Kinetic models

Parameters

C₀ (mmol/L)

4

6

8

Pseudo-first order:

$\log \left(q_e-q_t\right)=\log q_e-\frac{k_{1}t}{2.303}$

q_e,exp (mmol/g)

1.86

2.68

2.76

q_e,cal (mmol/g)

1.29

1.69

2.13

k₁ (g/mmol・h)

1.28

2.42

2.95

h₁ (1/h)

1.64

4.09

6.28

R²

0.9980

0.9925

0.9967

Type-1 pseudo-second-order:

$\frac{t}{q_t}=\frac{1}{h_2}+\frac{t}{q_e}$

q_e,exp (mmol/g)

1.86

2.68

2.76

q_e,cal (mmol/g)

1.90

2.70

2.78

k₂ (g²/mmol²・h)

2.48

5.49

7.05

h₂ (1/h)

8.97

40.00

54.50

R²

0.9998

0.9999

0.9999

Type 2 pseudo-second-order:

$\frac{1}{q_t}=\frac{1}{h_{2}t}+\frac{1}{q_e}$

q_e,exp (mmol/g)

1.86

2.68

2.76

q_e,cal (mmol/g)

2.00

2.94

2.94

k₂ (g²/mmol²・h)

1.67

1.66

2.36

h₂ (1/h)

6.67

14.32

20.45

R²

0.9974

0.9606

0.9778

Type 3 pseudo-second-order:

$\frac{1}{t}=\frac{h_2}{q_t}-\frac{h_2}{q_e}$

q_e,exp (mmol/g)

1.86

2.68

2.76

q_e,cal (mmol/g)

1.97

2.95

2.92

k₂ (g²/mmol²・h)

1.68

1.49

2.28

h₂ (1/h)

6.53

12.97

19.45

R²

0.9974

0.9606

0.9778

Type 4 pseudo-second-order:

$\frac{q_t}{t}=h_2-\frac{h_2}{q_e}{q}_t$

q_e,exp (mmol/g)

1.86

2.68

2.76

q_e,cal (mmol/g)

1.97

2.90

2.92

k₂ (g²/mmol²・h)

1.67

1.68

2.36

h₂ (1/h)

6.52

14.13

20.12

R²

0.9961

0.9488

0.9901

Type 5 pseudo-second-order:

$\frac{1}{\left(q_e-q_t\right)}=\frac{1}{q_e}+k_{2}t$

q_e,exp (mmol/g)

0.86

2.68

2.76

k₂ (g²/mmol²・h)

11.79

73.72

53.03

h₂ (1/h)

40.57

529.02

403.73

R²

0.8639

0.8459

0.8092

q_e,exp (mmol/g)

1.86

2.68

2.76

Elovich

$q_t=\frac{1}{\beta }\ln \left(\alpha \beta \right)+\frac{1}{\beta }\ln t$

q_e,cal (mmol/g)

2.03

2.93

2.84

α (mmol/g・h)

16.68

71.32

96.25

β (g/mmol)

2.50

2.08

2.00

R²

0.9959

0.9277

0.9747