# Removal of Methylene Blue from Aqueous Solution by Bone Char
## 3 Results and Discussion
This can be explained by the adsorption process, which follows a two-stage adsorption model governed by internal diffusion based on the Crank-Nicolson method. Intraparticle diffusion is expected to be the rate-limiting step during the adsorption process due to the predominant mesoporous structure of bone char. Figure 2d shows that the adsorption behavior of methylene blue onto bone char may change at different times: (a) fast adsorption of methylene blue in the first 10 min, (b) a gradual adsorption process (10-40 min) where approximately 10% of methylene blue is achieved because of the utilization of all active adsorption sites on the surface, macropores, and  
Figure 2: (**a**) Photograph of bone char with different sizes, (**b**) chemical structure of methylene blue, (**c**) effect of contact time on the removal rate of methylene blue (bone char particle size: 0.5–0.8 mm; \(T\): 303 K), (**d**) three stages of the removal process of methylene blue by bone char represented by three continuous tend lines, (**e**) effect of adsorption temperature on the adsorption, and (**f**) pseudo-second-order kinetic model of the adsorption process (bone char particle size: 0.50–0.80 mm). mesopores of bone char, and (c) methylene blue diffuses into pores, and an adsorption equilibrium is attained. The plot of \(q\) vs. \(t^{0.5}\) of the intraparticle region does not go through the original point, implying that the rate-limiting step contains not only the intraparticle diffusion but also the external diffusion in which methylene blue migrates from the solution onto the bone char surface (surface adsorption) [18; 39]. The same behavior has been reported in previous papers about the removal of methylene blue onto Jordanian diatomic [28]. Figure 2e shows that the removal rate of methylene blue decreases with an increase in adsorption temperature from 273 to 313 K, revealing that the removal process is exothermic in nature [40]. It is because the highly charged ions (MB\({}^{+}\))\({}_{3}\) is stabilized at lower temperatures, which may enhance their ion-pairing interactions with the active adsorption sites on bone char [40]. Figure 2f shows that the experimental data fit well with the pseudo-second-order kinetic curve because of the goodness of fit \(R^{2}\) highly closing to 1. The Freundlich, Langmuir, Temkin, and DKR models were applied to the adsorption isotherm. Their \(R^{2}\) values are shown in Figure 3. It turns out that the Freundlich isotherm model is the most relevant adsorption isotherm, with the highest value of \(R^{2}\) (>0.99). The \(n\) value in the Freundlich model was calculated to be 5.368, which showed that this adsorption occurs readily. In addition, Temkin and DKR models also fit for the adsorption process. The three aforementioned models explain that diffusion mainly occurs on the bone char surface, and the possible mechanism and the orientations of methylene blue on the surface of bone char are the same as what occurred on the surface of diatomic [28]. Figure 3d shows the plot of ln\(q_{e}\) against \(\varepsilon^{2}\) corresponding to the removal of methylene blue by bone char. The value of \(E\) is calculated to be 13.29 kJ mol\({}^{-1}\), implying that the adsorption interaction between methylene blue and bone char is ion-exchange. In other words, the cationic methylene  
Figure 3: The adsorption data of methylene blue dye on bone char fitted with (**a**) Freundlich, (**b**) Langmuir, (**c**) Temkin, and (**d**) DKR isotherm models (particle size: 0.50–0.80 mm, \(T\): 303 K, \(t\): 15.5 h). blue takes the place of the acidic hydrogen ions of bone char during the adsorption process. Similar conclusions have been reported in other literature [41; 42; 43; 44]. The calculated thermodynamic parameter values are shown in Table 2. The negative \(\Delta H^{0}\) and \(\Delta S^{0}\) values indicate a moderate exothermic adsorption and decreased chaos at the interface between solid and solution phases occurring during the adsorption process.