Thermodynamic Properties and Phase Equilibria in the WaterâTri-n

Article pubs.acs.org/jced

Thermodynamic Properties and Phase Equilibria in the Water− Tri‑n‑butyl Phosphate System Aleksey I. Maksimov* and Nikita A. Kovalenko Chemistry Department, Lomonosov Moscow State University, 119991 Moscow, Russia

ABSTRACT: Tri-n-butyl phosphate (TBP) is widely used as an extractant in many technological processes. A thermodynamic model of the base extraction system water−tributyl phosphate is of great importance for industry. In this work a threedimensional shape of the liquid phase Gibbs energy surface was modeled for the entire concentration range from pure water to pure TBP at temperatures from 273.15 K to more than 400 K and a pressure of 101325 Pa. Volumetric properties of the water−TBP solutions were measured at 288.15, 298.15, and 323.15 K. To obtain a thermodynamic description of the system of interest a new model of the excess Gibbs energy, the generalized local composition model (GLCM), was developed. Density of solutions, activity of components, enthalpy of mixing, and liquid−liquid equilibria in the water−TBP system were described by the GLCM expression.

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INTRODUCTION Tributyl phosphate is a common solvent and extractant used for the extraction of metal ions from acidic solutions. Its typical applications are recycling of the nuclear fuel (PUREX process), separation of zirconium from hafnium, extraction and separation of rare earth elements. Development and optimization of such a kind of industrial processes may be solved by the thermodynamic approach, which is based on the construction of the thermodynamic model of the multicomponent system. This method implies a description of the system Gibbs energy. The reliable thermodynamic model has to be based on the set of various experimental data. Whereas extraction systems have been experimentally studied very extensively, the essential subsystem water−tributyl phosphate does not have a strict thermodynamic description. Some efforts on the thermodynamic modeling of the binary system water−tributyl phosphate were made.1−7 Roddy and Mrochek1 found that solubility of water followed Henry’s law in the narrow concentration range below aH2O = 0.75. Water activity at 298.15 K was described using three-term Redlich−Kister model,2 the model of ideal associated solution, assuming monomers and dimer formation,3 the model of regular solution expressed in terms of volume fraction.4 A description of liquid− liquid equilibria in the water−TBP system was made in works devoted to the modeling of higher order systems which also included acids and additional solvents.5−7 Phase equilibria were © 2016 American Chemical Society

modeled with the help of different associates, extraction of water into TBP was described, but the solubility of tributyl phosphate in water was not. Formation of solvates in the water−TBP system was the reason for lively debates in scientific literature. Rozen and Khorkhorina4 analyzed different spectroscopical evidence and concluded that assumptions about their formation was untenable. Available thermodynamic descriptions of the water−TBP system are not applicable for the comprehensive modeling of the extraction process. Moreover, the fact that this problem was not solved during 50 years of intensive investigations shows that standard models cannot describe thermodynamic properties and phase equilibria in this system. In this work a new thermodynamic model of excess Gibbs energy, generalized local composition model (GLCM), was developed and applied to describe all experimental data on the properties of the system of interest. This model generalizes such well-known local composition models as Wilson,8 Tsuboka−Katayama,9 and universal quasichemical (UNIQUAC).10 As the previous results have been reported partly on the molarity scale, the density of the water− TBP solutions was measured for conversion between different Special Issue: Proceedings of PPEPPD 2016 Received: July 3, 2016 Accepted: November 8, 2016 Published: November 17, 2016 4222

DOI: 10.1021/acs.jced.6b00582 J. Chem. Eng. Data 2016, 61, 4222−4228

Journal of Chemical & Engineering Data

Article

concentration scales and finding out the pressure dependence of the Gibbs energy. Finally, strict a thermodynamic model describing density of solutions, activity of components, enthalpy of mixing and liquid−liquid equilibria in the water−TBP system was obtained.

