Thermophysical Study on the Mixing Properties of Mixtures Comprising 2 ‑ (2-Methoxyethoxy)ethanol, Butan-1-ol, Butan-2-ol, and Propan-1-ol

: Excess enthalpy ( H E ), dynamic and kinematic viscosities ( η , υ ), density ( ρ ), and refractive index ( n D ) of mixtures comprising 2-(2-methoxyethoxy)ethanol, butan-1-ol, butan-2-ol, and propan-1-ol are presented at p = 0.1 MPa and at T = 298.15 and 313.15 K. Deviations in refractive index ( Δ n D ) is generated from experimental data of refractive index. Experimental data of ρ for all binary mixtures are predicted using the PC-SAFT (Perturbed Chain-Statistical Associating Fluid) EoS. Furthermore, H E and Δ n D are adjusted using the Redlich − Kister equation. However, the correlation of measured data of H E is performed by using the UNIQUAC and NRTL models.


EXPERIMENTAL SECTION
Propan-1-ol 0.7874 47 1.379 64 1.3770 66 0.7885 64 1.379 65 0.7873 65 a The standard uncertainties u of temperature and pressure are u(T) = 0.04 K and u(p) = 0.001 MPa, respectively.The expanded uncertainties U c in density and refractive index are U c (ρ) = 0.0005 g•cm −3 and U c (n D ) = 0.005, respectively, with a 0.95 level of confidence.The relative expanded uncertainty U r in dynamic viscosity is U r (η) = 2%.
Q mixture : heat of mixing; V ̇1 and V ̇2: flows of pure components 1 and 2 driven by isocratic pumps, respectively; T: temperature; H E : excess enthalpy; x: mole fraction.
Figure 1.Percentage deviations versus temperature using our estimated PC-SAFT parameters for: (Δ), 1-butanol; ( □ ), 2-butanol; (○), 1propanol; and using PC-SAFT parameters for: (▲), 1-butanol, Grenner et al.; 72 ( ■ ), 2-butanol, Ahmadi et al.; 73 (•), 1-propanol, Grenner et al. 72 dividing the mixture's power by the flow rate of moles per second during the mixing process.For binary systems, the two liquids being pumped are pure compounds.The relative expanded uncertainty of H E is U r (H E ) = 1% (k = 2), and the standard uncertainty of mole fractions (x i ) of each mixture is u(x) = 0.0005.This experimental technique employed in this paper was deeply validated and described in our previous published work. 67The uncertainty budget for H E , as presented in Table 3, was calculated following the guidelines outlined in EA-4/02. 68.2.1.Dynamic and Kinematic Viscosities, (η, υ), Density, (ρ), and Refractive Index, (n D ).Measurement of η, υ, and ρ of pure components and their mixtures was reported at 298.15 and 313.15K using a Stabinger SVM 3000 viscosimeter.The expanded uncertainties of ρ and η are, respectively, equal to 0.0005 g•cm −3 and 0.01 mPa•s (0.95 level of confidence).Furthermore, experimental data of n D of pure components and their mixtures were also reported at 298.15 and 313.15K by using an Abbe digital refractometer.The expanded uncertainty of n D equals 0.005 (0.95 level of confidence).The Abbe digital refractometer (Model Abbemat 300, Anton Paar) is calibrated using air and water; however, the Stabinger SVM 3000 viscosimeter is calibrated using air, water, and decane.

ADJUSTMENT OF H E DATA
The adjustment of H E data was done using the following Redlich−Kister (R−K) equation 17 ) The standard uncertainties of pressure p, temperature T, and mole fraction x are as follows: The A i parameters are determined through the unweighted least-squares method, and the optimal number of A i was determined through the application of the F-test. 69

MODELING OF H E WITH UNIQUAC AND NRTL MODELS
The UNIQUAC 18 and NRTL 19 models are used to predict the H E data of each mixture in this work.The H E calculated by the UNIQUAC model is expressed as follows: where x i is the composition of the mixture; q i is the molecular surface area; is the parameter that has same meaning as in the NRTL model; and Δu ji (J mol −1 ) is the parameter that represents the mixture interaction energy.
The H E calculated by the NRTL model is generated using the following equation: where x i is the composition of the component i.
The μ i parameters are expressed as follows:   (6)   where g ji is the interaction energy between each pair of i−j molecules and α is the nonrandomness factor in the mixture.
The following parameters are calculated to have an idea about the quality of the adjusted and correlated data of where H exp E and H calc E are the experimental and adjusted data of H E , respectively, and n dat and n par are the number of experimental data and parameters of the corresponding model, respectively.

