How to Calculate Adsorption Isotherms of Particles Using Two-Parameter Monolayer Adsorption Models and Equations

Adsorption isotherm is the most important calculation to predict and analyze the various possible mechanisms that occur in adsorption process. However, until now, most studies only presented the adsorption isotherm theory, and there are no studies that explain the adsorption isotherm thoroughly and in detail from theory to calculation. Therefore, this study contains guidelines for selecting the type of adsorption isotherm to describe the entire adsorption data set, which is featured by the ten most common adsorption isotherms. The steps of how to analyze the two-parameter monolayer adsorption are presented. This study is expected to provide clear and useful information for researchers who are working and studying on the adsorption process. © 2021 Tim Pengembang Jurnal UPI Article History: Received 15 Nov 2020 Revised 30 Jan 2021 Accepted 20 Feb 2021 Available online 24 Feb 2021 ____________________ Keyword: Adsorption Isotherms, Carbon, Curcumin, Education, Silica, Tungsten. Indonesian Journal of Science & Technology Journal homepage: http://ejournal.upi.edu/index.php/ijost/ Indonesian Journal of Science & Technology 6 (1) (2021) 205-234 Ragadhita, R. How to Calculate Isotherm Adsorption of Particles Using Two-Parameter...| 206 DOI: https://doi.org/10.17509/ijost.v6i1.32354 pISSN 2528-1410 eISSN 2527-8045


A B S T R A C T S A R T I C L E I N F O
Adsorption isotherm is the most important calculation to predict and analyze the various possible mechanisms that occur in adsorption process. However, until now, most studies only presented the adsorption isotherm theory, and there are no studies that explain the adsorption isotherm thoroughly and in detail from theory to calculation. Therefore, this study contains guidelines for selecting the type of adsorption isotherm to describe the entire adsorption data set, which is featured by the ten most common adsorption isotherms. The steps of how to analyze the two-parameter monolayer adsorption are presented. This study is expected to provide clear and useful information for researchers who are working and studying on the adsorption process.

INTRODUCTION
Adsorption is a surface phenomenon that involves adhesion of atoms, ions or molecules from a gas, liquid, or dissolved solid on a surface of substance. The atoms, ions or molecules that attached on the solid surface is the adsorbate, and the place where the adsorbate accumulates is called the adsorbent. This process creates a film of the adsorbate on the surface of the adsorbent. Definition of adsorption is different from absorption. The absorption involves a fluid (as the absorbate) is dissolved by or permeates a liquid or solid (the absorbent), and the process involves the whole volume of the material. Illustration from the definition of adsorbate and adsorbent is presented in Figure 1.
Adsorption divided into two types based on molecular interactions: physical and chemical adsorptions (Al-Ghouti & Da'ana, 2020; Kong & Adidharma, 2019). Adsorption process is widely applied and well-practiced in water treatment, purification, and separation processes. This process is also one of the most effective and promising techniques, supported by facile, technically feasible, and economical processes (Rahmani & Sasani, 2016;Hegazi, 2013).
One of the important factors in the adsorption is adsorption isotherm. The relationship in the adsorption isotherm explains the phenomena and interactions between adsorbate and adsorbent. Generally, the adsorption performance can be predicted by modeling the adsorption isotherm data because the adsorption isotherm model can provide information about the adsorbent capacity, the adsorption mechanism, and the evaluation of the adsorption process performance (Nandiyanto et al., 2020a;Anshar & Raya, 2016). In previous studies, we have performed isotherm analysis on various adsorbent systems (Nandiyanto et al., 2020a;Nandiyanto et al., 2020b;Nandiyanto et al., 2020c;Nandiyanto et al., 2020d). In this study, we used the most widely applied isotherm models to evaluate adsorption performance, such as Langmuir, Freundlich, Temkin, Dubinin-Radushkevich, Florry-Huggins, Fowler-Guggenheim, Hill-Deboer, Jovanovic, Harkin-Jura, and Halsey, while other researches only described the theory and the calculation method was not discussed deeply. This study was also completed with the calculation strategies for getting the parameters in the adsorption isotherm.