Table 3. Experimental Values of Density ρ of the Water−TBP Solutions as a Function of TBP Mole Fraction XTBP and Temperature at Pressure p = 97590 Paa ρ/g·cm−3

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EXPERIMENTAL SECTION Reagents. Tributyl phosphate (TBP, C12H27O4P) was supplied by Acros Organics with a purity ≥99%. Water content was controlled by Karl Fischer titration and found to be 0.108 ± 0.003 mass %. For the preparation of mixtures, distilled water and pure TBP without purification were used. Water content in the TBP was considered in the calculation of solution concentration. Sources and purity of the used chemical samples are listed in Table 1.

tri-n-butyl phosphate (TBP) water

source Acros Organics

initial mass fraction purity ≥0.99 distilled

Density Measurements. Density was measured by means of vibrating densitometer TERMEX ≪VIP-2MP≫ with built-in thermostat. The stability of thermostat temperature is ±0.05 K, the accuracy of density measurement is ±0.0001 g·cm−3. The densitometer was calibrated with air, distilled water, and state standard samples (8580-2004, 8585-2004) produced by the D.I. Mendeleyev Institute for Metrology (VNIIM). Solutions for the density measurements were prepared by mixing TBP with water; the accuracy of weighing is ±0.001 g. Density was calculated with the following equation:

a

288.15 298.15 323.15

7183.9 7186.6 ± 2.7 7189.7 ± 3.6

−6406.1 −6405.1 ± 2.7 −6401.2 ± 3.7

2 4 3

i

ϕi xi

+

θi =

z 2

∑ qixi ln i

θi − ϕi

∑ qixi ln(∑ θτj ji) i

j

∑ xi ln(∑ xjρji ) i

xi × qi ∑j xj × qj

(2)

j

ϕi =

,

xi × ri , ∑j xj × rj

⎛ aij ⎞ τij = ρij × exp⎜ − ⎟ ⎝ T⎠

where xi is the mole fraction of the ith component; qi and ri are the structural parameters, relative area, and the van der Waals volume of the molecule i (see Table 4); z is the coordination

Table 2. Coefficients of the Calibration Function in Equation 1 Na

∑ xi ln +

where ρ is the density, g·cm−3; τ is the vibration period of measuring cell, ms; k and b are coefficients of calibration function, listed in Table 2.

b/g·cm−3

0.9530 0.9524 0.9519 0.9517 0.9516 0.9515 0.9515 0.9513

Gex = RT ∑i ni

(1)

k/ms−2

323.15 K

0.9755 0.9747 0.9740 0.9737 0.9734 0.9732 0.9730 0.9727

types of experimental data on the properties of the system of interest. The excess Gibbs energy and activity coefficients of components in this model are calculated by the eqs 2 and 3. Standard local composition models could be obtained from GLCM expression assuming ρij = 1 (UNIQUAC),10 qi = 1, ri = 1, ρij = 1 (Wilson equation),8 qi = 1, ri = 1 (Tsuboka−Katayama equation).9 This expression has four adjustable parameters for the description of a binary system, this makes it more flexible than other local composition models.

Karl Fischer titration

T/K

298.15 K

0.9845 0.9836 0.9828 0.9824 0.9821 0.9819 0.9817 0.9813

Standard uncertainties are u(x) = 0.0001, u(T) = 0.05 K, u(p) = 700 Pa. Expanded uncertainty for the density U(ρ) = 0.0005 g·cm−3 (0.95 level of confidence).

analysis method

ρ = kτ 2 + b

288.15 K

a

Table 1. Sources and Purity of the Chemical Samples chemical name

XTBP 0.5196 0.5954 0.6940 0.7419 0.7901 0.8413 0.8880 0.9843

Table 4. Relative Area and the van der Waals Volume of the Components

Number of standard samples.

water10 TBP13

Results of the water−TBP solutions density measurements at 288.15, 298.15, and 323.15 K are listed in Table 3.

q

r

1.40 9.000

0.92 10.475

number set equal to 10; aij and ρij are temperature and pressure dependent parameters of binary interactions between i and j molecules (aij ≠ aji, ρij ≠ ρji, aii = 0, ρii = 1).

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THERMODYNAMIC MODELING Generalized Local Composition Model. Different thermodynamic models were tested for the description of the water− TBP liquid phase properties: nonrandom two liquid (NRTL),11 universal quasichemical (UNIQUAC),10 Redlich−Kister series expansion.12 Very low solubility of tributyl phosphate in water makes it difficult to use listed models, none of them are applicable for the common description of all of the experimental data. This is confirmed by the fact that none of these widespread models was used for the thermodynamic description of the water−TBP system before. A new thermodynamic model, the generalized local composition model (GLCM), was developed to describe all

