Table 2 Kinetics parameters for Pb²⁺ adsorption by MMEC.

Pseudo-first order

C_o (mg/L)

50

100

150

200

250

300

Q_{e exp} (mg g^− 1)

22.165

42.33

58.93

69.37

81.26

96.28

Q_{e cal} (mg g^− 1)

17.28

33.28

47.52

56.08

77.94

93.28

k₁ (min^− 1)

0.045

0.183

0.373

0.673

1.046

1.263

R²

0.958

0.949

0.973

0.977

0.967

0.984

%SSE

0.099

0.096

0.087

0.086

0.018

0.014

RMSE

1.994

3.695

4.658

5.426

1.355

1.225

Pseudo-second order

Q_{e cal} (mg g^− 1)

21.95

40.23

56.89

70.62

81.92

97.47

k₂ (g mg^− 1 min^− 1)

0.568

0.864

0.886

1.047

1.25

1.354

R²

0.989

0.997

0.998

0.997

0.996

0.997

%SSE

0.004

0.022

0.015

0.008

0.004

0.006

RMSE

0.088

0.857

0.833

0.510

0.269

0.486

Elovich

α

0.068

0.153

0.431

0.848

1.532

1.967

β

1.353

1.946

2.134

2.615

2.365

2.449

R²

0.971

0.966

0.994

0.988

0.969

0.976

Intra-particle diffusion

K_1d (mg g^− 1 min^− 0.5)

7.695

9.967

10.896

13.85

16.07

20.283

C₁(mg g^− 1)

0.027

0.067

0.104

0.128

0.511

0.798

R²

0.967

0.966

0.991

0.984

0.946

0.987