Volumetric Properties for the Aqueous Solution of Yttrium Trichloride at Temperatures from 283.15 to 363.15K and Ambient Pressure

Tianjin Key Laboratory of Brine Chemical Engineering and Resource Eco-Utilization, College of Chemical Engineering and Materials Science, Tianjin University of Science and Technology, Tianjin 300457, China Central Laboratory of Geological Mineral Exploration and Development Bureau of Tibet Autonomous Region, Tibet 850033, China School of Chemistry and Chemical Engineering, Linyi University, Linyi 27600, China


Introduction
Rare earth elements (REEs) are vital ingredients of modern technologies, especially in energy, environmental protection, digital technology, the nuclear industry, and medical applications. REEs are also an integral part of electronic devices serving as magnets, catalysts, and superconductors, owing to their chemical, catalytic, electrical, magnetic, and optical properties [1][2][3][4][5][6][7]. What is more, in nuclear medicine, many radioisotopes such as yttrium have been used in diagnostic or therapeutic procedures to treat a wide range of diseases, including cancer [8]. e continuously increasing demand for yttrium has led to the high economic importance of yttrium. Tibet is one of the famous geothermally active regions, and the geothermal water resources with high concentrations of rare earth elements are distributed widely [9]. It is well known that thermodynamic properties such as solubilities of phase equilibria and apparent molar volumes at wide temperatures are essential to explore novel methods for more effective and efficient extraction of yttrium and provide information about the ion interactions. erefore, revealing the ion-interaction to construct a thermodynamics model at multitemperatures for the binary system (YCl 3 + H 2 O) is of great importance.
As to the volumetric behaviors of YCl 3 aqueous solutions, data reported in the literature [10,11] were mainly focused on 298.15 K, even using the traditional pycnometric measurement method [11]. With the progress of technology, the density measurement for the aqueous solution at multiple temperatures with a vibrating-tube densimeter is more convenient and accurate than that of the pycnometric measurement [12][13][14]. However, up to now, there are no data reported on the apparent molar volumes at temperatures from 283.15 K to 363.15 K and 101.325 kPa. Hence, studying the volumetric properties of the binary system (YCl 3 + H 2 O) at multitemperatures is essential for utilizing rare earth elements from geothermal water resources.
In this study, densities of YCl 3 aqueous solutions in the range of 0.08837-1.60639 mol·kg − 1 from 283.15 to 363.15 K and 101.325 kPa were measured by an Anton Paar digital vibrating-tube densimeter. e derived properties of apparent molar volumes (V ϕ ), partial molar volumes (V ϕ ), and the coefficients of thermal expansion of the solution (α) for YCl 3 aqueous solutions were obtained, and their variation tendency against temperature and molality have been discussed in detail. e Pitzer singlesalt parameters of YCl 3 at multitemperatures and temperature-dependence equations were also obtained for the first time.

Apparatus and
Procedure. Stock solutions of YCl 3 were prepared in the glove box filled with nitrogen gas (UNIlab Plus, MBraun, Germany), in which precise YCl 3 ·6H 2 O and DDW were weighted using the analytical balance (Mettler Toledo, Swiss) with an uncertainty 0.2 mg, followed by vigorous shaking of the solution and then filtering through a prewashed 0.2 μm Nylon "low extractable" membrane filtering unit. e stock solution concentration of YCl 3 expressed in molality was determined by titrimetric analysis using mercuric nitrate with uncertainty within 0.003 in the mass fraction [15]. e concentration of Y 3+ can be obtained via ion balance and evaluated through measurement by an inductively coupled plasma optical emission spectrometer (ICP-OES, Prodigy, Leeman Corporation, America) with an uncertainty of ±0.005 in mass fraction. Moreover, all the aqueous solutions employed in experimental measurements were prepared by mass dilution of the stock solution in the nitrogen glove box and stored in glass bottles at 4°C in the refrigerator.
All the density measurements for each solution were completed within two days after the stock solution was prepared. Densities of these solutions were measured using an Anton Paar digital vibrating-tube densimeter (DMA4500, Anton Paar Co., Ltd., Austria) with an uncertainty of ±1.4 mg·cm − 3 , and the densimeter has a heating attachment (Anton Paar) that keep the temperature fluctuations within ±0.01 K. Before the measurement, the densimeter was calibrated during each series of measures with dry air and freshly DDW at 293.15 K under atmospheric pressure. e results were 0.00120 g·cm − 3 for dry air and 0.99820 g·cm − 3 for DDW, which agree well with the values in the literature [16]. e reliability of the density data was ascertained by making measurements of DDW using the calibrated apparatus at a 10 K interval from 279.15 to 369.15 K and atmospheric pressure, and the density values of pure water are given in Table 1, which agree well with the data in the literature [17]. e maximum relative deviation is less than 0.003%. Finally, all measurements for the densities of YCl 3 (aq) were conducted at temperature intervals of 5 K from 283.15 to 363.15 K and atmospheric pressure.

Results and Discussion
3.1. Densities. Densities of YCl 3 aqueous solution against molality and temperature were determined in triplicate, and the results are given in Table 2.
Based on the experimental data in Table 2, a 3D diagram of the density for the YCl 3 aqueous solution against temperature and molality is shown in Figure 1. It was clearly seen that the densities of YCl 3 aqueous solutions decreased with the increasing temperature at constant molality.