⎛ ⎛ ϕ ⎞⎞ ϕ z × qi × ⎜⎜1 − i + ln⎜ i ⎟⎟⎟ xi xi 2 θi ⎝ θi ⎠⎠ ⎝ ⎡ θj × τij ⎤ ⎥ + qi⎢1 − ln(∑ θk × τki) − ∑ ⎢⎣ ⎥ k j ∑k θk × τkj ⎦

ln γi = 1 −

ϕi

+ ln

ϕi

−

⎡ − ⎢1 − ln(∑ xj × ρji ) − ⎢⎣ j

∑ j

⎤ ⎥ ∑k xk × ρkj ⎥⎦ xj × ρij

(3)

Calculation Procedure. The estimation of model parameters was performed by a least−squares procedure using liquid−liquid 4223



(6)

is the molar Gibbs energy of pure liquid i. Therefore

i

(7)

⎛ ∂μ ⎞ where ⎜ ∂pi ⎟ = V m0 , i is the molar volume of pure component i ⎝ ⎠T , n

T ,n

∑i Mixi

= ∑i xi

Mi ρi0

+

(

∂(G ex / ∑i ni) ∂p

)

T ,n

(8)

The density of pure water is known very accurately, in this work it was calculated with the Kell’s equation.15 Data on the density of pure TBP from different sources16−22 are contradictory. The discrepancy between values at 298.15 K presented in the literature is 0.005 g·cm−3. So, the temperature dependence of the pure TBP density was optimized in this work. Liquid−liquid equilibria calculations were performed in two ways. In the first stage of the parameters optimization, the convex hull method23 was used since it is not sensitive to the initial approximation. Final parameters optimization were performed with the calculation of phase equilibria by equality of the chemical potentials method, which is more accurate. The following temperature and pressure dependence of the parameters has been found satisfactory for fitting experimental data: aij = aij(0) + aij(1)T + aij(2)T 2 + aij(3)T 3 + (aij(4) + aij(5)T )p ρij = ρij(0) + ρij(1)T + ρij(2)T 2 + (ρij(3) + ρij(4)T )p (9) 4224

a(2) ij

−0.20272 ± 0.00027 (8.09827 ± 0.00028)·10−2

( )

a(1) ij

ρi

63.2949 ± 0.055 −884.672 ± 0.13

∑i Mini m = M ∂G ex V ∑i ni 0i + ∂p

a(0) ij

ρ=

1313.68 ± 1.9 258975.3 ± 22

ρi

is the density of the pure liquid i. Density of the solution is connected with its Gibbs energy by the following equation:

i−j

equal to M0i , where Mi is the molar mass of the ith component; ρ0i

(1)−(2) (2)−(1)

Table 5. GLCM Parameters with 95% Confidence Intervals for the Water (1)−TBP (2) System

0

1.887938 ± 0.00018 −6.587108 ± 0.00082

⎛ ∂μ 0 ⎞ ⎛ ∂Gex ⎞ i ⎟ +⎜ ⎟ ⎟ ⎝ ∂p ⎠T , n ⎝ ∂p ⎠T , n

∑ ni⎜⎜

−566.286 ± 0.05 1960.82 ± 0.23

V=

i

ρ(2) ij

where

i

ρ(1) ij

i

μ0i

ρ(0) ij

∑ niμi0 + RT ∑ ni ln xi + RT ∑ ni ln γi

(5649.3 ± 1)·10−6 −(19291.15 ± 2.9)·10−6

The Gibbs energy of the solution is calculated by the following expression:

(1)−(2) (2)−(1)

(5)

(4.87 ± 0.1)·10−5 (5.229 ± 0.19)·10−5

a(4) ij

−(7.6756 ± 0.032) 10−2 −2.528418 ± 0.00032 ρ(3) ij

a(3) ij

⎛ ∂G ⎞ V=⎜ ⎟ ⎝ ∂p ⎠T , n

(2.20123 ± 0.0098)·10−4 −(8.42598 ± 0.0097)·10−5

(4)

Volume of the phase is connected with its Gibbs energy by the partial derivative of the Gibbs energy with respect to pressure at constant temperature and amount of components:

G=

(18946.903 ± 3.5)·10−9 (64704.26 ± 2.1)·10−9

⎛ ∂(Gex /T ) ⎞ Δmix H = −T 2⎜ ⎟ ⎝ ∂T ⎠p

a(5) ij

equilibrium data, vapor−liquid equilibrium data, enthalpy of mixing, volumetric properties, and activity of water. The objective function was the sum of squared differences between experimental and calculated values. The ideal gas equation of state was used for the vapor pressure calculation. Data on the saturated vapor pressure of the water were taken from ref 14. The enthalpy of mixing could be calculated from Gibbs−Helmholtz equation:

0 (8480.377 ± 1.3)·10−6 ρ(4) ij

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Article

95% confidence intervals for the parameters were calculated from the Jacobian of the objective function. Only statistically significant parameters were used.