ADSORPTION ISOTHERM THEORY 2.1. Langmuir Isotherm
Langmuir isotherm defines that the maximum adsorbent capacity occurs due to the presence of a single layer (monolayer) of adsorbate on the adsorbent surface. There are four assumptions in this type of isotherm, namely (Langmuir, 1918): a. The molecules are adsorbed by a fixed site (the reaction site at the adsorbent surface). b. Each site can "hold" one adsorbate molecule. c. All sites have the same energy. d. There is no interaction between the adsorbed molecules and the surrounding sites. Adsorption process form monolayer. Illustration of monolayer formation during adsorption is shown in Figure 1 (a).
Langmuir isotherm model is represented by equation (1): where Qe is the amount of adsorbed adsorbate molecule per gram of adsorbent (mg/g), Qmax is the capacity of the adsorbent monolayer (mg/g), Ce is the adsorbate equilibrium concentration (mg/L), and KL is the Langmuir adsorption constant.
The important factor in the Langmuir isotherm is the dimensionless constant or separation factor (RL) (Langmuir, 1918) which is expressed by equation (2): This separation factor has the following values: (i) RL > 1, unfavorable adsorption process (allows the adsorption process to occur, most desorption processes occur). (ii) RL = 1, linear adsorption process (depending on the amount adsorbed and the concentration adsorbed). (iii) RL = 0, Irreversible adsorption process (strong adsorption). 0 < RL < 1, Favorable adsorption process (normal adsorption).

Freundlich Isotherm
Freundlich isotherm describes a physical type of adsorption in which the adsorption occurs in several layers and the bonds are not strong (multilayer). Multilayer formation is illustrated in Figure 1 (b). Freundlich isotherm also assumes that the sites of adsorption are heterogeneous (Dada et al., 2012). The empirical relationship for expressing Freundlich isotherm is given in equation (3): where Kf is Freundlich constant, Ce is the concentration of adsorbate under equilibrium conditions (mg/L), Qe is the amount of adsorbate absorbed per unit of adsorbent (mg/g), and is the value indicating the degree of linearity between the adsorbate solution and the adsorption process (Dada et al., 2012). The value of n is described as follows: (i) = 1, linear adsorption. (ii) < 1, adsorption process with chemical interaction. (iii) > 1, adsorption process with physical interaction. (iv) Favorable adsorption process is declared when 0 < 1/n < 1, and a cooperative adsorption process occurs when 1/n > 1.

Temkin Isotherm
Temkin isotherm assumes three postulates, namely that the adsorption heat decreases linearly with increasing surface adsorbent coverage, the adsorption process assumes a uniform binding energy distribution on the adsorbent surface, and the adsorption interaction involves the interaction between adsorbate-adsorbent (Romero-Gonzales et al., 2005). Temkin isotherm is given in equation ( where BT is the adsorption heat constant (if the BT < 8 kJ/mol, the adsorption process occurs physically), AT is the binding equilibrium constant, and T is the absolute temperature.

Dubinin-Radushkevich Isotherm
Dubinin-Radushkevich isotherm expresses the adsorption process on the adsorbent which has a pore structure or adsorbent which has a heterogeneous surface and expresses the adsorption free energy. its adsorption process is based on micropore volume filling (Romero-Gonzales et al., 2005). Dubinin-Radushkevich isotherm is written in equation (5): where β is the Dubinin-Radushkevich isotherm constant, QS refers to the saturation capacity of theoretical isotherms, and Ɛ is the Polanyi potential (J/mol) is calculated using equation (6): To calculate the free energy of adsorption per adsorbate molecule, it is calculated using equation (7): where Ce is the equilibrium concentration of solute and E is the adsorbate energy per molecule as the energy needed to remove molecules from the surface. The equation describes: (i) E < 8 kJ/mol, physical adsorption.