ADJUSTMENT AND MODELING OF ρ, η, υ, AND N D AND DERIVATIVE PROPERTIES
5.1.Adjustment.ρ, η, υ, and n D of each studied mixture are adjusted by using the following mathematical polynomial equation: where A could be ρ, η, υ, or n D ; x 1 is the composition of component 1; and A i are parameters generated through the application of the unweighted least-squares method.The determination of the optimal number of A i was achieved using the F-test. 69n D data of each studied mixture are adjusted by using the following R−K equation: ) where Δn D is the deviation in refractive index; x 1 is the composition of component 1; and A i are parameters that are generated by employing the unweighted least-squares technique.
The deviations of root-mean-square for each adjustment are expressed as follows: where N is the total number of measured data and p is the total number of parameters employed in the R−K equation.

Modeling of ρ Using PC-SAFT EoS.
The PC-SAFT EoS is created by Gross and Sadowski, 15,16 and it is expressed in terms of ăr es (residual Helmholtz energy), as the sum of ăh c , ăd isp , and ăa ssoc : where ăh c is the hard-chain energy contribution; ăd isp is the dispersive energy contribution; and ăa ssoc is the association interaction energy.The nonassociative parameters of PC-SAFT EoS are as follows: σ (segment diameter), m (segment number), and ε/k (segment energy parameter).
Two additional parameters in the case of associative fluids are added to the PC-SAFT EoS: ε A i BI (the association energy) and k A i B i (association volume).
The σ ij and ε ij parameters for the mixture are described by the Berthelot−Lorentz conventional mixing rule i k j j j j y where k ij is the parameter of binary interaction for correcting the interaction between unequal chain segments.In this work, the binary interaction parameters are assumed to be zero.The optimization of PC-SAFT EoS parameters was done using the following objective function: where M is the number of experimental data.The 2B association scheme (two associating sites) was used because of the good representation of density data of all studied mixtures.The association, the shape, and the size of  the molecules are explicitly taken into account by the PC-SAFT EoS for the reason that it is based on statistical mechanics, 70,71 which is crucial for modeling the density of liquid mixtures.Figure 1 illustrates the percentage deviations between experimental and calculated densities of pure components (1-butanol, 2-butanol, and 1-propanol) as a function of temperature.These calculations employ our estimated PC-SAFT parameters as well as the parameters reported by Grenner et al. 72 and Ahmadi et al. 73 Our estimated PC-SAFT parameters demonstrate a strong agreement with experimental data for the mentioned pure components, as depicted in Figure 1.The mean absolute deviations (MADs) are as follows: [0.009−.15%],[0.003−0.13%],and [0.23−0.87%]for 1butanol, 2-butanol, and 1-propanol, respectively, at temperatures of 298.15 and 313.15 K.The PC-SAFT parameters derived from Grenner et al. 72 present a tendency to underestimate the liquid densities of the pure components under investigation.The MADs for 1-butanol and 1-propanol at temperatures of 298.15 and 313.15K range from 5.70 to 7.85% and 7.98 to 10.49%, respectively.In contrast, for 2butanol, the PC-SAFT parameters as reported by Ahmadi et al. 73 perform well in predicting the liquid densities of the pure component, showing MADs of 1.18 and 1.52% at temperatures of 298.15 and 313.15 K, respectively.We observed higher deviations in Grenner et al. 72 findings compared to our deviations, and this disparity can be attributed to the fact that Grenner et al. 72 utilized a simplified PC-SAFT approach.In contrast, our parameters exhibit improved predictions when compared to those of Ahmadi et al., 73 and this can be attributed to our comprehensive fitting methodology.Our parametrization process involved the use of experimental density data exclusively, whereas Ahmadi et al. 73 incorporated both density and vapor pressure data, which could explain the enhanced predictive performance of our parameters in relation to pure component densities.As for 2-(2-methoxyethoxy)ethanol, no PC-SAFT parameters are available in the literature.4 and plotted in Figure 2. The A i parameters to adjust H E for each studied mixture using eq 1 are listed in Table 5, and Table 6 presents a set of parameters needed for the calculation of H E by UNIQUAC and NRTL models.
For the 2-(2-methoxyethoxy)ethanol (1) + butan-1-ol (2) mixture, the best fit of H E data is obtained with the R−K equation at 298.15 and 313.15 K, with an rms ΔH E of 0.8 and 2.2 J•mol −1 , respectively.The NRTL and UNIQUAC models also exhibit a good correlation, with an rms ΔH E of [3.5 J• mol −1 , 3.0 J•mol −1 ] and [9.1 J•mol −1 , 3.5 J•mol −1 ], respectively, at 298.15 and 313.15 K. Additionally, in the case of the mixture containing 2-(2-methoxyethoxy)ethanol (1) and butan-2-ol (2), the R−K equation was identified as the most suitable correlation equation for H E data at 298.15 K, presenting an rms ΔH E of 1.1 J•mol −1 .Conversely, at 313.15 K, the UNIQUAC model demonstrates favorable agreement, resulting in an rms ΔH E of 2.5 J•mol −1 .Finally, in the case of the mixture containing 2-(2-methoxyethoxy)ethanol (1) and propan-1-ol (2), the R−K equation provides the most accurate representation of H E data at both temperatures, with rms ΔH E values of 0.8 and 0.9 J•mol −1 , respectively.Furthermore, the NRTL and UNIQUAC models exhibit also favorable agreements at both temperatures.
