Determination and Analysis of Solubility of HC-290 (Propane) in [hmim][Tf₂N]

Abstract

Seeking the alternative working pairs used in absorption refrigeration cycles is one of the main issues in refrigeration fields due to the drawbacks of traditional H₂O/LiBr and NH₃/H₂O, such as corrosion, crystallization, and toxicity. The imidazolium-based ionic liquid [hmim][Tf₂N] has emerged as a promising candidate as an absorbent used in absorption refrigeration systems. In addition, due to having a higher specific heat and higher latent heat of evaporation, hydrocarbons such as HC-290 have been considered as good alternative refrigerants in compression refrigeration cycles. In order to explore the possibility of using HC-290 in the absorption refrigeration cycle, the exact phase behavior of HC-290 with absorbents should be known. Therefore, in this work, the isochoric saturation method was used to determine the solubility of HC-290 in [hmim][Tf₂N] over a temperature range of 283.15 K to 343.15 K. The experimental data were modeled using the non-random two-liquid (NRTL) activity coefficient model and the Krichevsky–Kasarnovsky (K-K) fugacity model. The average absolute relative deviations for the mole fraction of HC-290 in [hmim][Tf₂N] between this work and calculated results from the models were 0.76% (NRTL) and 0.78% (K-K), and the corresponding maximum relative deviations were 3.39% and 3.24%. Based on the NRTL model, the Gibbs free energy, enthalpy change, and entropy change in the dissolution process of HC-290 in [hmim][Tf₂N] were calculated and discussed. Furthermore, the Henry’s constants of various refrigerants in [hmim][Tf₂N] were calculated at 313.15 K and 333.15 K, and the results were systematically compared.

1. Introduction

The absorption refrigeration cycle (ARC) can be driven by low-grade energy, such as industrial waste heat, solar energy, and other forms of residual heat [1,2]. The performance of the ARC is predominantly influenced by the properties of the working pairs [3]. Commonly used working pairs in an ARC include H₂O/LiBr and NH₃/H₂O. However, the drawbacks of pairs are obvious, such as corrosion, crystallization, high operating pressures, and toxicity [4]. Consequently, the exploration of novel working pairs capable of addressing these limitations has attracted more and more attention in recent years.

Ionic liquids (ILs), also known as room-temperature molten salts, are novel compounds composed of organic cations and inorganic or organic anions that remain in a liquid state at ambient temperatures. ILs exhibit excellent thermal stability, low flammability, and extremely low vapor pressure [5,6]. These properties make it a promising potential absorbent for the ARC. Wu et al. compared the performance of ARCs using different ILs as absorbents, including [emim][BF₄], [hmim][BF₄], [omim][BF₄], and [hmim][Tf₂N], and found that the HFO-1234ze(E)/[hmim][Tf₂N] pair has the highest performance (COP = 0.606) [7]. In addition, Park et al. analyzed the performance of a simultaneous cooling and heating adsorption system [8], using four ILs ([dmim][DMP], [emim][DMP], [em im][BF₄], and [hmim][Tf₂N]) as absorbents and H₂O and HFC-32 as refrigerants. The results show that the HFC-32/[hmim][Tf₂N] pair has an advantage in subzero cooling temperatures, and the system size is more compact. Hence, [hmim][Tf₂N] can be considered as a good absorbent for use in the ARC.

The properties of a refrigerant/[hmim][Tf₂N] system are of importance for its application. Many researchers have studied the phase behavior of various refrigerants in [hmim][Tf₂N], as indicated in

Table 1. Summary of the solubility of refrigerants in [hmim][Tf₂N].

