Solubility of Rosmarinic Acid in Supercritical Carbon Dioxide Extraction from Orthosiphon stamineus Leaves

: Rosmarinic acid (RA) is present in a broad variety of plants, including those in the Lamiaceae family, and has a wide range of pharmacological effects, particularly antioxidant activity. To extract RA from Orthosiphon stamineus (OS) leaves, a Lamiaceae plant, a suitable extraction process is necessary. The present study used a green extraction method of supercritical carbon dioxide (SCCO 2 ) extraction with the addition of ethanol as a modiﬁer to objectively measure and correlate the solubility of RA from OS leaves. The solubility of RA in SCCO 2 was determined using a dynamic extraction approach, and the solubility data were correlated using three density-based semi-empirical models developed by Chrastil, del Valle-Aguilera, and Gonzalez. Temperatures of 40, 60, and 80 ◦ C and pressures of 10, 20, and 30 MPa were used in the experiments. The maximum RA solubility was found at 80 ◦ C and 10 MPa with 2.004 mg of rosmarinic acid/L solvent. The RA solubility data correlated strongly with the three semi-empirical models with less than 10% AARD. Furthermore, the fastest RA extraction rate of 0.0061 mg/g min − 1 was recorded at 80 ◦ C and 10 MPa, and the correlation using the Patricelli model was in strong agreement with experimental results with less than 15% AARD.

