# Carbon from Bagasse Activated with Water Vapor and Its Adsorption Performance for Methylene Blue
## 2 Materials and Methods
### Adsorption Test  
The adsorption test was conducted with the highest surface area found from the prepared activated-carbon. Before being used in the adsorption test, the activated-carbon powder was crushed in an alumina mortar and then sieved by a 50-mesh sieve. Then 5 mg of the prepared carbon powder was poured into 10 mL of methylene blue (MB) solution. The initial concentration of the MB solution was 15 ppm. The suspension was stirred for 0, 10, 20, 30, 40, 50, 60, and 70 min. After stirring under the specified times, 4 mL of solution was taken with a syringe for UV-Vis absorbance analysis (UV-Vis spectrometer Hitachi Double-Beam Spectrophotometer UH5300; optical system: Czerny-Turner mount, double beam monochromator; wave length range 190 to 1100 nm; photometric range absorbance of 0-3.3; and %T of 0 to 300) under the maximum wavelength absorbance of MB, \(\chi_{\rm max}\), which is 664 nm. Moreover, a standard curve of MB concentration was plotted by measuring the absorbance of 0-15 ppm of MB solution under 664 nm of light wavelength. The standardcurve was used to correlate the absorbance, \(A\), with the MB concentration, \(C\), through a linear equation plotted from the absorbance data. A Langmuir isotherm was applied to examine the relation between the equilibrium adsorbed molecules, \(q_{e}\) (mg/g adsorbent), and the equilibrium concentration of solute in the fluid phase, C\({}_{e}\) (mg/L), determined using Equation (1) [30]. \[q_{e}=\frac{abC_{e}}{1+bC_{e}} \tag{1}\]  
in which \(a\), mg/g adsorbent, denotes the maximum loading of MB molecules on adsorbent corresponding to the complete monolayer coverage of all available adsorption sites; and \(b\) represents a constant of the Langmuir isotherm in L/mg adsorbent [30]. The maximum loading was calculated based on the surface area of the adsorbent, in m\({}^{2}\)/g adsorbent, divided by the area of the MB molecule to cover, i.e., 102-108 A\({}^{2}\)[31]. For the Freundlich isotherm application, Equation (2) was used to understand the favorability of the MB adsorption on the produced activated-carbon, in which if the adsorption is favorable, \(n>1\), and if adsorption is unfavorable, \(n<1\)[32]. \[q_{e}=K_{F}C_{e}^{1/n} \tag{2}\]  
in which \(K_{F}\) and \(n\) are the characteristic constants of the particular adsorption system based on Freundlich isotherm, \(q_{e}\) represents the adsorbed MB on the adsorbent surface, in mg/g, and \(C_{e}\) denotes the MB concentration in the fluid phase, in mg/L. The Dubinin-Radushkevich (D-R) isotherm was also examined to understand the energy of adsorption, as described in Equation (3) [33]. \[q_{e}=X_{m}\exp\left(-Be^{2}\right) \tag{3}\]  
in which \(q_{e}\) represents the amount of adsorbed MB (mg/g), and \(X_{m}\) denotes the maximum capacity of adsorption (mg/g). \(B\) is the D-R constant (mol\({}^{2}\)/k\({}^{2}\)), and a constant of the mean free energy (\(E\)) of adsorption was determined by Equation (4). \[E=\frac{1}{\sqrt{2B}} \tag{4}\]  
The Polanyi potential \(\in\) can be calculated with Equation (5). \[\in=RTln\left(1+\frac{1}{C_{e}}\right) \tag{5}\]  
where \(R\) is the gas constant (J/mol), \(T\) denotes the temperature (K), and \(C_{e}\) represents the equilibrium concentration of MB (ppm). Kinetics of adsorption was studied by applying first-order and a second-order reaction kinetics. The kinetics study was only conducted on the initial adsorption, or the adsorption before reaching equilibrium, because after equilibrium the adsorption would be similar to the desorption rate, resulting a flat line curve. Moreover, the intra-particle diffusion resistance was investigated using the Weber-Morris model described in Equation (6). \[q_{t}=k_{i}t^{1/2}+C \tag{6}\]  
in which \(q_{t}\) denotes the adsorbed molecules at time t (min), and \(k_{i}\) is the intra-particle diffusion rate constant (mg/g min\({}^{1/2}\)) [34]. Data analysis and a graphic plot were conducted with Origin 6.0 Patch 4 (a trial version, OriginLab Corporation, Northampton, MA, USA).