Refrigerants	Authors	Years	T/K	p/MPa	Mole Fraction x1
HFC-134a	Ren and Scurto [9]	2009	298.15–343.15	0.042–1.878	0.0247–0.7642
HFC-227ea	Liu et al. [13]	2018	303.15–343.15	0.058–0.485	0.042–0.284
HFC-236fa	Liu et al. [13]	2018	303.15–343.15	0.030–0.315	0.046–0.279
HFC-245fa	Liu et al. [13]	2018	303.15–343.15	0.016–0.144	0.049–0.196
HFC-143a	Liu et al. [14]	2015	302.7–343.0	0.130–1.545	0.0434–0.3561
HFC-125	Liu et al. [10]	2015	302.6–332.8	0.1091–0.9172	0.0576–0.3282
HFC-152a	Liu et al. [10]	2015	302.3–343.4	0.0376–0.3074	0.0573–0.2528
HFC-161	Liu et al. [14]	2015	302.2–344.3	0.030–0.673	0.0305–0.3878
HFC-32	Liu et al. [10]	2015	302.5–344.1	0.1144–1.2208	0.0923–0.4972
HFO-1233zd(E)	He et al. [12]	2018	303.12–343.17	0.009–0.130	0.010–0.113
HFO-1234ze(E)	Liu et al. [11]	2016	292.98–353.23	0.0497–0.6937	0.0228–0.3312
HFO-1234yf	Liu et al. [11]	2016	292.29–353.21	0.0993–0.9251	0.0376–0.3536
HC-600a	Liu et al. [15]	2015	303.2–343.5	0.0482–0.4524	0.014–0.103
HC-50	Kumelan et al. [16]	2007	293.3–413.25	0.886–9.300	0.0632–0.5106 *
HC-170	Henni et al. [17]	2024	303.15–343.15	0.0199–1.3009	0.003–0.139
HC-50	Anderson et al. [18]	2007	298.15–333.15	0.0202–0.988	0.00116–0.0246
HC-170	Florusse et al. [19]	2008	293.19–368.40	0.388–13.070	0.0995–0.4016
RC-270	Liu et al. [15]	2015	303.5–343.3	0.1473–1.1578	0.028–0.206
CO2	Henni et al. [20]	2022	303.15–343.15	0.0195–1.4009	0.005–0.311
CO2	Shokouhi et al. [21]	2023	313.15–353.15	0.265–0.843	0.053–0.155
CO2	Yim et al. [22]	2013	303.15–373.15	0.42–45.28	0.165–0.824
CO2	Kumelan et al. [23]	2006	293.15–413.2	0.601–9.911	0.2459–4.6574 *
CO2	Aki et al. [24]	2004	298.1–333.3	1.315–11.558	0.1993–0.7586
CO2	Shiflett et al. [25]	2007	281.9–348.6	0.0089–1.9764	0.001–0.539

* indicates that the unit is mol/kg.

. With respect to hydrofluorocarbon (HFC) refrigerants, Ren and Scurto [9] measured the vapor–liquid equilibrium (VLE) of HFC-134a with [hmim][Tf₂N] at temperatures of 298.15 K~348.15 K and pressures up to 1.8 MPa. The results reveal that the anion has a greater influence on solubility than the cation. Liu et al. [10] systematically investigated the solubility of HFC refrigerants (HFC-32, HFC-152a, HFC-125, HFC-161, HFC-143a, HFC-245fa, HFC-236fa, and HFC-227ea) in [hmim][Tf₂N] in the temperature range of 302 K to 344 K. In addition, Liu et al. [11,12] also reported the solubility of hydrofluoroolefin (HFO) refrigerants such as HFO-1234ze(E), HFO-1234yf, and HFO-1233zd(E) in [hmim][Tf₂N] over a temperature range of 293 K to 353 K and pressures up to 0.93 MPa. The results show that HFO-1234ze(E) exhibits higher solubility than HFO-1234yf, and the two refrigerants show greater solubility in [hmim][Tf₂N] than HFC refrigerants.

Considering the environmental issues they pose, HFC refrigerants with high global warming potential (GWP) will be phased out, as required by the Kigali Amendment to the Montreal Protocol. Among the potential alternatives, hydrocarbon (HC) refrigerants have emerged as highly promising, owing to their zero ozone depletion potential (ODP), low GWP, high latent heat of evaporation, and superior cooling capacity [26]. For example, HC-290 has been considered as a good alternative refrigerant for use in household air conditioners due to its good thermophysical properties [27]. In order to explore the possibility of using HC-290 in the ARC, Al-Dadah et al. [28] studied the performance of a solar-assisted vapor absorption system using HC-290 as a refrigerant and AB300 lubricant as an absorbent. In addition, Liu et al. [29] and Sun et al. [30] investigated the phase equilibria of HC-290 with [hmim][FEP] and [P₆₆₆₁₄] Cl ILs to provide the essential data for the performance analysis of the ARC. However, to this author’s knowledge, there are no reports on the properties of an HC-290/[hmim][Tf₂N] mixture. To address this research gap, this study investigates the solubility of HC-290 in [hmim][Tf₂N] over a temperature range of 283.15 K to 343.15 K utilizing the isochoric saturation method. Furthermore, a comparative analysis is conducted to evaluate the solubility and absorption performance of [hmim][Tf₂N] with various refrigerants.

