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Adsorption isotherms describe how the adsorbate molecules distribute between the liquid phase and the solid phase when the adsorption process reaches an equilibrium state. In other words, at a constant temperature, adsorption isotherms are used to describe the relationship between the amount of adsorbate adsorbed by the adsorbent (qe) and the adsorbate concentration remaining in the solution after the system has reached the equilibrium state (Ce). In addition, some information about adsorption mechanism, the affinity of the adsorbate to the adsorbent, and surface properties can be obtained from the adsorption parameters of equilibrium models. In this study, the isotherms of adsorption of TC onto the Zn-AC were carried out at 293 K using the optimum experimental conditions described previously. Figure 5 shows the adsorption isotherms of TC onto the Zn-AC, and the other parameters predicted by the nonlinear adsorption models are presented in Table 4. Based on the SD values, it is clear that the Langmuir model do not describe the equilibrium data well since this model shows the highest SD value compared with the other three models. On the other hand, the Redlich–Peterson model presents the lowest SD value indicating this model provides the best fit to the experimental data; however, it should be stressed that the Freundlich and Liu models also fit the data well, but their SD values are slightly greater than the SD value of the Redlich–Peterson model (Table 4). The SD ratio was used to compare the studied isotherm models. The procedure used for calculating the SD ratio is described in the previous section (kinetic studies). The SD values of the Langmuir, Freundlich, and Liu models are 2.27, 1.06, and 1.09 times higher than the SD value obtained for the Redlich–Peterson model (Table 4). Overall, since the Redlich–Peterson model provides the highest adjusted R2 and the lowest SD values, this model best describes the equilibrium data. The maximum amount of TC adsorbed onto the Zn-AC (Qmax) predicted by the Liu model is 282.06 mg g−1 indicating this adsorbent is a good adsorbent for the removal of TC from aqueous solutions.
Table 4

Isotherm parameters for the adsorption of TC onto the Zn-AC adsorbent

Isotherm modelParameterValue
Langmuir Qmax (mg g−144.57 
KL (L mg−11.411 
R2adj 0.8452 
SD (mg g−15.946 
Freundlich KF [mg g−1 (mg L−1)−1/nF21.63 
nF 5.861 
R2adj 0.9664 
SD (mg g−12.769 
Liu Qmax (mg g−1282.1 
Kg (L mg−12.773 × 10−6 
nL 0.1951 
R2adj 0.9643 
SD (mg g−12.855 
Redlich–Peterson KRP L g−1 284.0 
aRP (mg L−1)g 11.87 
0.8517 
R2adj 0.9698 
SD (mg g−12.625 
Isotherm modelParameterValue
Langmuir Qmax (mg g−144.57 
KL (L mg−11.411 
R2adj 0.8452 
SD (mg g−15.946 
Freundlich KF [mg g−1 (mg L−1)−1/nF21.63 
nF 5.861 
R2adj 0.9664 
SD (mg g−12.769 
Liu Qmax (mg g−1282.1 
Kg (L mg−12.773 × 10−6 
nL 0.1951 
R2adj 0.9643 
SD (mg g−12.855 
Redlich–Peterson KRP L g−1 284.0 
aRP (mg L−1)g 11.87 
0.8517 
R2adj 0.9698 
SD (mg g−12.625 
Figure 5

Isotherm curves for the adsorption of TC onto the Zn-AC at 293 K. Conditions: original pH; adsorbent dosage 1 g L−1, contact time between the adsorbent and the adsorbate 4 h. Error bars represent the SD of two replicate experiments.

Figure 5

Isotherm curves for the adsorption of TC onto the Zn-AC at 293 K. Conditions: original pH; adsorbent dosage 1 g L−1, contact time between the adsorbent and the adsorbate 4 h. Error bars represent the SD of two replicate experiments.

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