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The literalized form of pseudo-first-order rate equation by Lagergren and Svenska (Lagergren 1898) is given as:
formula
2
where qe and qt are the amount of metal ion adsorbed at equilibrium and at contact time t (min) and Kad (min−1) is the rate constant. From the plot of log (qeqt) versus time t, the rate constant k1 and correlation co-efficient R2 are calculated and listed in Table 1.
Table 1

Kinetic models and other statistical parameters for metal ions sorption onto TDPI polymer

Kinetic modelParametersConcentration of lead(II) solution = 100 (mg/L)Concentration of copper(II) solution = 100 (mg/L)Concentration of nickel(II) solution = 100 (mg/L)Concentration of cadmium(II) solution = 100 (mg/L)
Pseudo-first-order equation kad (min−10.0716 0.0776 0.0672 0.0621 
qe, cal (mg/g) 131.21 168.96 113.92 110 
R2 0.9891 0.9838 0.9867 0.9880 
Pseudo-second-order equation k (g mg−1 min−18.58 × 10−4 7.06 × 10−4 7.79 × 10−4 7.14 × 10−4 
qe, cal (mg/g) 108.69 109.89 105.26 104.1 
h(mg.g−1 min−110.14 8.53 8.64 7.74 
 R2 0.9966 0.9946 0.9956 0.9957 
Intraparticle diffusion Kp (mg/g. min1/26.2933 6.8158 6.4047 6.5874 
41.101 34.649 35.05 31.4 
R2 0.8790 0.8793 0.879 0.8898 
Kinetic modelParametersConcentration of lead(II) solution = 100 (mg/L)Concentration of copper(II) solution = 100 (mg/L)Concentration of nickel(II) solution = 100 (mg/L)Concentration of cadmium(II) solution = 100 (mg/L)
Pseudo-first-order equation kad (min−10.0716 0.0776 0.0672 0.0621 
qe, cal (mg/g) 131.21 168.96 113.92 110 
R2 0.9891 0.9838 0.9867 0.9880 
Pseudo-second-order equation k (g mg−1 min−18.58 × 10−4 7.06 × 10−4 7.79 × 10−4 7.14 × 10−4 
qe, cal (mg/g) 108.69 109.89 105.26 104.1 
h(mg.g−1 min−110.14 8.53 8.64 7.74 
 R2 0.9966 0.9946 0.9956 0.9957 
Intraparticle diffusion Kp (mg/g. min1/26.2933 6.8158 6.4047 6.5874 
41.101 34.649 35.05 31.4 
R2 0.8790 0.8793 0.879 0.8898 
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