2. Experimental Method

2.1. Experimental Samples

The HC-290 (CAS No.: 74-98-6) used in this work was provided by Yonghe Refrigerant Co., Ltd. (Zhejiang, China), with a mass purity higher than 99.95%. [hmim][Tf₂N] (CAS No.: 382150-50-7) was supplied by Chengjie Chemical Co., Ltd. (Shanghai, China) with a claimed mass purity of 98%. Before use, it was dried under vacuum at 348.15 K for 72 h to remove trace water impurities. The final water content was measured using an MKC-710B Karl Fischer titrator (Kyoto, Japan) and lower than 100 ppm. The chemical structures of HC-290 and [hmim][Tf₂N] are shown in Figure 1.

2.2. Experimental Setup

Due to the extremely low vapor pressure of [hmim][Tf₂N], as indicated by Sarafov et al. [31], the isochoric saturation method is suitable for measuring the solubility of HC-290 in [hmim][Tf₂N]. A schematic diagram of the experimental system established based on the isochoric saturation method is shown in Figure 2. Detailed information about the experimental system is given in our previous work [32,33]. Here, a brief introduction is given. The core part of the experimental system is the gas chamber and the equilibrium cell, as shown in Figure 2. The volume of the gas chamber and the equilibrium cell was calibrated using carbon dioxide, and the values were 103.61 cm³ and 33.37 cm³ [34], respectively. The gas chamber and equilibrium cell are located in the thermostat bath, and the temperature of the bath was measured using a 100 Ω platinum resistance thermometer produced by Fluke (USA, model: Fluke 5608, accuracy: 0.01 K). In addition, the temperature of the bath was maintained constant through a Lauda ECO temperature controller, and the refrigeration system cooled the bath through the heat exchanger.

According to the principle of the isochoric saturation method, the pressure change in the gas chamber should be measured. Therefore, the pressure was measured using a Keller pressure sensor (Switzerland) with a maximum range of 3 MPa (model: Keller 33X, accuracy: 0.03% FS). The expanded uncertainties of the temperature and pressure measurement were estimated, and the values were less than 0.03 K and 2.0 kPa (k = 2), respectively.

Before the measurement, a specific amount of [hmim][Tf₂N] was injected into the equilibrium cell, and the injected weight was determined using an analytical balance (Mettler Toledo, Switzerland, model: ME204, accuracy: ±0.0002 g). Once the vacuum treatment of the system was completed and the temperature of the thermostat bath was stabilized, HC-290 was released into the gas chamber. The initial pressure was recorded when the pressure stabilized. Subsequently, valve V4 (as shown in Figure 2) was opened to allow the HC-290 in the gas chamber to enter into the equilibrium cell. When the pressure stabilized, the value was recorded again. The mole fraction of HC-290 dissolved in [hmim][Tf₂N] could be calculated based on the pressure change and temperature.

The mole fraction (x₁) of HC-290 in [hmim][Tf₂N] is calculated as:

$$x_1={\displaystyle \frac{n_1}{n_1+n_2}}$$

(1)

$$n_2={\displaystyle \frac{m_2}{M_2}}$$

(2)

where n₂ represents the mole number of [hmim][Tf₂N], which can be obtained from its mass, m₂ (4.1306 g), in the equilibrium cell and molar mass, M₂ (447.41 g/mol). n₁ represents the mole number of HC-290 dissolved in [hmim][Tf₂N]. Based on the mass conservation of HC-290 in the system, n₁ can be obtained using the following equation [34]:

$$n_1=n_1^0-n_1^1={\rho }_1^0{V}_{\mathrm{gc}}-{\rho }_1^1\left(V_{\mathrm{gc}}+V_{\mathrm{ec}}-V_{1,\mathrm{liquid}}-V_{\mathrm{IL}}\right)$$

(3)

where $n_1^0$ and $n_1^1$ are the mole number of vapor HC-290 in the initial condition and the equilibrium condition, respectively. ${\rho }_1^0$ and ${\rho }_1^1$ are the molar density of vapor HC-290 in the initial condition and the equilibrium condition. The values were obtained from Refprop 10.0 [35]. V_gc and V_ec represent the volumes of the gas chamber and the equilibrium cell, respectively. V_IL is the volume of [hmim][Tf₂N] in the equilibrium cell, which was obtained from the injected mass and liquid density [29]. V_1,liquid is the liquid volume of HC-290 dissolved in [hmim][Tf₂N] and can be calculated by:

$$V_{1,\mathrm{liquid}}=n_1/{\rho }_{1,\mathrm{liquid}}^1$$

(4)

where ${\rho }_{1,\mathrm{liquid}}^1$ is the liquid density of HC-290. Combined with Equations (3) and (4), the mole number of HC-290 dissolved in [hmim][Tf₂N] can be calculated via:

$$n_1=\left[{\rho }_1^0{V}_{\mathrm{gc}}-{\rho }_1^1\left(V_{\mathrm{gc}}+V_{\mathrm{ec}}-V_{\mathrm{IL}}\right)\right]/\left(1-{\rho }_1^1/{\rho }_{1,\mathrm{liquid}}^1\right)$$