Rosmarinic acid (RA) is caffeic acid and 3,4-dihydroxyphenyl lactic acid ester found in a variety of Lamiaceae species including lemon balm, peppermint, oregano, rosemary, sage, and thyme [14][15][16]. It is naturally synthesized in plants via the shikimate/phenylpropanoid pathway [17]. Caffeic acid ester compounds have poor lipophilicity and inhibit intracellular entrance. According to Akowuah and Zhari [18] and Abdul Aziz [19], RA is a major polyphenol found in OS leaves. Among phenolic compounds, RA is structurally interesting due to its strong natural antioxidant [20] and its variety of effects such as anti-inflammatory, antibacterial, antiviral, antidiabetic, and antiallergic properties [21,22]. Shekarchi [23] reported that RA has greater antioxidant activity than vitamin E. Because of these benefits, RA is frequently employed in the food, cosmetics, and pharmaceutical industries [24]. As a result, the demand for RA has skyrocketed, spurring the development of efficient extraction technologies from its natural sources, particularly OS leaves.
Supercritical carbon dioxide (SCCO 2 ) extraction has been widely explored for the extraction of polyphenols such as rosmarinic acid, squalene, catechin, lycopene, and others from diverse plant-derived matrices and has been proven to be a promising technology [25][26][27][28]. SCCO 2 extraction has a mild critical temperature, T c of 31.1 • C, and a critical pressure, P c of 7.38 MPa. A moderate extraction temperature of 40 to 80 • C may be helpful in avoiding thermal damage when isolating a high-purity bioactive compound. By adjusting the extraction parameters of temperature and pressure, SCCO 2 has outstanding properties such as high density, high dissolving power, high diffusivity, low surface tension, and low viscosity [28,29]. Furthermore, SCCO 2 facilitates the process of separating the extract by depressurizing it, resulting in a solvent-free extract. Due to these advantages, SCCO 2 extraction is highly valued in replacing the organic solvents in traditional extraction processes.
The concentration of RA extracted using SCCO 2 from dragonhead (Dracocephalum moldavica) seed was reported to be approximately 1.20 mg/g [30]. Meanwhile, Bakota [31] extracted 28.4 mg RA/g from sage (Salvia officinalis) leaves at 80 • C and 55.2 MPa. In contrast, Lefebvre [32] reported that RA from rosemary was not extracted in pure SCCO 2 , but with the addition of 10% ethanol yielded approximately 78 mg/g of RA. Al-Suede [4] discovered a similar pattern in which RA is not present in the SCCO 2 extract yield of OS leaves. This is due to the fact that RA is a hydrophilic or polar compound that has a strong attraction to water or polar solvent molecules. Meanwhile, CO 2 is a non-polar solvent and has a disadvantage in extracting polar compounds. Thus, adding a small amount of cosolvent or modifier to SCCO 2 can significantly improve both its solvent power and polarity. Modifiers that are commonly used include benzene, methylene chloride, petroleum ether, hexane, acetone, methanol, ethanol, toluene, and water as typical co-solvents [33][34][35]. Because of the hazardous nature of most organic solvents and the concomitant challenge of completely eliminating modifier residue from processed material, the function of a modifier has been limited in the food and pharmaceutical industries. Furthermore, the presence of a modifier in SCCO 2 may increase solute melting point depressivity, which is associated with a reduction in the system's upper critical endpoint pressure [36]. Dipole-dipole interactions and hydrogen bonds created between the solute and the modifier significantly increase the solute's solubility, according to Huang [37] and Bitencourt [38]. Therefore, ethanol is a polar solvent in nature due to the presence of a hydroxyl group and has been authorized in food industries due to being less harmful than other organic solvents [39,40]. As a consequence, our earlier investigation of OS leaves extraction using SCCO 2 -assisted ethanol revealed that the concentration of RA is greatest at 931.44 mg/kg, followed by sinensetin and isosinensetin at 469.54 and 419.07 mg/kg, respectively [19].
A thorough understanding of solubility data and compound behavior in SCCO 2 is essential for determining the feasibility of supercritical separation of the target compound and defining suitable operating conditions. The correct information about the solute solubility is required for the successful application of SCCO 2 [41]. Therefore, much research has sought to offer information on the solubility of various bioactive compounds in SCCO 2 [41][42][43][44][45][46]. To date, there have been no published studies on the solubility of RA in the SCCO 2 system. There are numerous ways to determine the solubility of a compound in SCCO 2 . A dynamic approach is the most commonly used by researchers to calculate solubility. This method has been proven to be effective since it allows for the collection of a large number of fractionation data in a short amount of time. However, because acquiring equilibrium or solubility data at high temperatures and pressures is tedious and expensive, predictive models are critical.
Various mathematical models have been established, including the equation of state (EOS) and semi-empirical models. Because thermodynamic data are limited, the latter is significantly more recommended and favored. Rosales-García [47] observed squalene solubility in SCCO 2 at various temperatures and pressures. They also used a number of semi-empirical models with an average absolute relative deviation of less than 10% (AARD%) to predict the measured solubility data. In another work, the solubility of cinnamic acid in SCCO 2 was obtained via a dynamic approach at various temperatures and pressures [48]. The authors used 10 density-based semi-empirical models of Chrastil [49], Adachi-Lu [50], Kumar-Johnston [51], Sung-Shim [52], Mendez-Santiago-Teja [53], Bartle [54], Gonzalez [55], Sovova [56], Tang [57], and Sauceau [58]. They reported that these models showed great agreement with the experimental data for less than 10% of AARD. Zhan [59], Jin [60], Wei [61], and Jia [62] showed that several semi-empirical models were the most accurate in forecasting compound solubility in SCCO 2 with the lowest AARD%. This is due to the fact that these models have the benefit of fitting all experimental data for each solute with as few as three to six parameters. These models are also beneficial for data correlations and testing the model fit due to their simplicity, as previously reported [63].
For the first time, the solubility data of RA in assisted-ethanol SCCO 2 systems at varied temperatures (40, 60, and 80 • C) and pressures (10, 20, and 30 MPa) were correlated using three well-known density-based semi-empirical models of Chrastil, del Valle-Aguilera (dVA), and Gonzalez. The versatility of these models in terms of the number of configurable parameters and their capacity to predict thermodynamic parameters such as total enthalpy, enthalpy of vaporization, and enthalpy of solvation were the primary reasons for their consideration. Furthermore, the influence of co-solvent in the system can be evaluated. The semi-empirical models are widely used in the previous study due to its accuracy in correlating with solubility data in the SCCO 2 extraction process. In addition, the mass transfer coefficient and RA extraction rate in the ethanol-assisted SCCO 2 system were calculated concurrently using the Patricelli model.

Chemicals and Materials
All of the chemicals and reagents were analytical reagent grade. Kras Instrument and Services (Johor, Malaysia) supplied 99.99% pure carbon dioxide. Sigma-Aldrich, Darmstadt, Germany, provided the RA reference standard. The physical properties of RA were predicted using the group contribution method generated from the ICAS 17 software and are listed in Table 1. Analytical-grade ethanol, acetonitrile, isopropyl alcohol, orthophosphoric acid, and sodium dihydrogen phosphate anhydrous phosphate buffer were utilized. Dry OS aerial parts were provided by Bioalpha Holdings Berhad (Selangor, Malaysia). The leaves were segregated from the aerial part and triturated to a mean particle size of 400 to 500 µm. To avoid contamination, the ground samples were packed and stored in a refrigerator at −20 • C [64]. Table 1. Properties of rosmarinic acid.