Our experimental H E data for the 2-(2-methoxyethoxy)ethanol (1) and butan-1-ol (2) mixture were compared to data reported by Cobos et al. 74 The comparison, as illustrated in Figure 2a, reveals close agreement between our experimental data and the referenced data, with a MAD of only 4.4%.Importantly, at a temperature of 313.15 K, we found no reference data available in the literature for a similar comparative analysis.Moreover, no reference data were found in the literature for the mixtures of 2-(2methoxyethoxy)ethanol (1) + butan-2-ol (2) and 2-(2methoxyethoxy)ethanol (1) + propan-1-ol (2) at the two temperatures under investigation.
The understanding of enthalpic effects (H E ) plays a crucial role in grasping the nonideal characteristics of the final mixture solution.This particular concept relates to the impact of variations in shape and size among different molecules, as well as the diverse interactions between them, which can result in either an increase or a decrease in H E values. 75Within this context, the mixtures 2-(2-methoxyethoxy)ethanol (1) + butan-1-ol (2), 2-(2-methoxyethoxy)ethanol (1) + butan-2-ol (2), and 2-(2-methoxyethoxy)ethanol (1) + propan-1-ol (2)  show an endothermic behavior at the studied temperatures and throughout the entire range of x 1 .The observed behavior in these three mixtures was expected, as it can be attributed to the disruption of intermolecular hydrogen bonds during the combination of 2-(2-methoxyethoxy)ethanol, a glycol ether, with various alcohols, including butan-1-ol, butan-2-ol, and propan-1-ol.
The H E of these mixtures may be influenced by different factors such as (i) liberation of heat as a result of possible  2), + butan-2-ol (2), and + propa-1-ol (2).These thermophysical properties of each studied mixture are presented in Table 7 and plotted in Figures 3−6.The A i parameters used to adjust ρ, η, υ, and n D of each studied mixture using eq 11 are listed in Table 8.Figures 3 and  6 indicate, respectively, that the values of ρ and n D increase with an increase in x 1 and decrease with an increase in temperature.While Figures 4 and 5 show that η and υ values decrease as the temperature increases from 298.15 to 313.15 K, they also decrease vs x 1 , and until they have reached certain fractions, the viscosities increase with the augmentation of x 1 .We compared our experimental density data at 298.15 K for the mixture of 2-(2-methoxyethoxy)ethanol (1) and butan-1-ol (2) to the data reported by Mozo et al. 77 The comparison (Figure 3a) revealed a strong agreement with a MAD of only 0.05%.Similarly, at 313.15 K, we compared our experimental density and refractive index data for three studied mixtures: 2-(2-methoxyethoxy)ethanol (1) + butan-1-ol (2), 2-(2methoxyethoxy)ethanol (1) + butan-2-ol (2), and 2-(2methoxyethoxy)ethanol (1) + propa-1-ol (2) to the data reported by Belhadj et al. 78 In all cases, the comparison showed excellent agreement, with MADs of 0.09, 0.05, and 0.08% for density (Figure 3) and 0.04, 0.03, and 0.03% for refractive index (Figure 6), respectively.
The PC-SAFT EoS parameters of each studied component are listed in Table 9, and as shown in Figure 3, the associated  densities are also represented using the PC-SAFT EoS.The results show that all studied mixtures accord well with experimental data.In addition, the MAD values for the studied mixtures 2-(2-methoxyethoxy)ethanol (1) + butan-1-ol (2), + butan-2-ol (2), and + propa-1-ol (2), at 298.15 and 313.15K are, respectively, within [0.03−0.72%],[0.06−0.77%],and [0.18−1.16%].There is a good agreement between the predicted values of density and the experimental data when compared, 70,71 and this is due to the effect that PC-SAFT EoS clearly takes into account the association, the shape, and the size of the molecules, which is crucial for modeling the studied mixtures.
where n i is the component i refractive index and n D is the mixture refractive index.Figure 7 presents the calculated Δn D for the mixtures of 2-(2-methoxyethoxy)ethanol (1) + butan-1-ol (2), + butan-2-ol (2), and + propa-1-ol (2), at 298.15 and 313.15 K, and over the entire range of x 1 .The A i parameters used to adjust the Δn D of each studied mixture using eq 12 are listed in Table 10.The calculated values of Δn D are all positive for all of the studied mixtures.While the chain length of the alkanol decreases, the change in Δn D becomes more positive.It is also true that Δn D values of these mixtures changed slightly more positively at higher temperatures compared to the change observed between 298.15 and 313.15 K.