(5)

According to the uncertainty propagation [36], the combined expanded uncertainty of the mole fraction can be calculated by:

$$U\left(x_1\right)=k\cdot \sqrt{{\left({\displaystyle \frac{\partial x_1}{\partial n_1}}\right)}^2\cdot u^2\left(n_1\right)+{\left({\displaystyle \frac{\partial x_1}{\partial n_2}}\right)}^2\cdot u^2\left(n_2\right)}$$

(6)

where k is the coverage factor (k = 2 in this work). u(n₁) and u(n₂) are the uncertainties of the mole number of HC-290 and [hmim][Tf₂N]:

$$u\left(n_1\right)=\sqrt{\begin{array}{l}{\left({\displaystyle \frac{\partial n_1}{\partial {\rho }_1^0}}\right)}^2\cdot u^2\left({\rho }_1^0\right)+{\left({\displaystyle \frac{\partial n_1}{\partial {\rho }_1^1}}\right)}^2\cdot u^2\left({\rho }_1^1\right)+{\left({\displaystyle \frac{\partial n_1}{\partial {\rho }_{1,\mathrm{liquid}}^1}}\right)}^2\cdot u^2\left({\rho }_{1,\mathrm{liquid}}^1\right)\\ +{\left({\displaystyle \frac{\partial n_1}{\partial V_{\mathrm{gc}}}}\right)}^2\cdot u^2\left(V_{\mathrm{gc}}\right)+{\left({\displaystyle \frac{\partial n_1}{\partial V_{\mathrm{ec}}}}\right)}^2\cdot u^2\left(V_{\mathrm{ec}}\right)+{\left({\displaystyle \frac{\partial n_1}{\partial V_{\mathrm{IL}}}}\right)}^2\cdot u^2\left(V_{\mathrm{IL}}\right)\end{array}}$$

(7)

$$u\left(n_2\right)=\sqrt{{\left({\displaystyle \frac{\partial n_2}{\partial m_2}}\right)}^2\cdot u^2\left(m_2\right)}$$

(8)

The uncertainty for each parameter is given in

Table 2. Sources of uncertainty for each parameter.

Source of Uncertainty	Relative Value	Source of Uncertainty	Relative Value
u(ρ1)	0.03%	u(m2)	0.001%
u(${\rho }_{1,\mathrm{liquid}}^1$)	0.01%	u(Vgc)	0.1%
u(VIL)	0.05%	u(Vec)	0.1%

. The calculated results show that the combined relative expanded uncertainty of the mole fraction U_r(x₁) was less than 2.78% (k = 2).

3. Experimental Results and Discussion

In order to validate the reliability of the experimental system, the solubility of carbon dioxide in pentaerythritol tetraoctanoate (Abbreviate as PEC8, CAS:3008-50-2) and HFO-1234yf in [hmim][TfO] (CAS:460345-16-8) was measured at 303.15 K, and the results were compared with those from the literature [37,38]. The maximum deviation between this work and literature was 2.50%, indicating that the experimental system has good reliability, as indicated in Figure 3.

3.1. Experimental Data and Correlation

In this work, the solubility of HC-290 in [hmim][Tf₂N] was measured in the temperature range of 283.15 K to 343.15 K, which corresponds to the typical temperature range of an ARC. It should be noted that the maximum pressure here was 0.428 MPa; this is because the equilibrium cell was designed with a glass observation window, and the pressure resistance of the cell was limited to within 0.6 MPa. The experimental data are listed in

Table 3. Experimental data on the solubility of HC-290 in [HMIM][Tf₂N].

p/MPa	x1	p/MPa	x1	p/MPa	x1	p/MPa	x1
283.15 K		293.15 K		303.15 K		313.15 K
0.121	0.068	0.129	0.058	0.135	0.050	0.142	0.044
0.160	0.088	0.170	0.074	0.179	0.064	0.188	0.05
0.198	0.106	0.211	0.091	0.222	0.077	0.233	0.067
0.236	0.125	0.251	0.106	0.265	0.091	0.278	0.079
0.280	0.148	0.298	0.125	0.314	0.106	0.330	0.092
0.319	0.166	0.340	0.141	0.359	0.120	0.378	0.103
323.15 K		333.15 K		343.15 K
0.148	0.038	0.155	0.033	0.161	0.029
0.197	0.048	0.205	0.042	0.213	0.037
0.244	0.058	0.254	0.051	0.264	0.045
0.290	0.069	0.303	0.061	0.315	0.053
0.346	0.080	0.360	0.071	0.375	0.062
0.395	0.091	0.412	0.081	0.428	0.072

, and the trends of the mole fraction of HC-290 at different temperatures and pressures are given in Figure 4. As expected, the absorption capacity of [HMIM][Tf₂N] for HC-290 increased with decreasing temperature and increasing pressure. Moreover, HC-290 and [HMIM][Tf₂N] were completely miscible within the experimental temperature and pressure ranges.