Jovanovic Isotherm
Jovanoic isotherm is based on the assumptions found in the Langmuir model, without allows some mechanical contact between the adsorbate and the adsorbent (Ayawei et al., 2017). The linear correlation of the Jovanovic model is shown in equation (8): where Qe is the amount of adsorbate in the adsorbent at equilibrium (mg/g), Qmax is the maximum uptake of adsorbate, and KJ is the Jovanovic constant.

Halsey Isotherm
Halsey isotherm evaluates a multililayer adsorption system (Dada et al., 2012). The Halsey model follows equation (9): where KH dan n are the Halsey model constants.

Harkin-Jura Isotherm
Harkin-Jura isotherm describes that the adsorption occurring on the adsorbent surface is a multilayer adsorption because the adsorbent has a heterogeneous pore distribution (Ayawei et al., 2017). This model is expressed by equation (10): where value is related to specific surface area of adsorbent and are the Harkin Jura isotherm constants.
The modification of the Harkin-Jura equation (   Then, the specific surface area of adsorbent is determined by equation (12).
For surface area calculations, Table 1 shows several of q value.

Flory-Huggins Isotherm
Flory-Huggins isotherm takes into account the degree of surface coverage of the adsorbate on the adsorbent. This isotherm also assumes that the adsorption process occurs spontaneously (Saadi et al., 2015). Flory-Huggins isotherm is expressed by equation (13):  (14): The negative sign on the value ΔG⁰ confirms that the adsorption process is spontaneous, which is a function of temperature (T).

Fowler-Guggenheim Isotherm
Fowler-Guggenheim isotherm suggests that there is a lateral interaction at a set of localized sites with weak interactions (Van der Waals interaction effect) between adsorbed species at neighboring sites (Hamdaoui and Naffrechoux, 2007). The empirical relationship of Fowler-Guggenheim model is expressed by equation (15): where KFG is the constant, W (kJ/mol) for the adsorbed adsorbate at the active site representing the interaction between the adsorbate and the adsorbent, Ce is the equilibrium constant, W is the empirical interaction energy between two adsorbed molecules at the adjacent neighboring site (kJ/mol), and  is the fractional coverage of the surface. The empirical interaction energy (W) has the following value:
The quantity adsorbed by the unit mass of the adsorbent at equilibrium (Qe) is calculated using equation (17): where C0 is the initial concentration (mg⁄L), Ce is the concentration at equilibrium (mg⁄L), m is the mass of the adsorbent (grams), and V is the volume of the adsorbate solution (L).

MATERIAL AND METHOD
There were several materials used as adsorbents which were the result of conversion from agricultural waste such as carbon converted from peanut shells (CPS), carbon obtained from rice husks (CRH), silica from rice husks (SRH). Inorganic materials such as tungsten (WO3) was also used as adsorbents in this study. Detailed information on how the process of converting agricultural waste into carbon and silica and fabrication process of WO3 was presented in our previous studies (Ragadhita et al., 2019;Faindini et al., 2020;Nandiyanto et al., 2020a;Nandiyanto et al., 2017;Nandiyanto et al., 2020e). The adsorbate solution used as an experimental model was curcumin solution. Information on curcumin production was carried out in the same manner as provided in our previous study (Ragadhita et al., 2019;Nandiyanto et al., 2020f).
In general, the adsorption process was carried out in the following steps: specific mass amount of each CPS, CRH, SRH, and WO3 adsorbents were put into 200 mL of curcumin solution with variations concentrations of 20, 40, 60, 80 ppm at constant pH and temperature. The solution mixture was mixed in a borosilicate batch (glass reactor) with a capacity of 400 mL and has dimensions of 10 and 8 cm, respectively, for height and diameter.
Then, the solution mixture was stirred at 1000 rpm for 1 h. Next, the solution mixture was filtered. The filtrate was measured and analyzed with a UV-VIS spectrophotometer (Model 7205; JENWAY; Cole-Parmer; US; analyzed at wavelengths between 200 and 600 nm).
After the adsorption process was completed, the next step was to evaluate the adsorption process. Several adsorption isotherm models were used for the analysis of the adsorption process including Langmuir, Freundlich, Temkin, Dubinin-Radushkevich, Florry-Huggins, Fowler-Guggenheim, Hill-Deboer, Jovanovic, Halsey, and Harkin-Jura isotherms.