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RESULTS AND DISCUSSION Obtained GLCM parameters with their confidence intervals are listed in Table 5. Parameters are given with an excess number of significant digits to avoid a poor description of experimental data due to their mutual correlation. The following types of experimental data on the properties of the water−TBP system are presented in the literature: partial water vapor pressure (or activity of water), mutual solubility of components at wide range of temperatures, enthalpy of mixing, density of solutions at 298.15 K. All the data that were used for modeling are summarized in Table 6. Table 6. Experimental Data Used for Modelling of the Water− TBP system data type

ref

water vapor pressure

1 2 3 4 24 25

liquid− liquid equilibria

16 26 27 28 29 30 31 32 1 16 17 18 21 22 present work

heat of mixing density

T/K 298.15 298.15 298.15 298.15 298.15 298.15, 317.9, 330.6 298.15 273.15−407.15 289.15−295.15 276.45−323.15 298.15 273.15−333.15 298.15 298.15 298.15 298.15 298.15 288.04−357.2 288.15−308.15 298.15−323.15 288.15, 298.15, 323.15

XTBP

MRDa/%

0.488−0.989 0.485−0.961 0.757−0.978 0.658−0.825 0.564−0.951 0.507−0.913

5 5 15 5 3 4

0.691−0.947 0.556−0.839 0.488−0.948 1 1 1 1 1 0.519−0.984

3 3 32 4 9 3 21 33 0.007 0.02 0.04 0.03 0.01 0.005 0.005

a Mean relative deviation MRD(X)% = 1/N·∑|Xexp − Xcalc|/Xexp·100, where Xexp and Xcalc are the experimental and calculated values and N is the number of experimental points.

The density of the pure TBP was measured at a wide range of temperatures,16−22 while the density of the water−TBP solutions was investigated only at 298.15 K.1 Data on the density of pure TBP from different sources are contradictory, so it was decided to optimize this value with GLCM binary interaction parameters simultaneously. Results of the measurements of Swain et al.19 and Tian and Liu20 differ from others largely, thus these values of TBP density were excluded from optimization procedure. Linear dependence of TBP density from temperature in the range from 288 to 357 K is found to be

Figure 1. Density of the water−TBP solutions at (a) 298.15 K, (b) 288.15 K, (c) 323.15 K. Black line, calculations with the obtained model; black circles, present work measurements; red pluses, ref 1; red asterisk, ref 16; red cross, ref 17; red circle, ref 18; red triangle, ref 19; blue triangle, ref 20; blue circle, ref 21; green circle, ref 22

It can be seen that our measurements are in a good agreement with the existing experimental data, while obtained model parameters describe all of the data on the density of solutions. Vapor pressure in the water−TBP system was measured by the isopiestic and isoteniscope methods.1−4,16,24,25 The saturated vapor pressure of pure TBP at 298.15 K was measured29 and found to be more than three orders of magnitude lower than that of water. This difference in the saturated vapor pressure of components allows treating results of the total vapor pressure

ρTBP = ( −850.613 ± 8.3)10−6 × T + 1.22619 ± 0.00009 [g/cm 3]

Results of the density measurements and their description by the model at 288.15, 298.15, and 323.15 K are shown in Figure 1. 4225



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thermodynamic model. Experimental and calculated activities of water are shown in Figure 2. There is a large discrepancy in the literature data, results of the measurements of Johnson et al.3 differ the most from others and have the worst description with the obtained thermodynamic model. The values of water activity

measurements as partial pressure of water, but Kirgintsev and Luk’yanov24 observed significant overstating of water activity even with a small volatilization of TBP and took this fact into account. Most of the data were obtained at 298.15 K, Apelblat25 also made measurements at higher temperatures (317.9 and 330.6 K). The partial vapor pressure of water was measured by Mikhailov et al.16 without thermostatting the system, so this data were considered as the least reliable. Hardy et al.30 presented data on the dependence of the organic phase composition from water activity. The system in those experiments included salts for keeping constant water activity and cannot be regarded as binary, so the result of this work was not used for the construction of

Figure 3. Enthalpy of mixing of TBP with water at 298.15 K. Black line, calculations with the obtained model; red circles, ref 31; blue circles ref 32.