The non-random two-liquid (NRTL) model and Krichevsky–Kasarnovsky (K-K) model were used to correlate the obtained solubility data in this work. The expression of the NRTL model is [39]:

$$\ln {\gamma }_1=x_2^2\left[{\tau }_{21}{\left({\displaystyle \frac{\exp \left(-\alpha {\tau }_{21}\right)}{x_1+x_2\exp \left(-\alpha {\tau }_{21}\right)}}\right)}^2+{\displaystyle \frac{{\tau }_{12}\exp \left(-\alpha {\tau }_{12}\right)}{{\left[x_2+x_1\exp \left(-\alpha {\tau }_{12}\right)\right]}^2}}\right]$$

(9)

$$\ln {\gamma }_2=x_1^2\left[{\tau }_{12}{\left({\displaystyle \frac{\exp \left(-\alpha {\tau }_{12}\right)}{x_2+x_1\exp \left(-\alpha {\tau }_{12}\right)}}\right)}^2+{\displaystyle \frac{{\tau }_{21}\exp \left(-\alpha {\tau }_{21}\right)}{{\left[x_1+x_2\exp \left(-\alpha {\tau }_{21}\right)\right]}^2}}\right]$$

(10)

where x₁ and x₂ are the mole fraction of HC-290 and [hmim][Tf₂N] in the liquid mixture in the equilibrium condition. γ₁ is the activity coefficient of HC-290 in the liquid phase. γ₂ is the activity coefficient of [hmim][Tf₂N]. τ₁₂ and τ₂₁ are the binary interaction parameters, which were calculated using the following expression:

$${\tau }_{12}={\tau }_{12,0}+{\tau }_{12,1}(T-273.15)+{\tau }_{12,2}{(T-273.15)}^2$$

(11)

$${\tau }_{21}={\tau }_{21,0}+{\tau }_{21,1}(T-273.15)+{\tau }_{21,2}{(T-273.15)}^2$$

(12)

Here, α, τ_21,0, τ_21,1, τ_21,2, τ_12,0, τ_12,1, and τ_12,2 are coefficients obtained through experimental data.

With respect to the activity coefficient of HC-290 in the liquid phase, γ₁, it can be calculated from the vapor–liquid equilibrium (VLE) relationship [40]:

$${\gamma }_1{x}_1{p}_1^{\mathrm{s}}={\zeta }_1{y}_{1}p$$

(13)

where p₁^s is the saturation vapor pressure of HC-290, and p is the pressure of the HC-290/[hmim][Tf₂N] mixture in the equilibrium condition. y₁ represents the mole fraction of HC-290 in the vapor phase. Due to the extremely low vapor pressure of [hmim][Tf₂N] [31], y₁ is assumed to be 1 here. ζ₁ is the correction factor:

$${\zeta }_1=\exp \left[{\displaystyle \frac{\left(B_1-v_1\right)\left(p-p_1^{\mathrm{s}}\right)}{RT}}\right]$$

(14)

where B₁ is the second virial coefficient, v₁ is the molar volume of HC-290 in the liquid phase, and R is the universal gas constant. B₁, p₁^s, and v₁ are obtained from Refprop 10.0 [35].

In the K-K model, the expression for the liquid-phase mole fraction (x₁) of HC-290 is given as follows [41]:

$$\ln \left({\displaystyle \frac{f_1}{x_1}}\right)=\ln He+{\displaystyle \frac{v_1^{\infty }p}{RT}}$$

(15)

where f₁ represents the fugacity of HC-290 at a given temperature and pressure. v₁^∞ denotes the infinite dilution molar volume of HC-290, and He represents the Henry’s law constant. He and v₁^∞ can be determined using the following equations:

$$\ln He=A_0+{\displaystyle \frac{A_1}{T}}$$

(16)

$$v_1^{\infty }=B_0+B_{1}T+B_2{T}^2$$

(17)

The coefficients A₀, A₁, B₀, B₁, and B₂ are regressed from the experimental results. The optimized coefficients in the NRTL model and K-K model are listed in

Table 4. Optimized coefficients in NRTL model and K-K model.