Linearization and Curve Plotting to Obtain Two-Parameter Adsorption Isotherms from Several Models
The adsorption process includes a series of adsorption experiments to calculate the adsorption parameters used to express the adsorption equilibrium model. Several adsorption isotherm models were used to evaluate the adsorption process in this study are Langmuir, Freundlich Guggenheim, Hill-Deboer, Jovanovic, Harkin-Jura, and Halsey isotherms. The calculation of the adsorption isotherm is carried out through data fitting to obtain a linear equation (y = mx + c). Then, we also need to consider the value of R 2 . The greater R 2 relates to similarity data to the model proposed. The fitting of this data is adjusted to the linear expression of the mathematical model of each adsorption isotherm. From the results of the data fitting, several parameters in the adsorption process were obtained. The phenomena occurring during the adsorption were predicted. Information regarding curve data fitting, calculations, and parameters of the adsorption isotherm model that must be analyzed is presented in Table 2.

Experimental Results from The Adsorption Process
Data from the adsorption process of curcumin solution using CPS, CRH, SRH, and WO3 adsorbents are presented in Table 3. Table 3 shows the adsorption data of curcumin solution for data fitting using twoparameter isotherm adsorptions: Langmuir, Freundlich, Temkin, Dubinin-Radushkevich, Jovanovic, Halsey, Harkin-Jura, Flory-Huggins, Fowler-Guggenheim, and Hill-Deboer isotherm.

Plotting Analysis for Adsorption
Isotherms using a Two-Parameter Adsorption Isotherm

Langmuir
Langmuir model adsorption parameters were obtained using equation (1) as presented as 1 = 1 1 + 1 . To get the Langmuir model parameters, we need to convert Ce and Qe values into the form of 1 and 1 , which are used for fitting data (see Table 2). The curves of fitting data result from equation (1) are presented in Figures 2 (a-d).
The result of fitting data was used to determine the adsorption parameters. The result of data fitting in the form of a gradient obtained is the 1 × value and the intercept is the 1 value. Table 4 show parameters of the Langmuir model using CPS, CRH, SRH, and WO3 adsorbents.
Qmax and KL in Table 4 are the maximum monolayer adsorption capacity and Langmuir adsorption constant, respectively. Based on Qmax value, adsorption process using CRH adsorbent is very good due to it has the highest maximum monolayer adsorption capacity (Qmax) value than others. Langmuir adsorption constant (KL) shows the degree adsorbate-adsorbent interaction. Higher KL value indicating strong adsorbate-adsorbent interaction while smaller KL value indicating weak interaction between adsorbate molecule and adsorbent surface. The KL value for all adsorption systems show a relatively small value means weak interaction between the absorbent and adsorbate molecules due to the active site only adsorb one molecule. Plotting analysis shows that CPS, SRH, and WO 3 have relatively high correlation value (R 2 > 0.70) than CRH, informing that CPS, SRH, and WO3 are good represented by Langmuir isotherm.

Freundlich
The Freundlich model adsorption parameters were obtained using equation (3) as presented as ln = ln + 1 ln . To get the Freundlich model parameters, we need to convert and values into the form of lnCe and lnQe, which are used for fitting data (see Table 2). The curves of data fitting result are presented in Figures 3 (a-d). The result of fitting data also used to determine adsorption parameters. The result of data fitting in the form of a gradient obtained is 1 n value, and the intercept is lnKF value. Table 5 shows parameter results of Freundlich model using CPS, CRH, SRH, and WO3 adsorbents. Freundlich isotherm is good represent of SRH and WO3 adsorption systems than CPS and CRH adsorption system, this is confirmed by the R 2 value of higher than 0.70. Thus, SRH and WO3 adsorption system were assumed that adsorption process occurs in heterogeneous surface in multilayer form with weak adsorbate and adsorbent interaction.