Figure 4. Liquid−liquid equilibria in the water−TBP system: (a) solubility of water in tributyl phosphate; (b) solubility of tributyl phosphate in water. Black line, calculations with the obtained model; blue triangles, ref 16; red circles, ref 26; blue crosses, ref 27; blue circles, ref 28; green triangle, ref 29; green circles, ref 30.

Figure 2. Activity of water in the water−TBP system at (a) 298.15 K, (b) 317.9 K, (c) 330.6 K. Black line, calculations with the obtained model; red triangles, ref 1; green crosses, ref 2; black squares, ref 3; black circles, ref 4; blue triangles, ref 24; purple circles, ref 25. 4226



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obtained by Kirgintsev and Luk’yanov24 have the best description, thus these data are regarded as the most reliable. Enthalpy of mixing data in the water−TBP system obtained by Kertes and Tsimering31 and Liu et al.32 at 298.15 K are compared with the calculations results in Figure 3. There is an inconsistency between experimental data from different sources. The calculation results mostly agree with experimental data of Liu et al.,32 thus data of Kertes and Tsimering31 may be considered as unreliable. Mutual solubility in the water−TBP system was investigated at a range of temperatures from 273 to 520 K.2,4,16,26−30,33 Critical review of these data was made,34 all experimental results were classified as doubtful, tentative, or recommended; an equation for the calculation of reference solubility values was also suggested. Since we used only initial experimental data for the modeling, results of calculations of Goral et al.34 were not used. Liquid−liquid equilibria were calculated in the water−TBP system. As can be seen from Figure 4, the thermodynamic model represents all existing experimental data, even the very small solubility of TBP in water. Parameters of the suggested thermodynamic model have cubic and linear dependence from temperature and pressure, respectively. Their strong dependence from temperature may be explained by the quite complicated temperature dependence of mutual solubility of TBP and water. Nevertheless, obtained GLCM parameters are statistically significant, and the thermodynamic model has physically correct behavior; it describes existing experimental data and extrapolates thermodynamic properties of the

Our results at 298.15 K are in a good agreement with the data occurring in the literature, while the density of solutions at 288.15 and 323.15 K was obtained for the first time. It was found that such widespread models as NRTL, UNIQUAC, and Redlich−Kister are not applicable for the thermodynamic description of the water−TBP system because of the very low solubility of tributyl phosphate in water. A new thermodynamic model, the generalized local composition model (GLCM), was developed and suggested for the common description of all of the experimental data. There are four adjustable binary interaction parameters in the GLCM expression, which makes it more flexible then other local-composition models. Using GLCM requires the control of the statistical significance of parameters. It is recommended to use only significant parameters. Obtained temperature- and pressure-dependent parameters of the model could be used for the calculation of density of solutions, activity of components, enthalpy of mixing and liquid− liquid equilibria in the water−TBP system in a whole range of concentrations and at temperatures from 273.15 K to more than 400 K. To the best of our knowledge, this is the first full assessment of this system. Suggested model with the determined parameters form a good basis for the calculation of the extraction equilibria in the systems of higher dimension.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Aleksey I. Maksimov: 0000-0003-4557-5513 Funding

The work was financially supported by RFBR (Grant No. 16-3301038 mol_a) and URALCHEM Holding P.L.C. This article was written within the implementation of the Agreement for subsidies No. 14.578.21.0014 of June 5, 2014 (unique identifier of the Agreement: RFME-FI57814X0014) between National University of Science and Technology “MISiS” and the Ministry of Education and Science of Russian Federation within the realization of the Federal Target Program “Investigations and developments of priority ways of development of scientifictechnological complex of Russia for 2014−2020”, approved by the Decree of the Government of Russian Federation of November 28, 2013, No. 1096. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Authors would like to thank Prof. G. F. Voronin for the helpful discussions. REFERENCES

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Figure 5. Calculations with the obtained thermodynamic model: (a) density of the water−TBP solutions; (b) activity of water.

water−TBP system at temperatures from 273.15 K to more than 400 K rightly (Figure 5).

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CONCLUSIONS The density of the water−TBP solutions was measured at 288.15, 298.15, and 323.15 K by means of a vibrating densitometer. 4227



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