Parameters	Values	Parameters	Values
α	−0.0172	A0	7.001
τ12,0	17.726	A1	−1827
τ12,1	−0.0132	B0	−11,044
τ12,2	1.0963	B1	70.97
τ21,0	−23.0298	B2	−0.1087
τ21,1	0.02296
τ21,2	−0.00000423

.

The deviation distribution between the calculated values from the model and experimental data for the liquid-phase mole fraction is presented in Figure 5. For the NRTL and K-K models, the average absolute relative deviations (AARDs) were 0.76% and 0.78%, respectively. The maximum relative deviations (MRDs) were 3.40% and 3.24%. The AARD and MRD were calculated according to the equations shown below.

$$AARD={\displaystyle \frac{{\displaystyle \sum _i^n\left|(x_{\mathrm{cal}}-x_{\exp })/x_{\exp }\right|}}{n}}\times 100\%$$

(18)

$$MRD=\max \left(\left|{\displaystyle \frac{(x_{\mathrm{cal},i}-x_{\exp ,i})}{x_{\exp ,i}}}\right|\right)\times 100\%$$

(19)

3.2. Derived Thermodynamic Properties of HC-290/[hmim][Tf₂N]

To better understand the dissolution process of HC-290 in [hmim][Tf₂N], it was necessary to analyze the derived thermodynamic properties, such as enthalpy change (Δh_total) and entropy change (Δs_total). Typically, the dissolution of a gaseous solute in a liquid solvent at a given temperature occurs in two steps. In the first step, HC-290 condenses from the gas phase to a saturated liquid phase. The change in enthalpy (∆h_con) and entropy (∆s_con) in the condensation process can be obtained from REFPROP 10.0 [35]. In the second step, the saturated liquid HC-290 mixes with [hmim][Tf₂N], resulting in mixing enthalpy (∆h_mixing), mixing Gibbs free energy (∆g_mixing), and mixing entropy (∆s_mixing). The total enthalpy (∆h_total) and total entropy (∆s_total) for the entire dissolution process can be calculated using the following equations:

$$\Delta h_{\mathrm{total} }=\Delta h_{\mathrm{con} }+\Delta h_{\mathrm{mixing}}$$

(20)

$$\Delta s_{\mathrm{total} }=\Delta s_{\mathrm{con} }+\Delta s_{\mathrm{mixing} }$$

(21)

For an ideal solution, the expressions for the properties (∆h^ideal, ∆g^ideal, and ∆s^ideal) are:

$$\Delta h^{\mathrm{ideal} }=0$$

(22)

$$\Delta g^{\mathrm{ideal} }=RT\left(x_1\ln x_1+x_2\ln x_2\right)$$

(23)

$$\Delta s^{\mathrm{ideal} }=-R\left(x_1\ln x_1+x_2\ln x_2\right)$$

(24)

For a real solution, the values of the derived thermodynamic properties are the sum of the ideal properties and the excess properties:

$$\Delta h_{\mathrm{mixing} }=\Delta h^{\mathrm{ideal} }+\Delta h^{\mathrm{excess}}$$

(25)

$$\Delta g_{\mathrm{mixing} }=\Delta g^{\mathrm{ideal} }+\Delta g^{\mathrm{excess}}$$

(26)

$$\Delta s_{\mathrm{mixing} }=\Delta s^{\mathrm{ideal} }+\Delta s^{\mathrm{excess}}$$

(27)

The expressions for the excess thermodynamic properties (∆h^excess, ∆g^excess, and ∆s^excess) can be calculated based on the NRTL model:

$$\Delta h^{\mathrm{excess}}=-R{T}^2\left[{\displaystyle \frac{\partial \left(\Delta g^{\mathrm{excess}}/RT\right)}{\partial T}}\right]=-R{T}^2\left[x_1{\displaystyle \frac{\partial \left(\ln {\gamma }_1\right)}{\partial T}}+x_2{\displaystyle \frac{\partial \left(\ln {\gamma }_2\right)}{\partial T}}\right]$$

(28)

$$\Delta g^{\mathrm{excess}}=RT{\displaystyle \sum x_i}\ln {\gamma }_i=RT\left(x_1\ln {\gamma }_1+x_2\ln {\gamma }_2\right)$$

(29)

$$\Delta s^{\mathrm{excess}}={\displaystyle \frac{\Delta h^{\mathrm{excess}}-\Delta g^{\mathrm{excess}}}{T}}$$

(30)

where γ₁ is the activity coefficient of HC-290 in the liquid phase and γ₂ is the activity coefficient of [hmim][Tf₂N].

