*3.6. Thermodynamic Study*

In order to study the effect of temperature on the adsorption of DB78 by eggshell, the experiments were conducted at three temperatures (Figure 6) at a concentration of 50 mg/L, pH 5, 80 min of contact time, and constant stir (500 rpm). The values of the thermodynamic parameters obtained at different temperatures are presented in Table 3.

**Figure 6.** Van't Hoff plot for the adsorption of Direct Blue 78 onto eggshell at different temperatures.


**Table 3.** Thermodynamic parameters for the adsorption of Direct Blue 78 onto eggshell at different temperatures.

The standard free energy (Δ*G*◦) of the adsorption of DB78 onto eggshell was −24,417.19 J/mol, −30,886.69 J/mol, and −34376.63 J/mol at temperatures of 29, 55, and 75 ◦C, respectively. The exergonic values obtained of Δ*G*◦ indicated that the process is spontaneous at the three temperatures tested, confirming the viability of the process. The enthalpy change (Δ*H*◦) was 41,690.71 J/mol. The positive value of Δ*H*◦ indicated the endothermic nature of the adsorption process. Table 3 shows that the value of Δ*G*◦ decreased with the increasing temperatures. The value decreased from −24,417.19 to −34,376.63 J/mol, which indicates a clear trend in the process. The adsorption process was favoured at high temperatures.

As stated before, the thermodynamic analysis revealed that, at 29 ◦C, there was not an increase in the adsorption abilities of eggshell, however, the best conditions to entrap the dye were achieved at 75 ◦C. At this temperature, the ability of the adsorbent to adsorb more dye molecules increased, as can be observed in Figure 7.

**Figure 7.** Effect of temperature for the adsorption of Direct Blue 78 onto eggshell at a concentration of 50 mg/L at different temperatures.