CONCLUSIONS
Experimental data of H E , η, υ, ρ, and n D are reported for mixtures containing 2-(2-methoxyethoxy)ethanol (1) with 1butanol or 2-butanol or 1-propanol at T = 298.15and 313.15K and over a wide range of composition.From the presented experimental results, the derivative property as Δn D was also determined.The PC-SAFT EoS was used to predict the ρ values for all studied mixtures, and it showed good agreement with the reported experimental results of ρ.The impacts of intermolecular interaction are examined for each studied mixture.

a
The standard uncertainties u of temperature and pressure are u(T) = 0.04 K and u(p) = 0.001 MPa, respectively.The expanded uncertainties U c in mole fraction, density, and refractive index are U c (x) = 0.003, U c (ρ) = 0.0005 g•cm −3 , and U c (n D ) = 0.005, respectively, with a 0.95 level of confidence.The relative expanded uncertainty U r in dynamic and kinematic viscosities are U r (η) = 2% and U r (υ) = 2%, respectively.b x 1 : mole fraction of component 1 (2-(2-methoxyethoxy)ethanol).

Table 1 .
is used to Chemical Data for the Studied Components a Determined by gas chromatography (GC) by the supplier Sigma-Aldrich.b Racemic mixture.

Table 2 .
Comparison of Experimental Data of Dynamic Viscosities, η, Density, ρ, and Refractive Index, n D , of 2-(2-Methoxyethoxy)ethanol, Butan-1-ol, Butan-2-ol, and Popan-1-ol with the Corresponding Literature Data at p = 0.1 MPa and T = 298.15and 313.15K a Measurement of H E of studied mixtures was generated at the studied temperatures by employing a quasi-isothermal calorimeter.By utilizing the flow rates, molecular weights, and densities of the liquids involved, we determined the various mole fractions (x i ) of the mixtures under investigation.Table2provides the densities, ρ, of pure liquids at the measured temperatures.The dependence of H E on x i is established by analyzing mixtures of diverse compositions.The H E is 2.1.Chemicals.Chemicals 2-(2-methoxyethoxy)ethanol, butan-1-ol, butan-2-ol, and propan-1-ol are used in this work.Table1lists the formula, molar mass, state mole fraction purity, and CAS number of each used chemical.Mixtures comprising 2-(2-methoxyethoxy)ethanol, butan-1-ol, butan-2ol, and propan-1-ol were generated by mass using an OHAUS balance (precision of 0.0001 g).Table2presents a comparison between our reported thermophysical properties (ρ, υ, and n D ) ixture is the number of moles per second and Q mixture is the mixing heat.The H E of binary mixtures is determined by

Table 8 .
Sets of Parameters A i , with Standard Deviations σ, Needed for Adjustment of Dynamic and Kinematic Viscosities, (η, υ), Density, (ρ), and Refractive Index, (n D ), by Employing Equation 11 for the Studied Mixtures at p = 0.1 MPa and T = 298.15and 313.15K