[THTDP][Br] was supplied by Sigma-Aldrich with purity >0.95 in mass fraction, determined by NMR. The water content of the ionic liquid after the vacuum process, determined by Karl Fischer titration (Metrohm, model 915 KF), was 350 ppm. ACN and THF were of HPLC grade with purity >0.999 in mass fraction and were supplied by J. T. Baker. Water of high purity (standard reference fluid) for vibrating tube densimeter calibration was supplied by Anton Paar. Chemicals were used without further purification except for a careful degassing of samples under vacuum and low temperature (2°C). Characteristics of chemicals used are summarized in Table 1.

Densities of pure compounds and binary mixtures were measured using a vibrating tube densimeter (Anton Paar DMA 4500 M). Measurements were carried out at atmospheric pressure; the laboratory is located in Mexico City where the atmospheric pressure is 0.78 bar; saturation temperatures at this pressure calculated using the Wagner equation are 73.7°C and 58.1°C for ACN and THF, respectively. Densities are reported for the liquid phase; however, the closer the mixture is to the saturation temperature of the pure compound, the more likely the mixture undergoes partial vaporization, which leads to the formation of bubbles. Indeed, this also depends on the composition of the mixture. To avoid this issue, measurements were restricted to the short range of 293.15–313.15 K. For example, in the case of tetrahydrofuran, instabilities occurred approximately at 50°C, reflected by the presence of bubbles in the cell, so it is impossible to perform measurements. The densimeter performs the function of detecting these bubbles, and it is possible to see them with an internal camera. The volume of a U-shape measuring cell is approximately 1 mL. A volume of 2 mL of the sample was used for the measurements, taking into account cell and hose volumes; however, considering only 1 mL of cell volume, the masses fed varied approximately between 0.76 and 0.96 g at 20°C. The vibrating tube densimeter has an accuracy of 1 × 10 − 5  g·cm^–3 and uncertainty in the temperature of ± 0.01 K. Air and water were used as reference fluids for the calibration of the vibrating tube densimeter. Densities of air were taken from the DMA 4500 M instruction manual and from the reference equation CIPM-2007 described by [15]; meanwhile, densities of water were calculated from the reference equation of the state of water reported by [16]. Uncertainty in density measurements was estimated to be better than ± 2 × 10 − 4  g·cm^–3. The sources of uncertainties are vibration periods of water, air, and sample mixture, uncertainties of density of water and air, and temperature. Binary mixtures were prepared gravimetrically in a room with controlled humidity and temperature. Additionally, a glove box with an argon atmosphere was utilized to avoid any contamination of water [12]. A Metler-Toledo mass balance (model AB204), with an accuracy of ± 0.1 mg, was used and calibrated periodically by means of a 200 g reference mass. Uncertainty in the mole fraction was estimated to be < ± 0.0001 . The samples were degassed under vacuum in the injection syringe (10 mL) before being injected into the vibrating tube densimeter. The syringe was cooled using a PolyScience recirculation bath (model PD15R-40) at 2°C to avoid evaporation and shifting of the composition in the binary mixtures.

Reliability of the vibrating tube densimeter and procedure used in this work has been tested previously by [12,17–19]. Densities of [THTDP][Br], ACN, and THF were measured in the temperature interval of 293.15–313.15 K at 0.78 bar and compared with some selected literature data. Experimental data measured in this work along with literature values are reported in Table 2. For comparison purposes, the following average absolute relative deviation (AARD) is defined: A A R D = 100 ρ e x p − ρ l i t / ρ l i t / n p , (1) where ρ e x p and ρ l i t are experimental densities derived from this work and literature, respectively. Meanwhile, n p is the number of data points of every dataset compared. Comparisons of densities for the ionic liquid [THTDP][Br] were as follows: good agreement was found with the data from [7], with an AARD of 0.05%. Larger deviations were observed with the datasets reported by [5,6,9], with AARD values of 0.49, 0.31, and 0.11%, respectively. Deviations among datasets can be explained from the purities of the samples used in each work. [7] used a sample of the same purity of that used in this work; meanwhile, [5,6] used a sample with higher purities of 0.98 and 0.96 mass fractions, respectively. For ACN, excellent agreement was found when data were compared with those from [20] (sample purity was not reported), [21] (sample purity: 0.998 mass fraction), and [22] (sample purity: 0.999 mass fraction), with AARD values of 0.03, 0.03, and 0.02%, respectively. An AARD value of 0.05% was obtained for the comparison with the dataset described by [23] (sample purity: 0.999 mass fraction), which is in good agreement. Regarding THF, excellent agreement was observed with the dataset reported by [24] with an AARD of 0.01% (puriss p. a. reagent by Sigma-Aldrich, 107 ppm of water content). A good agreement was observed with the data reported by [25] (sample purity: 0.993 mass fraction) with an AARD of 0.04%. Larger deviations were observed when compared with datasets reported by [26] (sample purity: 0.995 mass fraction) and [27] (sample purity: 0.993 mass fraction), with AARD values of 0.14% and 0.16%, respectively. These comparisons validated the experimental procedure used in this work. The increasing order of densities of the pure compounds used in this study is given as follows: ρ A C N < ρ T H F < ρ T H T D P B r .