Based on experimental solubility data and the NRTL model, the values of ∆h_con, ∆s_con, ∆h_mixing, ∆g_mixing, ∆s_mixing, ∆h_total, and ∆s_total were calculated, and the results are listed in

Table 5. The calculated results of ∆h_con, ∆s_con, ∆h_mixing, ∆g_mixing, ∆s_mixing, ∆h_total, and ∆s_total for HC-290/[hmim][Tf₂N] system.

T/K	x1	∆hcon	∆scon	∆hmixing	∆gmixing	∆smixing	∆htotal	∆stotal
		/J∙mol−1	/J∙mol−1∙K−1	/J∙mol−1	/J∙mol−1	/J∙mol−1∙K−1	/J∙mol−1	/J∙mol−1∙K−1
283.15	0.068	−15,887.91	−56.11	21.37	−411.64	1.53	−15,866.54	−54.58
283.15	0.088	−15,887.91	−56.11	35.15	−473.60	1.80	−15,852.75	−54.32
283.15	0.106	−15,887.91	−56.11	49.75	−518.50	2.01	−15,838.15	−54.11
283.15	0.125	−15,887.91	−56.11	67.07	−556.78	2.20	−15,820.84	−53.91
283.15	0.148	−15,887.91	−56.11	90.17	−592.70	2.41	−15,797.73	−53.70
283.15	0.166	−15,887.91	−56.11	109.56	−614.12	2.56	−15,778.35	−53.56
293.15	0.058	−15,184.07	−51.80	1.62	−388.41	1.33	−15,182.45	−50.46
293.15	0.074	−15,184.07	−51.80	8.16	−447.58	1.55	−15,175.91	−50.24
293.15	0.091	−15,184.07	−51.80	17.43	−499.74	1.76	−15,166.64	−50.03
293.15	0.106	−15,184.07	−51.80	27.38	−538.19	1.93	−15,156.69	−49.87
293.15	0.125	−15,184.07	−51.80	42.05	−578.38	2.12	−15,142.02	−49.68
293.15	0.141	−15,184.07	−51.80	55.95	−605.91	2.26	−15,128.12	−49.54
303.15	0.05	−14,407.91	−47.52	−14.70	−366.20	1.16	−14,422.61	−46.36
303.15	0.064	−14,407.91	−47.52	−13.39	−425.78	1.36	−14,421.31	−46.16
303.15	0.077	−14,407.91	−47.52	−10.38	−473.13	1.53	−14,418.29	−46.00
303.15	0.091	−14,407.91	−47.52	−5.37	−517.00	1.69	−14,413.28	−45.83
303.15	0.106	−14,407.91	−47.52	1.84	−557.06	1.84	−14,406.07	−45.68
303.15	0.12	−14,407.91	−47.52	10.12	−588.88	1.98	−14,397.79	−45.55
313.15	0.044	−13,541.35	−43.24	−28.54	−347.83	1.02	−13,569.89	−42.22
313.15	0.05	−13,541.35	−43.24	−30.32	−377.55	1.11	−13,571.66	−42.13
313.15	0.067	−13,541.35	−43.24	−32.93	−451.02	1.34	−13,574.27	−41.90
313.15	0.079	−13,541.35	−43.24	−32.76	−494.96	1.48	−13,574.11	−41.76
313.15	0.092	−13,541.35	−43.24	−30.87	−536.45	1.61	−13,572.22	−41.63
313.15	0.103	−13,541.35	−43.24	−27.98	−567.26	1.72	−13,569.33	−41.52
323.15	0.038	−12,562.33	−38.87	−39.87	−324.78	0.88	−12,602.20	−37.99
323.15	0.048	−12,562.33	−38.87	−46.53	−378.42	1.03	−12,608.86	−37.85
323.15	0.058	−12,562.33	−38.87	−51.76	−425.83	1.16	−12,614.09	−37.72
323.15	0.069	−12,562.33	−38.87	−55.94	−471.99	1.29	−12,618.27	−37.59
323.15	0.08	−12,562.33	−38.87	−58.59	−512.83	1.41	−12,620.91	−37.47
323.15	0.091	−12,562.33	−38.87	−59.79	−549.06	1.51	−12,622.12	−37.36
333.15	0.033	−11,431.60	−34.31	−49.13	−302.99	0.76	−11,480.74	−33.55
333.15	0.042	−11,431.60	−34.31	−59.12	−356.24	0.89	−11,490.73	−33.42
333.15	0.051	−11,431.60	−34.31	−67.78	−403.63	1.01	−11,499.38	−33.31
333.15	0.061	−11,431.60	−34.31	−75.90	−450.60	1.12	−11,507.50	−33.19
333.15	0.071	−11,431.60	−34.31	−82.52	−492.50	1.23	−11,514.13	−33.08
333.15	0.081	−11,431.60	−34.31	−87.74	−530.03	1.33	−11,519.34	−32.99
343.15	0.029	−10,082.14	−29.38	−57.03	−310.39	0.66	−10,139.17	−28.72
343.15	0.037	−10,082.14	−29.38	−69.77	−364.90	0.77	−10,151.91	−28.61
343.15	0.045	−10,082.14	−29.38	−81.31	−413.40	0.88	−10,163.46	−28.51
343.15	0.053	−10,082.14	−29.38	−91.70	−461.48	0.97	−10,173.85	−28.42
343.15	0.062	−10,082.14	−29.38	−102.07	−504.39	1.06	−10,184.21	−28.32
343.15	0.072	−10,082.14	−29.38	−112.02	−542.84	1.16	−10,194.16	−28.23

