Kinetic models Parameters C0 (mmol/L) 4 6 8 Pseudo-first order: $\mathrm{log}\left({q}_{e}-{q}_{t}\right)=\mathrm{log}{q}_{e}-\frac{{k}_{1}t}{2.303}$ qe,exp (mmol/g) 1.86 2.68 2.76 qe,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: $\frac{t}{{q}_{t}}=\frac{1}{{h}_{2}}+\frac{t}{{q}_{e}}$ qe,exp (mmol/g) 1.86 2.68 2.76 qe,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: $\frac{1}{{q}_{t}}=\frac{1}{{h}_{2}t}+\frac{1}{{q}_{e}}$ qe,exp (mmol/g) 1.86 2.68 2.76 qe,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: $\frac{1}{t}=\frac{{h}_{2}}{{q}_{t}}-\frac{{h}_{2}}{{q}_{e}}$ qe,exp (mmol/g) 1.86 2.68 2.76 qe,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: $\frac{{q}_{t}}{t}={h}_{2}-\frac{{h}_{2}}{{q}_{e}}{q}_{t}$ qe,exp (mmol/g) 1.86 2.68 2.76 qe,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: $\frac{1}{\left({q}_{e}-{q}_{t}\right)}=\frac{1}{{q}_{e}}+{k}_{2}t$ qe,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 qe,exp (mmol/g) 1.86 2.68 2.76 Elovich ${q}_{t}=\frac{1}{\beta }\mathrm{ln}\left(\alpha \beta \right)+\frac{1}{\beta }\mathrm{ln}t$ qe,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