Binary mixtures were studied covering the complete interval of compositions. The [THTDP][Br] (1) + ACN (2) mixture was studied at the following compositions in [THTDP][Br] mole fraction: x 1 = 0.0433, 0.0941, 0.1499, 0.1916, 0.2215, 0.2982, 0.4217, 0.4521, 0.5215, 0.6978, and 0.7916; meanwhile, for the [THTDP][Br] (1) + THF (2) binary system, the following compositions were studied: x 1 = 0.0500, 0.1499, 0.2000, 0.2472, 0.2973, 0.4052, 0.5068, 0.5068, 0.6075, 0.7211, and 0.8423. Experimental densities of the two binary systems along with pure compound densities in the temperature interval of 293.15–313.15 K at p = 0.78 bar are reported in Table 3. Figures 1, 2 show the behavior of densities of the [THTDP][Br] (1) + ACN (2) system as a function of temperature and composition x 1 , respectively. Density decreased with the increase in temperature, as shown in Figure 1, for different compositions of the mixture. Once the behavior of density as a function of temperature is known at constant pressure, the thermal expansion α can be estimated according to the following thermodynamic definition: α = − 1 ρ ∂ ρ ∂ T p . (2)

This property is also known as volume expansivity. A linear trend was observed for density as a function of temperature (Figure 1) for all compositions studied; therefore, α -values highly depend on the slopes of lines presented in Figure 1, and α -values showed very little change with change in temperature. Slopes presented in Eq. 2 are reported in Table 4 for the different compositions studied. Slopes became almost constant after the composition of x 1 = 0.1916 and can be ascribed to the predominant effect of the ionic liquid in the mixture. This effect is better illustrated in Figure 2. Densities of the mixtures increased with the increase in the ionic liquid content in the mixture; this effect can be seen in Figure 1 but is better described in Figure 2. After the composition of x 1 = 0.1916 , changes in density are less significant and tend toward the values of pure ionic liquid density. Figures 3, 4 show the behavior of densities of the [THTDP][Br] (1) + THF (2) system as a function of temperature and composition x 1 , respectively. Similar behavior was found for this binary system. As expected, density decreased as the temperature increased. A linear dependency of density on temperature was found, as depicted in Figure 3 and was used to calculate slopes presented in Eq. 2 and are reported in Table 4. After the composition of x 1 = 0.2472 , slopes are almost constant, reflecting the effect of the presence of the increasing content of the ionic liquid. This effect is also better illustrated in Figure 4. Similar to the aforementioned binary system, the influence of the ionic liquid on the density of the mixture is more noticeable after the composition of x 1 = 0.2472 , and after this point, densities tend toward the values of the pure ionic liquid density. A dominant effect of the ionic liquid on the densities of the binary systems was observed, and this effect can be ascribed to the higher density of the ionic liquid and the asymmetric nature of the binary mixtures.