. The variations in mixing Gibbs free energy, total entropy change, and total enthalpy changed with respect to the mole fraction, and are shown in Figure 6.

Both ∆h_total and ∆s_total exhibited negative values, indicating that the dissolution process of HC-290 in [hmim][Tf₂N] is an exothermic process. Furthermore, the positive value of ∆s_mixing suggests that the mixing process of HC-290 with [hmim][Tf₂N] is thermodynamically irreversible. However, ∆h_mixing did not follow a strictly positive or negative trend. This phenomenon can be primarily attributed to two competing effects. On one hand, the dissolution of HC-290 in [hmim][Tf₂N] disrupts the hydrogen bonding network and ionic interactions within the ionic liquid, necessitating energy absorption and resulting in an endothermic contribution. On the other hand, according to van der Waals interactions and Lewis acid−base theory [42], the intermolecular interactions between the refrigerant and the ionic liquid introduce an exothermic effect. The balance between these opposing thermodynamic effects determines the overall sign of ∆h_mixing. As illustrated in Figure 6, the Gibbs free energy of mixing ∆G_mixing for HC-290 in [hmim][Tf₂N] remains negative and decreases with increasing temperature, indicating that the dissolution process is thermodynamically spontaneous and becomes more favorable as temperature rises.

3.3. Comparison of the Solubility of Different Refrigerants in [hmim][Tf₂N]

To systematically evaluate the absorption performance of [hmim][Tf₂N] with various refrigerants, the experimental data on the solubility of 16 refrigerants, including HFCs [10,12,13], HFOs [11,14], HCs [15,17,19], and CO₂ [21], in [hmim][Tf₂N] reported in the literature were summarized in this work. The Henry’s constants of these refrigerants at 313.15 K and 333.15 K were calculated and compared, as indicated in Figure 7.

With respect to HC refrigerants, it can be observed that at 313.15 K, the Henry’s constant followed the order: HC-170 > HC-290 > RC-270 > HC-600a. However, at 333.15 K, the values followed the order: HC-170 > RC-270> HC-290 > HC-600a. This indicates that the solubility of RC-270 in [hmim][Tf₂N] exhibits greater temperature sensitivity. In addition, in comparing the He values of HC-170, HC-290, and HC-600a in [hmim][Tf₂N], it can be concluded that the Henry’s constant increases as the carbon number decreases. Additionally, it was observed that most HFO and HFC refrigerants exhibited lower He values compared to the HC refrigerants, meaning that [hmim][Tf₂N] has a higher absorption capacity for HFOs and HFCs than HCs.

4. Conclusions

In this work, the solubility of HC-290 in [hmim][Tf₂N] was reported over a temperature range of 283.15 K to 343.15 K and pressures up to 0.428 MPa. The experimental data were correlated using the NRTL model and the K-K model. Both the NRTL and K-K models provided excellent correlative results with absolute average relative deviations of 0.76% and 0.78%, respectively. The Gibbs free energy, enthalpy change, and entropy change during the dissolution process of HC-290 in [hmim][Tf₂N] were calculated based on the NRTL model. The results confirm that the dissolution process is spontaneous, exothermic, and not entropy-driven. The Henry’s constants of 16 refrigerants (including HCs, HFCs, HFOs, CO₂) in [hmim][Tf₂N] at 313.15 K and 333.15 K were calculated and compared. The results show that HFOs and HFCs exhibited lower He values compared to HCs.

This work provides valuable solubility data for HC-290 in [hmim][Tf₂N] for the first time, filling this gap and offering essential insights into the behavior of this refrigerant in ionic liquids. Ionic liquids, as promising green solvents, are considered key materials for low-emission, sustainable refrigeration technologies. The findings contribute to a better understanding of HC-290′s potential in enhancing the performance and environmental sustainability of refrigeration systems.