4.2.6 Adsorption Kinetic Models
In this study, three (3) different models were applied to evaluate the experimental data of the adsorption kinetic of 2,6-DCP onto MTCNS namely: Lagergren’s Pseudo-first-order and Pseudo-second-order, and Webber-Moris intra-particle diffusion models. The pseudo-first order kinetic model equation describes the rate of adsorption is directly proportional to the number of unoccupied sites by the solutes (Lagergren ; Svenska, 1898). Pseudo-second-order equation describes the rate of occupation of adsorption sites is proportional to the square of the number of unoccupied sites (Dada et al., 2012). Intra-particle diffusion plays a significant role in controlling the kinetics of the adsorption process. The linear forms of these three models are expressed by equations (2.4), (2.8) and (2.9) respectively, where the terms qe and qt have the same meaning as previously described in chapter 2 with unit mg g -1 while k1, k2 and kp are pseudo-first-order, pseudo-second-order and intra-particle diffusion model rate constants, expressed in min-1, g / mg min and mg / g min0.5 respectively.
Table 4.9: Kinetic Study Data for the Removal of 2,6-DCP at Different Initial Concentration
Time (t) Min. Initial 2,6-DCP Concentration (Co) in mg/L
100 mg/L 200 mg/L 300 mg/L 400 mg/L 500 mg/L
Ct qt Ct qt Ct qt Ct qt Ct qt
30 4.32 4.784 12.22 9.389 21.30 13.935 32.28 18.386 43.95 22.803
60 3.61 4.820 11.72 9.414 20.22 13.989 31.72 18.414 43.05 22.848
90 1.11 4.945 10.84 9.458 19.14 14.043 30.92 18.454 41.85 22.908
120 0.83 4.959 10.20 9.490 18.60 14.070 29.96 18.502 41.05 22.948
150 0.75 4.963 9.92 9.504 18.18 14.091 29.32 18.534 40.80 22.960
Note: Final 2,6-DCP Concentration (Ct) in mg/L and Adsorption Capacity (qt) in mg/g @ Time (t)
The slopes and intercepts of plots were used to calculate qe, k1, k2 and kp as illustrated in Figures 4.8 – 4.10. These model parameters and constants along with the corresponding linear regression coefficient R2 values are depicted in Table 4.10. The applicability of the kinetic model is compare by judging the correlation coefficient R2 and the agreement between the calculated and experimental qe values.
Table 4.10: Kinetic Parameters and Correlation Coefficients (R2) obtained for the Adsorption of 2,6-DCP onto MTCNS (Adsorbent)
Kinetic Models Parameters Initial Concentration Co (mg/L)
100 200 300 400 500
qe, Exp. (mg g-1) 4.963 9.504 14.091 18.534 22.960
Pseudo First Order
log?(q_e ?-? q_t )=log??q_e ?-k_1/(2.303) t
k1 (min-1) 0.045 0.023 0.023 0.017 0.028
qe, Cal. (mg g-1) 1.070 0.292 0.344 0.286 0.480
% ?qe 78.44 96.93 97.56 98.46 97.91
R2 0.9284 0.9163 0.9812 0.9058 0.9179
Pseudo Second Order
t/q_t =1/(k_2 ?q_e?^2 )+t/q_e
k2 (g mg-1 min-1) 0.107 0.113 0.132 0.120 0.122
qe, Cal. (mg g-1) 5.028 9.560 14.144 18.587 22.989
% ?qe 1.29 0.59 0.37 0.29 0.13
R2 0.9999 1.0000 1.0000 1.0000 1.0000
Intra-particle Diffusion
kp (mg g-1 min-0.5) 0.0301 0.0312 0.0237 0.0225 0.0248
C (mg g-1) 4.6176 9.1444 13.8080 18.251 22.665
R2 0.8843 0.9233 0.9891 0. 9697 0.9804
It can be observed that the correlation coefficients (R2) obtained from the plots of log (qe – qt) versus time (t) (Appendix D) for pseudo-first-order equation (Fig. 4.8) were moderately high (0.9058 – 0.9812), but the calculated qe values from pseudo-first-order kinetic plots were deviating (% ?qe) much as compared to the experimental qe values, and were not in agreement with the experimental qe values suggesting that the removal of 2,6-DCP by adsorption on MTCNS did not fit the pseudo-first-order model.

Fig. 4.8: Pseudo-first-order Kinetic plots for Removal of 2,6-DCP by MTCNS

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Fig. 4.9: Pseudo-second-order Kinetic plots for Removal of 2,6-DCP by MTCNS

Fig. 4.10: Intra-particle Diffusion Kinetic plots for Removal of 2,6-DCP by MTCNS
On the other hand, the R2 values from the plots of t/qt versus time (t) (Appendix D) for pseudo-second-order model (Fig. 4.9) were extremely high (0.9999 – 1) for all the initial concentrations of 2,6-DCP. The calculated qe values were closer to the experimental qe values and the calculated qe values agreed well with the experimental ones. This indicated that the kinetics data fitted perfectly well with the pseudo-second-order model. This model assumes that, the rate-controlling step in the removal of 2,6-DCP by adsorption with MTCNS is chemisorptions involving valence forces through sharing or exchanging of electrons between adsorbent and adsorbate (Parate ; Talib, 2015).
According to Intra-particle diffusion model, the intercept (C) of the plots qt versus t1/2 (Appendix D) give an idea about boundary layer thickness. The larger the intercept, greater the boundary layer effect, and if the plots qt versus t1/2 pass through the origin then intra-particle diffusion is the rate-controlling step. When the plots do not pass through the origin, this is indicative of some degree of boundary layer control and this further show that the intra-particle diffusion is not the only rate-limiting step, but also other kinetic models may control the rate of adsorption, all of which may be operating simultaneously (Arami et al., 2008). It can be seen from Figure 4.10; the interception of the line does not pass through the origin showing that the mechanism of adsorption is not solely governed by intra-particle diffusion process.
In a view of these both considerations, we may conclude that the pseudo-second-order mechanism is predominant. Similar observations have been reported for the adsorption of chlorophenols onto other single adsorbents (Wang et al., 2011; Agarry et al., 2013).