Properties Rosmarinic Acid
Chemical Structure

Supercritical Carbon Dioxide (SCCO2) Extraction
SCCO2 extraction at the laboratory scale was carried out at temperatures and pressures of 40, 60, and 80 °C and 10, 20, and 30 MPa, respectively, using ethanol as a modifier. Figure 1 depicts a schematic diagram of the extraction process based on previous work [19,65,66]. The apparatus setup consists of a carbon dioxide (CO2) tank, a circulating water bath (WiseCircu), a CO2 pump (Lab Alliance, Supercritical 24: Constant flow with dualpiston pump), a pressure gauge, an oven with a 10 mL extraction vessel, and a back pressure regulator (BPR) (Jasco, Model BP-2080, Pfungstadt, Germany) with a restrictor valve. For a modifier, a 10 mL Series II pump (Scientific Systems, Inc., Woburn, MA, USA) was employed. The tubing system used was 1/16 inches in diameter. The temperature of the process was set in the extraction chamber or oven and pressure was controlled by BPR. The restrictor valve released the pressure when the system achieved the desired pressure by depressurization.

Supercritical Carbon Dioxide (SCCO 2 ) Extraction
SCCO 2 extraction at the laboratory scale was carried out at temperatures and pressures of 40, 60, and 80 • C and 10, 20, and 30 MPa, respectively, using ethanol as a modifier. Figure 1 depicts a schematic diagram of the extraction process based on previous work [19,65,66]. The apparatus setup consists of a carbon dioxide (CO 2 ) tank, a circulating water bath (WiseCircu), a CO 2 pump (Lab Alliance, Supercritical 24: Constant flow with dual-piston pump), a pressure gauge, an oven with a 10 mL extraction vessel, and a back pressure regulator (BPR) (Jasco, Model BP-2080, Pfungstadt, Germany) with a restrictor valve. For a modifier, a 10 mL Series II pump (Scientific Systems, Inc., Woburn, MA, USA) was employed. The tubing system used was 1/16 inches in diameter. The temperature of the process was set in the extraction chamber or oven and pressure was controlled by BPR. The restrictor valve released the pressure when the system achieved the desired pressure by depressurization.

Supercritical Carbon Dioxide (SCCO2) Extraction
SCCO2 extraction at the laboratory scale was carried out at temperatures and pressures of 40, 60, and 80 °C and 10, 20, and 30 MPa, respectively, using ethanol as a modifier. Figure 1 depicts a schematic diagram of the extraction process based on previous work [19,65,66]. The apparatus setup consists of a carbon dioxide (CO2) tank, a circulating water bath (WiseCircu), a CO2 pump (Lab Alliance, Supercritical 24: Constant flow with dualpiston pump), a pressure gauge, an oven with a 10 mL extraction vessel, and a back pressure regulator (BPR) (Jasco, Model BP-2080, Pfungstadt, Germany) with a restrictor valve. For a modifier, a 10 mL Series II pump (Scientific Systems, Inc., Woburn, MA, USA) was employed. The tubing system used was 1/16 inches in diameter. The temperature of the process was set in the extraction chamber or oven and pressure was controlled by BPR. The restrictor valve released the pressure when the system achieved the desired pressure by depressurization.

Quantification of RA
The amount of RA extracted from OS leaves was measured using High-Performance Liquid Chromatography (HPLC). The complete analysis approach has also been previously disclosed here [19]. A calibration curve was used to examine the quantification of bioactive chemicals by graphing standard concentrations of the standards (20,40,60,80, and 100 ppm) vs. its peak areas. The RA standard curve is Y = 55.3X, with a regression correlation (R 2 ) of 0.995 and a retention duration of 1.859 min.