Excess molar volumes V E are defined as follows: V E = V − V i d , (3) where V is the molar volume of the mixture and V i d represents the ideal molar volume of the mixture. Eq. 3 can be rewritten in terms of density as expressed in the following equation: V E = x 1 M 1 + 1 − x 1 M 2 ρ − x 1 M 1 ρ 1 + 1 − x 1 M 2 ρ 2 , (4) where ρ is the density of the mixture, x 1 is the mole fraction of the ionic liquid [THTDP][Br], M 1 and M 2 are the molar masses, and ρ 1 and ρ 2 are the densities of pure compounds [THTDP][Br] (1) and ACN or THF (2), respectively. Excess molar volumes were calculated using the densities reported in Table 3 and the molar masses listed in Table 1. These results are presented in Table 5 for the two binary mixtures studied and are plotted in Figures 5, 6 as a function of x 1 at different temperatures. Excess molar volumes exhibited negative deviations from ideality, and these became more negative for both binary systems as the temperature increased. Excess molar volumes for the [THTDP][Br] (1) + ACN (2) binary system were smaller than those obtained for the [THTDP][Br] (1) + t THF (2) binary system. Negative values of the excess molar volumes imply that a more effective arrangement and/or attractive interactions happened when the ionic and the organic molecular liquids were mixed. Negative values of excess molar volumes can also be ascribed to the large differences in molar volume between the ionic liquid and ACN or THF molecules. For example, at 293.15 K, the molar volumes are 596.85, 52.48, and 81.25 cm³·mol^-1 for pure [THTDP][Br], ACN, and THF, respectively. These large differences between the molar volumes of [THTDP][Br] and ACN or THF suggest a high probability for the relatively small organic molecules of ACN or THF to fit into the interstices of the ionic liquid upon mixing. Therefore, the filling effect of organic molecular liquids in the interstices of the ionic liquid and the ion–dipole interactions between organic molecular liquid and the ionic liquid contributed to the negative values of excess molar volumes [28,29].

A Redlich–Kister-type equation was used to fit the excess molar volumes [30]. This equation can be expressed as a generalized equation as follows: V E = x 1 1 − x 1 ∑ i = 0 i = n A i 2 x 1 − 1 i , (5) where A i is an adjustable parameter, x 1 denotes the mole fraction of the ionic liquid [THTDP][Br], and n is the order of the expansion. The order of the expansion used in this work was determined by fitting the excess molar volumes for different values of n ( n = 0 , 1 , 2 , a n d   3 ). Because of the asymmetric shape of the parabolic curves of V E as a function of x 1 , as depicted in Figures 5, 6, the use of expansions of n = 0   a n d   1 for one- and two-parameter equations, respectively, failed to represent the excess molar volumes accurately. Using expansions of n = 2   a n d   3 , three- and four-parameter equations, respectively, represented the excess molar volumes with almost the same accuracy; therefore, parameters A 0 , A 1 , a n d   A 2 for the expansion of n = 2 are reported in Table 6 along with the standard deviation of the fits σ . Solid lines in Figures 5, 6 represent values obtained using the Redlich–Kister equation.

The ERAS model was applied for modeling the excess molar volumes reported in this study at 298.15 K [31–36]. Only data at 298.15 K were modeled due to some restrictions in isothermal compressibility availability. Parameters of the model are reported in Tables 7, 8. Physical and chemical contributions are plotted in Figures 7A, B for both systems. Chemical contributions have higher magnitude than physical contributions for both systems, and for the [THTDP][Br] + THF system, these contributions have higher magnitude than those for the [THTDP][Br] + ACN system (Figure 7).

Partial molar volumes V ¯ 1   a n d   V ¯ 2 were calculated using the Redlich equation with the parameters reported in Table 6, in accordance with the following equations: V ¯ 1 = V E + V 1 + 1 − x 1 d V E d x 1 T , p , (6) V ¯ 2 = V E + V 2 − x 1 d V E d x 1 T , p , (7) by differentiation of V E (Eq. 5) with respect to x 1 , and using Eqs 6, 7, the following expressions are obtained: V ¯ 1 = V 1 + 1 − x 1 2 ∑ i = 0 i = n A i 2 x 1 − 1 i + 2 x 1 1 − x 1 2 ∑ i = 0 i = n i A i 2 x 1 − 1 i − 1 , (8) V ¯ 2 = V 2 + x 1 2 ∑ i = 0 i = n A i 2 x 1 − 1 i + 2 x 1 2 1 − x 1 ∑ i = 0 i = n i A i 2 x 1 − 1 i − 1 . (9)

Partial molar volumes of the two binary systems studied are reported in Table 9 and plotted as a function of the mole fraction of the ionic liquid in Figures 8A, B for the [THTDP][Br] (1) + ACN (2) system and in Figures 8C, D for the [THTDP][Br] (1) + THF (2) system. These plots show that V ¯ 1 values did not change significantly, reflecting the influence of the denser ionic liquid. V ¯ 2 decreases continuously with the increase in the mole fraction of the ionic liquid. Both partial molar volumes change consistently within the temperature range.