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In the treatment of aqueous effluents by adsorption process, it is important to evaluate adsorption kinetics because some valuable pieces of information on the reaction pathways as well as on the possible mechanisms involved in the adsorption process can be obtained from adsorption kinetics (Cardoso et al. 2011b). The kinetic plots for the adsorption of TC onto the Zn-AC are shown in Figure 4(a)4(f). It is found from Figure 4 that the adsorption of TC is faster during the initial stages so that for the initial concentrations of 25 and 50 mg L−1, 90% of the total removal occurs during the first 30 min of contact time. For the initial concentration of 100 mg L−1, 84% of the total removal takes place during the first 30 min of the adsorption. The adsorption then becomes slow and finally reaches equilibrium at approximately 120 min for all the studied concentrations. The fitting parameters of the kinetic models are presented in Table 3. In addition to the adjusted R2 values, the SD values were also used to explain the suitability of the fitted model since the experimental data were fitted to the nonlinear kinetic models. A higher SD value is an indication showing that a higher deviation exists between q value calculated theoretically by the model and q value measured experimentally. It has been reported in the literature (Prola et al. 2013) that the number of parameters in nonlinear models could have influence on the fitted curves. Therefore, due to this fact, we took into consideration the number of parameters of each model (p term in Equation (13)) for calculating the SD values and evaluating the kinetic models. The minimum SD value was used to divide the SD value of each model (SD ratio); and, subsequently, the SD ratio value was utilized to compare the fitness of each individual model. For the initial TC concentrations of 25, 50, and 100 mg L−1, the lowest SD values were obtained for the general order kinetic model. In this work, the SD value for the pseudo-first-order kinetic model varies from 0.497 to 1.70 for the evaluated concentrations. Whereas the SD values of the pseudo-second-order and general order kinetic models are in the range of 0.33 to 0.593 and 0.317 to 0.343, respectively (Table 3). For TC concentration of 25 mg L−1, the SD ratio values of the pseudo-first-order, pseudo-second-order, and general order kinetic models are 1.57, 1.018, and 1, respectively, while the corresponding values for TC concentration of 100 mg L−1 are 4.97, 1.73, and 1, respectively (Table 3). The results obtained by the fitted models clearly show that the general order kinetic model better explains the adsorption of TC onto the Zn-AC because this model exhibits the lowest SD ratio values compared to the other kinetic models. Additionally, this model shows the highest R2adj values, as well as the qe values predicted by the general order kinetic model are relatively closer to the qe values measured experimentally. It should be taken into account that the general order kinetic model has different orders (n) when the adsorbate concentration is changed (see Table 3); thus, it is difficult to compare the parameters of the kinetic model. Therefore, the initial sorption rate (h0) is a useful tool to evaluate the kinetics of a given model using the following equation (Equation (15)).
formula
15
where h0 is the initial sorption rate (mg g−1 min−1); KN is the rate constant [min−1(g mg−1)n−1]; qe is the amount of adsorbate adsorbed at equilibrium (mg g−1), and n is the order of the kinetic model. It is worth noting that when n = 2, this equation is the same as the initial sorption rate developed by Ho & Mckay (1988). The general order kinetic model provided the most confident initial sorption rates (h0) because our experimental kinetic data were better described by this model. Based on the general order kinetic model, the order of an adsorption process should follow the same logic as in a chemical reaction, where the order of reaction is experimentally measured (Machado et al. 2012) instead of being confined by a given model. The intra-particle diffusion model was also used to investigate the influence of mass transfer resistance on the binding of TC to the adsorbent, Zn-AC (see Table 3 and Figure 4(d)4(f)). Intra-particle diffusion constant (kid) in terms of mg g−1 h−0.5 can be obtained from the slope of the plot of qt (the amount adsorbed at any time) versus the square root of time. The plots of qt versus t0.5 are shown in Figure 4(d)4(f) for the three initial TC concentrations. The plots have multi-linearity relationship indicating that the adsorption process involves more than one adsorption rate (Alencar et al. 2012). Each line can be attributed to each stage of the adsorption process. Accordingly, the process in which TC molecules diffuse through the solution to the external surface of the adsorbent can be referred to the first linear section, which is the fastest sorption stage, can be regarded as external surface adsorption or instantaneous adsorption (Ribas et al. 2014). The second stage is a delayed process, and can be attributed to the intra-particle diffusion (dos Santos et al. 2014). The third portion is obtained after the equilibrium and describes diffusion through smaller pores (dos Santos et al. 2014). The kinetic studies reveal that the minimum contact time to reach the equilibrium for the adsorption of TC onto the Zn-AC is about 120 min. For the rest of our experiments, the contact time was fixed at 240 min to ensure that the equilibrium would be attained between the adsorbate even at higher concentrations and the Zn-AC adsorbent (Cardoso et al. 2011b).
Table 3

