^− 1)

0.85

0.85

1.69

R²

0.75

0.93

0.97

Pseudo-second order

Q_e (mg g^− 1)

12.52

15.26

15.39

K₂ (g (mg·min)⁻¹)

0.09

0.08

0.17

R²

0.90

0.99

0.97

Elovich

a (mg g^− 1 s^− 1)

75.17

101.42

125.24

b

0.56

0.47

0.64

R²

0.97

0.93

0.86

Intramaterial diffusion

External surface sorption

K_int1 (g mg^− 1 min^− 0.5)

4.88

8.05

13.52

C₁

1.94

0.22

-1.55

R²

0.74

0.99

0.87

Gradual adsorption

K_int2 (g mg^− 1 min^− 0.5)

2.32

2.64

0.82

C₂

4.16

6.68

12.37

R²

0.94

0.99

0.98

Final equilibrium

K_int3 (g mg^− 1 min^− 0.5)

0.30

0.11

0.02

C₂

11.03

14.28

14.86

R²

0.96

0.81

0.90

25 °C

35 °C

45 °C

25 °C

35 °C

45 °C

25 °C

35 °C

45 °C

Langmuir

q_max (mg g^− 1)

74.79

91.85

101.36

73.48

82.20

104.73

82.74

87.23

110.80

K_L (L mg^− 1)

0.01

0.01

0.01

0.02

0.02

0.02

0.02

0.03

0.02

R²

0.97

0.97

0.96

0.96

0.95

0.96

0.94

0.96

0.96

Freundlich

K_F (mg^1 − nLⁿ g^− 1)

3.15

3.99

7.37

7.31

10.40

13.09

10.85

14.37

14.69

1/n

−1.97

−1.99

−2.31

−2.48

−2.87

−2.82

−2.93

−3.21

−2.88

R²

0.98

0.99

0.97

0.99

0.99

0.99

0.98

0.98

0.99

Thermodynamics

△G° (KJ mol^− 1)

−0.12

−5.23

−9.63

△H° (KJ mol^− 1)

69.14

64.78

20.09

△S° (J molK^− 1)

231.79

236.40

99.32

R²

0.99

0.87

0.90