Journal of Chemistry 3
Nevertheless, at the same temperature, the density values of YCl 3 aqueous solutions are increased indistinctively with the increase of YCl 3 molality. e clear changing trend for density data may be caused by the rise in solvent-solvent and solute-solvent interactions. As the temperature increases, the volume of the aqueous solutions increases, and the density decreases. e density values at constant molality have been fitted against (T − 273.15) by the least-squares method.
where ρ is the density (g·cm − 3 ) of the solution; θ � (T − 273.15) K, T is the absolute temperature, and A i is the empirical constant. e relevant parameters and the correlation coefficients r related to the density-temperature fit obtained by applying equation (1) are given in Table S1 (Supplementary Materials). e values of the correlation coefficients (r) are close to 1.
According to the definition [18], the coefficient of thermal expansion of the solution is expressed with the following equations.
Based on the calculation using equation (4), the thermal expansion α (K − 1 ) values of YCl 3 aqueous solutions with various molalities at different temperatures were calculated and are given in Table 3. According to the calculated data, the relation diagram of the thermal expansion coefficient (α) and the molality at temperature intervals of 5 K from 283.15 to 363.15 K is shown in Figure 2. It can be seen that the thermal expansion coefficient of YCl 3 aqueous solution is increased with the increase of temperature at the constant molality. With the rising of molality, the thermal expansion coefficient increased obviously at T � (283.15-303.15) K, almost unchanged at T � 308.15 K, and then decreased slightly at T � (313.15-363.15) K.

Apparent Molar Volumes.
e apparent molar volumes can be derived from the measured densities of pure water and YCl 3 aqueous solutions. eir values are calculated with the following equation [19]: where ρ w and ρ are the densities (g·cm − 3 ) of the pure water and YCl 3 aqueous solutions, respectively; m i is the molality (mol·kg − 1 ) for YCl 3 aqueous solution, and M a is the molar mass (g·mol − 1 ) of YCl 3 . e calculated apparent molar volumes are given in Table 4, and the 3D surfaces (m i , T, V ϕ ) are shown in Figure 3. It can be seen that the apparent molar volumes of YCl 3 aqueous solutions increased with the increase of molality at the constant temperature. With the increasing temperature, the apparent molar volumes increase when the temperature is varied within 283.15-308.15 K, and the variation tendency is opposite when the temperature is higher than 308.15 K. It can be concluded that the ionic association of yttrium and chlorine ions is strong at low temperatures [20].

Partial Molar Volumes of Solute.
e relationship between the apparent molar volume, V ϕ (m i , T), and the partial molar volume can be expressed.  Journal of Chemistry 5 where V ϕ refers to the apparent molar volume (cm 3 ·mol − 1 ), m i is the molality (mol·kg − 1 ) for YCl 3 , and (zV ϕ /zm i ) P,T can be obtained from equations (7) and (8).
zV ϕ zm i P,T � 1 2 where B i is the empirical constant for fitting apparent molar volume and molality at invariable temperature by the least squares, and the values of the parameters with the correlation coefficients r are presented in Table S2.

Substitution of the above equation into equation (6) yields
e calculated values for partial molar volumes of solute are given in Table 5 and shown in Figure 4. It shows that the partial molar volumes of YCl 3 are increased with the increase of molality at the constant temperature.

Pitzer Parameters of YCl3.
Pitzer's electrolyte solution theory was developed based on ion-interaction and statistical mechanics, and it can accurately express the thermodynamic properties of the aqueous electrolyte solution [21]. e apparent molar volumes of YCl 3 were calculated using the following Pitzer equation [22].
In the case of B v M,X (m i ), the ionic strength dependence of a solution can be imposed as follows.
where M and X are Y 3+ and Cl − , m i is the molality (mol·kg − 1 ) of the aqueous YCl 3 solutions, given in Table 4, v w is the volume of 1 kg pure water, v (m r ) is the volume of m r , in which A v is the Debye-Hückel limiting law slope for the apparent molar volume [23,24], α B1 � 2.0 kg 1/2 ·mol 1/2 , b � 1.2 kg 1/2 ·mol -1/2 , I is the total ionic strength given by I � (1/2) m i z 2 i , R � 8.314472 cm 3 ·MPa K − 1 ·mol − 1 is the gas constant, T is a temperature in K. Pitzer's parameters B v M,X (m i ) account for short-range interactions between M and X, and the third virial coefficient C v M,X means for triple ion interactions. e Pitzer ion-interaction parameters are expressed as functions F (i, p, T).
with F (i, p, T) represented as [23] F(i, p, T) � a 1 + a 2 ln T 298.15 where T is a temperature in Kelvin, p is a pressure in kPa, and a i are the polynomial coefficients for equation (16). All parameters were calculated by the IAPWS-95 for the thermodynamic properties of water and the international formulation for the dielectric properties of water [25]. e available experimental data were fitted by the leastsquares method to evaluate single-salt parameters by Pitzer ion-interaction theory. Based on the apparent molar volumes for (YCl 3 + H 2 O) from 283.15 to 363.15 K in Table 4, the single-salt parameters for YCl 3 at each temperature were fitted based on equations (10)- (12) and are given in Table 6. e multiple correlation coefficients (r) were almost equal to 1, and the mean standard deviations (σ) were within ±0.0359. e temperature correlation coefficients (a i ) were fitted based on equations (13)- (16) and are given in Table 7.
e deviation of single-salt parameters (β (0)v MX , β (1)v MX , and C v MX ) for YCl 3 between all parameterization data obtained by the Pitzer model and temperature-dependence data obtained by equation (16) is within ±0.022, which indicated that the temperature-dependence equation (16) and the temperature correlation coefficients fitted in this work are reliable.  Journal of Chemistry 9

Conclusions
β (1)v MX , and C v MX ) of YCl 3 were parameterized from the Pitzer ion-interaction model, the temperature-dependence equation was established, and its correlation coefficients (a i ) were obtained for the first time.

Data Availability
e data used to support the findings of this study are available in the article and the supplementary materials.

Conflicts of Interest
e authors declare that they have no conflicts of interest.