Kinetic parameters obtained from the nonlinear models for the adsorption of TC onto the Zn-AC

Kinetic modelTC concentration mg L−1
2550100
Pseudo-first-order 
 Kf (min−10.1521 0.1137 0.1116 
 qe (mg g−124.09 32.25 37.65 
 h0 (mg g−1 min−13.664 3.667 4.202 
 SD (mg g−10.4974 0.8158 1.706 
 R2adj 0.9936 0.9907 0.9705 
Pseudo-second-order 
 Ks (g mg−1 min−10.01610 0.007122 0.005620 
 qe (mg g−124.74 33.49 39.29 
 h0 (mg g−1 min−19.849 7.991 8.674 
 SD (mg g−10.3227 0.3784 0.5930 
 R2adj 0.9973 0.9980 0.9964 
General order 
 KN [min−1(g mg−1)n−10.02948 0.01568 3.042 × 10−4 
 qe (mg g−124.51 33.04 41.59 
 n 1.728 1.719 2.918 
 h0 (mg g−1 min−17.412 6.395 16.13 
 SD (mg g−10.3171 0.3332 0.3434 
 R2adj 0.9974 0.9985 0.9988 
Intra-particle diffusion 
 kid (mg g−1 h−0.5)a 1.646 3.465 3.410 
 R2 0.9962 0.9860 0.9938 
Kinetic modelTC concentration mg L−1
2550100
Pseudo-first-order 
 Kf (min−10.1521 0.1137 0.1116 
 qe (mg g−124.09 32.25 37.65 
 h0 (mg g−1 min−13.664 3.667 4.202 
 SD (mg g−10.4974 0.8158 1.706 
 R2adj 0.9936 0.9907 0.9705 
Pseudo-second-order 
 Ks (g mg−1 min−10.01610 0.007122 0.005620 
 qe (mg g−124.74 33.49 39.29 
 h0 (mg g−1 min−19.849 7.991 8.674 
 SD (mg g−10.3227 0.3784 0.5930 
 R2adj 0.9973 0.9980 0.9964 
General order 
 KN [min−1(g mg−1)n−10.02948 0.01568 3.042 × 10−4 
 qe (mg g−124.51 33.04 41.59 
 n 1.728 1.719 2.918 
 h0 (mg g−1 min−17.412 6.395 16.13 
 SD (mg g−10.3171 0.3332 0.3434 
 R2adj 0.9974 0.9985 0.9988 
Intra-particle diffusion 
 kid (mg g−1 h−0.5)a 1.646 3.465 3.410 
 R2 0.9962 0.9860 0.9938 

aSecond zone.

Figure 4

Kinetic curves for the adsorption of TC onto the Zn-AC at 293 K: (a) Co = 25 mg L−1; (b) Co = 50 mg L−1; (c) Co = 100 mg L−1; (d), (e), and (f) are intra-particle diffusion model for Co = 25, 50, and 100 mg L−1, respectively. Conditions: original pH; adsorbent dosage 1 g L−1. Error bars represent the SD of two replicate experiments.

Figure 4

Kinetic curves for the adsorption of TC onto the Zn-AC at 293 K: (a) Co = 25 mg L−1; (b) Co = 50 mg L−1; (c) Co = 100 mg L−1; (d), (e), and (f) are intra-particle diffusion model for Co = 25, 50, and 100 mg L−1, respectively. Conditions: original pH; adsorbent dosage 1 g L−1. Error bars represent the SD of two replicate experiments.

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