Solubility Measurement and Correlation
A dynamic extraction method was used to extract RA from OS leaves. The initial slope of the extraction curve known as the constant extraction rate (CER) phase on the graph of solute concentration vs. solvent used was used to calculate the experimental solute solubility. To anticipate the solubility behavior of RA in SCCO 2 , three density-based semiempirical models were utilized to correlate the experimental solubility data. Chrastil [49] was the first to use the system's density and temperature to develop a semi-empirical model that correlates solids' and liquids' solubility in supercritical gases (binary system), as described below: where S (g/L) is the compound's solubility, k is an association coefficient, ρ mix (g/L) is the density of the solvent mixture, and T (K) is the temperature. Constant a is an adjustable parameter that incorporates the total heat of the reaction. In contrast, constant b is an adjustable parameter that relates to the association number and molar masses of the solute and solvent. The del Valle and Aguilera [67] (dVA) model expended on Chrastil's by including one more parameter that connects the temperature to the solute solubility in quadratic form, as indicated in the equation below: where constants a and b indicate the temperature effect involved in the solubilization process, while constant c represents the molecular weight of the solute and solvent. We refer readers to our previous work to calculate the density of the solvent mixture [64]. Gozález [55], on the other hand, adapted the Chrastil model to account for the formation of compound-modifier complexes in the presence of the modifier (ternary system), as illustrated below: where γ is the modifier's association number and c is its concentration.

Extraction Rate
The Patricelli method was used to calculate the rate of RA extraction in the SCCO 2 extraction. In a Patricelli model, the extraction curve is governed by two-phase boundaries known as washing and diffusion. Solutes dissolve into the solvent via a damaged cell wall with minimal mass transfer resistance during the washing phase. Meanwhile, during the diffusion phase, solutes from the interior cell wall diffuse into the solvent. The Patricelli model [68] was then stated as the following equation: where C w (mg/g) is the solute equilibrium concentration during washing, C d (mg/g) is the solute equilibrium concentration during the diffusion, k w and k d (min −1 ) are the mass transfer coefficients during the washing and diffusion phases, respectively, and t (min) is the extraction time. The extraction rate is therefore shown as in Equation (5):

Validation
Non-linear regression data fits were evaluated using a Microsoft Excel 2019 (Redmond, WA, USA) with Solver tool. As mentioned in Equation (6), the best-fitting models will look at the percentage of average absolute relative deviation (AARD%): where n is a number of data points, N exp is the value of the experiments, and N calc is the calculated value from the models.

Solubility of RA in the SCCO 2 System
Dynamically, the solubility of RA from OS leaves in ethanol-assisted SCCO 2 was investigated utilizing the CER gradient at temperatures ranging from 40 to 80 • C and pressures ranging from 10 to 30 MPa. The solubility of RA was changed from 0.056 to 2.004 mg/L solvent, as indicated in Table 2. The highest RA solubility was obtained at 80 • C and 10 MPa, which corresponded to the lowest density at 229.611 g/L, whereas the lowest RA solubility was obtained at 40 • C and 20 MPa, which corresponded to a greater density of 836.246 g/L.  Table 2 demonstrates that as pressure increases from 10 MPa to 20 MPa at each isotherm, RA solubility is reduced while it increases to 30 MPa as the RA solubility increases. These phenomena occur when pressure increases, causing the solvent's ability to extract more polar molecules, while becoming less selective and extracting more by-products. Increasing the pressure generally raises the density of SCCO 2 , which improves its solvating power before boosting the extraction process and solubility. As pressure increases, however, diffusivity falls as viscosity increases [69]. The solvent molecules are unable to dissolve the solute because they are difficult to disperse into pores. Furthermore, raising the SCCO 2 pressure results in a more robust solid matrix, reducing both the void fraction and the extraction efficiency. The pressure increases from 10 to 30 MPa caused competing influences, leading to a change in the RA solubility data.
The improved RA solubility at higher extraction temperatures should aid in both the breaking of hard structures and the desorption of RA bound to the plant matrix, as well as increasing the rate of solute diffusion out of the matrix pores into the supercritical bulk flow. The greater the density, however, the greater the solvating power of SCCO 2 can be obtained by increasing the pressure. Indeed, as pressure increases, the compactness of the molecules increases, resulting in higher density and more solvent solvating power.
In general, supercritical fluid density and solute vapor pressure are two important parameters that influence solute solubility in the supercritical fluid system. Temperature has two contradictory effects: The first is a reduction in density as the temperature rises, and the second is a change in solid sublimation pressure or solute vapor pressure, which can have an increasing influence on the solubility in the SCCO 2 . As a result, there may be a net influence of these two competing effects (occurring throughout all temperature ranges) indicating that temperature has an increasing or reducing effect on the solute solubility. The solubility of RA, on the other hand, displays an increasing effect only when the temperature is increased from 40 to 80 • C at isobaric conditions ranging from 10 to 30 MPa.