Temkin
Temkin model parameters were obtained using equation (4) as presented as = ln + ln . To get the Temkin model parameters, we need to convert Ce and Qe values into the forms of ln Ce and Qe, which are used for data fitting (see Table 2). The curves of data fitting result are presented in Figures 4 (a-d). The result of fitting data also used to determine adsorption parameter. The result of data fitting in the form of a gradient obtained is the value to calculate value and the intercept is the value. Table 6 shows parameter results of Temkin model using CPS, CRH, SRH, and WO3 adsorbents. AT value in Table 6 is the Temkin equilibrium constant corresponding to the maximum binding energy where the high AT shows attractive interaction between adsorbateadsorbent system. The AT value for all adsorption systems shows a relatively small value means less affinity between the absorbent and adsorbate molecules since there are physical interaction dominate that confirmed by BT parameter. Physical interaction only involves more interaction weak, for example in the form of adsorbate polarization with adsorbent. Base on correlation coefficient value (R 2 > 0.70), SRH and WO3 are suitable with Temkin isotherm, while CPS and CRH adsorption system are not suitable. Temkin isotherm informs that adsorption is characterized by uniform distribution adsorbate to adsorbent surface.

Dubinin-Radushkevich
Dubinin-Radushkevich model adsorption parameters were obtained using equation (5) as follow as ln = ln − ( Ɛ 2 ). To get the Dubinin-Radushkevich model parameters, we need to convert Qe into the form of lnQe value and looking for the ² value which are used for data fitting (see Table 2). The curves of data fitting result are presented in Figures 5 (a-d). The result of data fitting also used to determine adsorption parameter. The result of data fitting in the form of a gradient obtained is the value to calculate value. Table 7 shows parameter results of Dubinin-Radushkevich using CPS, CRH, SRH, and WO3 adsorbents. Parameter in Table 7 is Dubinin-Radushkevich isotherm constant related saturation capacity. High value shows high adsorption capacity. Based on parameter, WO3 has higher value while CRH has smaller value than others. value influenced by pore volume. The larger pore volume impact on highest maximum binding energy value. Plotting data of Dubinin-Radushkevich show that SRH and WO3 adsorption system have the best correlation coefficient since correlation coefficient value is high (R 2 > 0.70). Thus, SRH and WO3 adsorption system are considered by Dubinin-Radushkevich have adsorbent size proportional to the micropore size.

Jovanovic
Jovanovic model adsorption parameters were obtained using equation (8) as presented as = − . To get the Jovanovic model parameters, we need data and we need to convert into the form of which are used for data fitting (see Table 2). The curves of fitting data are presented in Figures 6 (a-d). The result of fitting data also used to determine adsorption parameter. The result of data fitting in the form of a gradient obtained is the value and intercept is the value. surface area and pore. The Jovanovic isotherm reflects well the entire adsorption system (i.e., CPS, CRH, SRH, and WO3) which is shown from the relatively high correlation coefficient value of each adsorption system (R 2 > 0.70). Compatibility with Jovanovic's model indicates that there is existence of monolayer adsorption.  To get the Halsey model parameters, we need to convert and data into the form of and , which are used for data fitting (see Table 2). The curves of data fitting result are presented in Figures 7 (a-d). The result of data fitting also used to determine the adsorption parameter. The result of data fitting in the form of a gradient obtained is the 1 value and intercept is the 1 value. Table 9 shows parameter results of Halsey using CPS, CRH, SRH, and WO3 adsorbents. KH and n in Table 9 are the Halsey isotherm constants. Halsey isotherm reflect good adsorption system for SRH and WO3 since (R 2 > 0.70) is relatively high. While, CPS and CRH adsorption system are not suitable with Halsey isotherm. Compatibility with Halsey model due to high R 2 indicates that there is existence of multilayer adsorption. From Halsey's parameter, we can identify that the higher the adsorption capacity (Qe) correlates with the increase in the value of n.