Solubility Correlation of RA in SCCO 2 System
Chrastil, dVA, and Gonzalez models were used to correlate RA solubility data. Table 3 lists the density-based semi-empirical model constants as well as AARD. It can be seen from there that the AARD values (%) of the three models range from 5.184 to 8.566%. All models demonstrated a strong correlation with experimental data on RA solubility. The dVA model provides the lowest AARD (%) value for RA solubility, followed by the Chrastil and Gonzalez models. The negative sign of k indicated that increasing the system pressure could reduce the solubility of RA. Meanwhile, Chrastil and dVA models were able to calculate the thermodynamic enthalpy (∆H t , ∆H v , and ∆H s ). Constant a in the Chrastil equation, where a = (∆H t )/R and R is the gas constant (8.314 J mol −1 K −1 ), was used to calculate the value of ∆H t for RA, which was 3.711 kJ/mol. Meanwhile, the del Valle-Aguilera model could calculate the enthalpy of vaporization for RA (∆H v (T) = R(a + 2b/T)) at 4.309 kJ/mol [63]. As a result, subtracting ∆H v from ∆H t yielded a value of enthalpy of sublimation for RA (∆H s ) of approximately −0.598 kJ/mol. Our findings are consistent with our previous work [64], which concluded that vaporization is an endothermic process while solvation is exothermic. The Gonzalez model, on the other hand, reveals that ethanol has a considerable effect on the solubility of RA (γ > k). Table 2 shows that the prediction solubility values have a high correlation (R 2 ) with the experimental data of RA of approximately 0.938.
In comparison to other bioactive components from OS, such as sinensetin and isosinensetin, the solubility of RA is lowest in our earlier work on Abdul Aziz [64]. The presence of four hydroxyl groups (-OH) in the RA structure, which formed hydrogen bonds between its molecules, explains this occurrence. The RA solute-solute interactions were optimized with Gaussian version 09 software (Gaussian, Inc., Wallingford, CT, USA) utilizing density functional theory (DFT) at the B3LYP level of theory and the 6-311G (d.p) basis set ( Figure 2). As a result, the carboxyl group (-COOH) in the RA structure resulted in greater RA solute-solute interactions, with an intermolecular distance of 1.669 Å. This leads to the formation of dimerization, which creates a steric hindrance. The intermolecular distances of sinensetin and isosinensetin were reported to be approximately 2.454 Å and 2.395 Å, respectively, implying that the solubility of sinensetin and isosinensetin is higher than RA. Because there is no hydrogen bonding in the structure, dipoles-dipoles interactions are weaker than hydrogen bonds.
ChemEngineering 2022, 6, x FOR PEER REVIEW 8 of 13 between its molecules, explains this occurrence. The RA solute-solute interactions were optimized with Gaussian version 09 software (Gaussian, Inc., Wallingford, CT, USA) utilizing density functional theory (DFT) at the B3LYP level of theory and the 6-311G (d.p) basis set ( Figure 2). As a result, the carboxyl group (-COOH) in the RA structure resulted in greater RA solute-solute interactions, with an intermolecular distance of 1.669 Å. This leads to the formation of dimerization, which creates a steric hindrance. The intermolecular distances of sinensetin and isosinensetin were reported to be approximately 2.454 Å and 2.395 Å, respectively, implying that the solubility of sinensetin and isosinensetin is higher than RA. Because there is no hydrogen bonding in the structure, dipoles-dipoles interactions are weaker than hydrogen bonds.

Rate of RA Extraction and Its Mass Transfer Coefficient
The rate of RA extraction and its mass transfer coefficient were evaluated at temperatures of 40 °C to 80 °C and pressures ranging from 10 to 30 MPa. Table 4 shows the mass transfer coefficient and extraction rate of RA using the Patricelli [68] model. Based on the low percentage value of AARD (<16%), the results demonstrate that the model matches the experimental data significantly. The fastest extraction rate of RA in the ethanol-assisted SCCO2 system was 0.0061 mg/g min −1 at 80 °C and 10 MPa, according to Table 4. Furthermore, the maximum equilibrium yield of RA was produced under the same conditions, which was approximately 0.9314 mg/g. As shown in the same table, the concentration of RA was higher during the washing phase than during the diffusion phase. During the washing phase, reduced mean particle size may have contributed to the quick dissolving of RA from the fractured cell walls into the solvent. As the extraction advanced to the diffusion phase, the extraction rate declined and grew slower. The washing phase has a larger mass transfer coefficient than the diffusion phase ( > ), which could explain this phenomenon. Furthermore, the model aligned well with experimental data, with R 2 values greater than 0.9652 for each extraction condition at constant pressures ranging from 10 to 30 MPa, as shown in Figures 3-5, respectively.

Rate of RA Extraction and Its Mass Transfer Coefficient
The rate of RA extraction and its mass transfer coefficient were evaluated at temperatures of 40 • C to 80 • C and pressures ranging from 10 to 30 MPa. Table 4 shows the mass transfer coefficient and extraction rate of RA using the Patricelli [68] model. Based on the low percentage value of AARD (<16%), the results demonstrate that the model matches the experimental data significantly. The fastest extraction rate of RA in the ethanol-assisted SCCO 2 system was 0.0061 mg/g min −1 at 80 • C and 10 MPa, according to Table 4. Furthermore, the maximum equilibrium yield of RA was produced under the same conditions, which was approximately 0.9314 mg/g. As shown in the same table, the concentration of RA was higher during the washing phase than during the diffusion phase. During the washing phase, reduced mean particle size may have contributed to the quick dissolving of RA from the fractured cell walls into the solvent. As the extraction advanced to the diffusion phase, the extraction rate declined and grew slower. The washing phase has a larger mass transfer coefficient than the diffusion phase (k w > k d ), which could explain this phenomenon. Furthermore, the model aligned well with experimental data, with R 2 values greater than 0.9652 for each extraction condition at constant pressures ranging from 10 to 30 MPa, as shown in Figures 3-5, respectively.

Conclusions
In conclusion, the solubility of RA from OS leaves in ethanol-assisted SCCO2 extraction range from 0.056 to 2.004 mg/L solvent at temperatures ranging from 40 to 80 °C and pressures ranging from 10 to 30 MPa. At temperatures ranging from 40 to 80 °C and pressures ranging from 10 to 30 MPa, the solubility of RA in ethanol-assisted SCCO2 is the lowest when compared to other bioactive solutes from OS, viz. sinensetin, and isosinensetin. In the SCCO2 system, the solute-solute interaction has a major impact on the solute's solubility. The hydrogen bonds produced between the RA molecules cause a strong solute-solute interaction, causing the solvent to face steric hindrance in dissolving the solute. In this work, the density-based semi-empirical models used revealed a high correlation of RA solubility data with less than 10% AARD. Furthermore, using the Patricelli model, the extraction rate of RA in the ethanol-assisted SCCO2 system was correctly determined in the range of 0.0003 to 0.0218 mg/g min −1 in 40 to 80 °C and 10 to 30 MPa extraction conditions. Therefore, the information reported in this study can be used for further research and scaling up to extract RA via SCCO2 extraction.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.

Acknowledgments:
The authors would like to acknowledge the Centre of Lipids Engineering and Applied Research (CLEAR), UTM for the facilities provided, especially the supercritical carbon dioxide extraction unit. The authors would want to express their gratitude to Universiti Malaysia Sabah for providing financial assistance for APC.

Conflicts of Interest:
The authors declare no conflict of interest.

Conclusions
In conclusion, the solubility of RA from OS leaves in ethanol-assisted SCCO 2 extraction range from 0.056 to 2.004 mg/L solvent at temperatures ranging from 40 to 80 • C and pressures ranging from 10 to 30 MPa. At temperatures ranging from 40 to 80 • C and pressures ranging from 10 to 30 MPa, the solubility of RA in ethanol-assisted SCCO 2 is the lowest when compared to other bioactive solutes from OS, viz. sinensetin, and isosinensetin. In the SCCO 2 system, the solute-solute interaction has a major impact on the solute's solubility. The hydrogen bonds produced between the RA molecules cause a strong solute-solute interaction, causing the solvent to face steric hindrance in dissolving the solute. In this work, the density-based semi-empirical models used revealed a high correlation of RA solubility data with less than 10% AARD. Furthermore, using the Patricelli model, the extraction rate of RA in the ethanol-assisted SCCO 2 system was correctly determined in the range of 0.0003 to 0.0218 mg/g min −1 in 40 to 80 • C and 10 to 30 MPa extraction conditions. Therefore, the information reported in this study can be used for further research and scaling up to extract RA via SCCO 2 extraction.