Harkin-Jura
Harkin-Jura model adsorption parameters were obtained using equation (10) as presented as . To get the Harkin-Jura model parameters, we need to convert Ce and Qe data into the form of logCe and 1 ² which are used for data fitting (see Table 2). The curves of data fitting result are presented in Figures 8 (a-d). The result of data fitting also used to determine adsorption parameter. The result of data fitting in the form of a gradient obtained is the 1 value and intercept is the value. . For example, if we use the assumption of q value of carbon, silica, and WO3 as in Table 1, and the temperature used is room temperature (298 K), then the surface area value is presented in Table 11.

Flory-Huggins
Flory-Huggins model adsorption parameters were obtained using equation (11) as presented as = + log (1 − ). To get the Flory-Huggins model parameters, we need to convert data into the form of 0 and log (1 − ) and which are used for data fitting (see Table 2). The curves of data fitting result are presented in Figures 9 (a-d). The result of data fitting also used to determine adsorption parameter. The result of data fitting in the form of a gradient obtained is the nFH value and intercept is the logKFH value. Table 12 shows parameter results of Flory-Huggins using CPS, CRH, SRH, and WO3 adsorbents. KFH in Table  12 are the number of adsorbates occupying adsorption sites and the Flory-Huggins constant. Adsorbent SRH and WO3 have good KFH value than CPS and CRH. This condition showed SRH and WO3 have better adsorbentadsorbate interaction. Moreover, SRH and WO3 form multilayer adsorption which makes the adsorbate more attached to the adsorbent due to chemical bonds. Fowler-Huggins is poor suitable with all adsorption system (i.e., CPS, CRH, SRH, and WO3) because R 2 < 0.70.  . To get the Fowler-Guggenheim model parameters, we need to plot vs (1− ) data (see Table 2).
The curves of data fitting result are presented in Figures 10 (a-d). The result of data fitting also used to determine adsorption parameter. The result of data fitting in the form of a gradient obtained is the 2 value and intercept is the value. Table 13 shows parameter results of Fowler-Guggenheim using CPS, CRH, SRH, and WO3 adsorbents. KFG in Table 13 is Fowler-Guggenheim constant represent adsorbentadsorbate interaction. Higher KFG value indicates a good interaction between adsorbent-adsorbate. All adsorbent system shows identically small KFG value means weak interaction adsorbent-adsorbate since there are surface active site is less efficient in adsorbing the adsorbate molecules due to domination of physical interaction. Fowler-Guggenheim is poor suitable with all adsorption system (i.e., CPS, CRH, SRH, and WO3) because R 2 < 0.70.   data. The curves of data fitting result are presented in Figures 11 (ad). The result of fitting data also used to determine adsorption parameter. The result of data fitting in the form of a gradient obtained is the 2 value and intercept is the lnK1 value. Table 14 shows parameter results of a Hill-Deboer using CPS, CRH, SRH, and WO3 adsorbents. K1 in Table 14 is the Hill-Deboer constant interaction between adsorbent and adsorbate. Higher K1 value indicates a good interaction between adsorbent-adsorbate.
However, all adsorbents system indicate a small value of K 1 means poor interaction between adsorbent-adsorbate since active site is not effective in carrying out adsorption process. Hill-Deboer is poor suitable with all adsorption system (i.e., CPS, CRH, SRH, and WO3) because R 2 < 0.70.

Approximately Isotherm Model
The experimental data of the adsorption process in Table 2 were analyzed through regression analysis to match the linear correlation of the adsorption isotherm mathematical models. Fitting data based on the plotted way in Table 1 for each adsorption model is used to determine the adsorption parameters that correspond to each adsorption model. The parameters obtained after the data fitting process are summarized in Tables 3-12. Figures 2-11 present the plotting of the experimental results. Figures 2 (a-d) show the fitting data based on the Langmuir adsorption isotherm. The Langmuir isotherm for the study of the adsorption of curcumin solution with the and CRH show poor adsorption characteristics because it gives a low correlation coefficient value (R 2 <1) is too far closer to the 0.90. Meanwhile, adsorption of CPS, SRH, and WO3 adsorbents matches the Langmuir model with a coefficient correlation (R 2 > 0.90). This means that the adsorption system using CRH does not allow monolayer formation. However, the reverse phenomenon is for the adsorption system using cps, SRH, and WO3 adsorbents. The analysis of the separation factor (RL) shows RL value in the range between 0 and 1 for all cases which indicates that the adsorption process has favorable adsorption characteristics. Figures 3 (a-d) show the Freundlich isotherm curve. Freundlich isotherm curve shows very small correlation coefficient value for adsorption system using CPS and CRH adsorbent compared to adsorption system with SRH and WO3 adsorbent. This model suggests that the adsorption system with SRH and WO3 fits into the Freundlich model, which allows the formation of a multilayer structure. Figures 4 (a-d) are the linear curve of the Temkin adsorption. The adsorption system with CPS and CRH adsorbents does not match with the Temkin model isotherm because the R 2 value is less than 0.90. While, the adsorption system with SRH and WO3 adsorbents are compatible with Temkin isotherm model.   Figure 11. Hill-Deboer isotherm model for adsorption system using a) CPS, b) CRH, c) SRH, and d) WO3 adsorbents Figures 5 (a-d) are an analysis fitting based on the Dubinin-Radushkevich model. Based on the correlation coefficient value, the adsorption system with SRH and WO3 adsorbents are compatible with the Dubinin-Radushkevich model, whereas the adsorption system with CPS and CRH adsorbents does not. Therefore, the adsorption system with CPS and CRH adsorbents was not well reflected by the Dubinin-Radushkevich isotherm model. The Dubinin-Radushkevich isotherm reflects a good fit for the SRH and WO3 adsorbent. Figures 6 (a-d) are the isotherm curve of the Jovanovic model. Based on the analysis of the coefficient correlation value, the Jovanovic isotherm model is the most suitable and most reflective of all cases of adsorption systems because the value of R 2 > 0.9. Figures 7 (a-d) are an analysis fitting based on the Halsey model. The adsorption system that is most suitable for this model is the adsorption system with SRH and WO3 adsorbents. Meanwhile, the Halsey model is not suitable in representing the adsorption system with CPS and CRH. Figures 8 (a-d) show the fitting analysis using the Harkin-Jura adsorption isotherm. The adsorption system with CPS and CRH adsorbent are the least suitable because the R 2 value is <0.9. The incompatibility with the Harkin-Jura isotherm represents that the adsorption process does not follow a multilayer adsorption model. On the other hand, the Harkin-Jura isotherm is compatible with the adsorption system with SRH, and WO3 adsorbents because the R 2 value is close to 0.9 which allows the formation of multilayers on the adsorbent surface. Figures 9 (a-d), 10 (a-d) adsorption cases (i.e., CPS, CRH, SRH, and WO3), meaning that they reflect an adsorption system that is not suitable for all cases.

Discussion
Based on the R 2 value for each adsorption model, the adsorption system in CPS is compatible with Langmuir, Harkin-Jura, and Jovanovic isotherm models. CRH adsorbents is only compatible with the Jovanovic model. Langmuir and Jovanovic model have same assumption that adsorption process occurs by forming a monolayer structure without the presence of adsorbate-adsorbent lateral interactions for CPS and CRH adsorbents (Ayawei et al., 2017). Besides assuming the adsorption is monolayer, the adsorption system with the CPS adsorbent is also assumed to have adsorption by forming a multilayer. This is confirmed because it fits the Harkin-Jura model.
For adsorption systems with SRH and WO3 adsorbents, both of them are incompatible with the Harkin Jura, Flory Huggins, Fowler Guggenheim, and Hill-Deboer models. Meanwhile, the other six models are suitable. The adsorption system with the SRH adsorbent followed suit with the order of the Temkin > Dubinin-Radushkevich > Freundlich > Halsey > Langmuir > Jovanovic models. Meanwhile, the order of compatibility of the adsorption system with the WO3 adsorbent is summarized as follows Dubinin Radushkevich > Langmuir > Freundlich > Halsey > Jovanovic > Temkin models. The adsorption system with SRH and WO3 adsorbents has a good correlation with the Langmuir model informing the monolayer adsorption process, in which the adsorbate molecules are distributed on all adsorbent surfaces (Langmuir, 1918). This monolayer adsorption process is also confirmed by the Jovanovic model, which describes monolayer adsorption without the presence of lateral interactions (Ayawei et al., 2017). In the Langmuir model, adsorption is advantageous or not explained by the RL value, where the resulting RL value is between 0 and 1, which indicates the adsorption process is favorable. Meanwhile, Freundlich, Temkin, Dubinin-Radushkevich, and Halsey isotherms support multilayer adsorption processes. The degree of linearization between adsorbate and adsobent is indicated by the values of n < 1 and 1/n > 1 in the Freundlich model, the values show that adsorption follows cooperative adsorption with chemical interactions. Cooperative adsorption informs the occurrence of chemical and physical interactions at one time (Liu, 2015). The chemical interaction in the adsorption system is in accordance with the parameter value BT > 8 J/mol in the Temkin model. The Dubinin-Radushkevich model also confirmed the physical interaction because the parameter value E < 8 kJ/mol.

Prediction Model for CPS Adsorbent
The adsorption system uses CPS adsorbent following the Langmuir and Jovanovic model which assumes monolayer adsorption. The CPS adsorption system is also compatible with the Harkin-Jura model which assumes multilayer adsorption. Adsorption system using CPS shows weak physical interaction (adsorbent-adsorbate interaction) and chemical interaction (adsorbate-adsorbate interaction). Prediction model for CPS adsorbent is illustrated in Figure 12.

Prediction Model for CRH Adsorbent
The adsorption system uses CRH adsorbent following the Langmuir and Jovanovic model which assumes monolayer adsorption with weak interaction between adsorbate-adsorbent (physical interaction) since the KL has small values based on Langmuir. Prediction model for CPS adsorbent is illustrated in Figure 13. Figure 13. Prediction model for system adsorption using CRH adsorbent

Prediction Model for SRH and WO3 Adsorbents
The adsorption system uses SRH and WO3 adsorbents following monolayer and multilayer adsorption with weak chemical interaction (adsobate-adsorbate interaction) and physical interaction (adsorbateadsorbent interaction) since the KL and AT have small values based on Langmuir and Temkin parameter respectively. The multilayer adsorption process results from the presence of a heterogeneous structure in the adsorbent which is assumed by the Temkin, Dubinin-Radushkevich, Harkin-Jura, and Halsey isotherm where filling pores occur (Dada et al., 2012). Prediction model for CPS adsorbent is illustrated in Figure 14.

CONCLUSION
This study demonstrates a simple way of understanding the calculation of the results of the adsorption data analysis by matching and reviewing the adsorption data in several adsorption isotherm models and demonstrating its application for the adsorption system of various adsorbents. The criteria for selecting a suitable and optimal adsorption isotherm model for the adsorption process have also been discussed in this study. Based on our study, the adsorption system with carbon obtained from peanut shells and carbon obtained from rice husks followed the Jovanovic isotherm. Adsorption system with silica adsorbent extracted from rice husk and WO3 following Langmuir, Freundlich, Temkin, Dubinin-Radushkevich, Halsey, Jovanovic isotherms.

AUTHORS' NOTE
The authors declare that there is no conflict of interest regarding the publication of this article. Authors confirmed that the paper was free of plagiarism.