Thermodynamics Studies on the Solubility of Inorganic Salt in Organic

Article pubs.acs.org/IECR

Thermodynamics Studies on the Solubility of Inorganic Salt in Organic Solvents: Application to KI in Organic Solvents and Water− Ethanol Mixtures Bingwen Long,a,b Dong Zhao,a and Wei Liu*,a a

College of Chemical Engineering, Beijing University of Chemical Technology, Beijing 100029, China Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta T6G 2G6, Canada

b

ABSTRACT: A thermodynamic framework is established to calculate the solubility of inorganic salts in nonaqueous solvents. New solubility data of potassium iodide in selected organic solvents of acetone, ethanol, and 1-propanol are determined in the temperature range of 278−343 K. The experimental solubility is modeled by the methodology proposed in this work, and the solubility products of potassium iodide in organic solvents are estimated. Following this, the experimental mean activity coefficients are modeled with the electrolyte activity coefficient models of Pitzer, e-NRTL, e-Wilson equations, and their modified forms. Model parameters are optimized by fitting the experiment data. It turns out that the three-parameter e-Wilson equation presents the best correlation results with an overall average percentage relative deviation ARD of 1.36%. When the models are extrapolated to predict the low temperature solubility of potassium iodide in acetone down to 215 K, the three-parameter eNRTL gives the most reliable predictions. A novel simple predictive mixing rule for the e-Wilson equation is proposed to estimate the solubility of potassium iodide in binary mixed solvents. The predictions are in good agreement with the experimental data of potassium iodide in water and ethanol over wide ranges of concentration and temperature.

1. INTRODUCTION The solubility of inorganic salts in different solvents (both single and mixtures) has been an important subject for both experimental and theoretical studies for many years.1,2 Water is the most frequently used solvent for inorganic salts and thus the solubility of inorganic salts and related thermodynamic properties in water have been extensively studied and well documented.3,4 However, in many industrial and natural processes such as precipitation and crystallization in drilling mud, liquid extraction, distillation, and absorption with inorganic salts, the solubility of electrolytes in nonaqueous solvents especially in pure organic solvents is essential. But such solubility phenomena are less studied. The necessary data are often very scarce and sometimes reports from different sources can even be contradictory. Therefore, many more experimental efforts still should be made to get reliable solubility data. On the other hand, effort has been put forth to thermodynamically model electrolyte solubility, which can help us gain in-depth understanding of the nature of the nonideal behavior and the intermolecular interactions behind the solubility phenomena. Modeling work on electrolyte solutions is rather rich and several detailed reviews on the progress of thermodynamic modeling of electrolyte solutions are available.5−7 In comparison with aqueous electrolyte systems, however, the calculation of phase equilibrium of solid electrolytes in pure organic solvent is much less studied, and its thermodynamic modeling is still very challenging, because the necessary thermodynamic functions such as the Gibbs free energy and enthalpy of formation for the individual ions and salts are not available to most organic solvents. A feasible method is to use water as a reference solvent and introduce the thermodynamic functions of transfer from water to the desired solvent. In this way, the well-determined © 2012 American Chemical Society

properties and modeling methods for an aqueous system can be utilized, and the key step is to accurately calculate the thermodynamic functions of transfer. Marcus has made excellent reviews on this method and given critical evaluations of the thermodynamic functions of transfer for various ions and salts.8,9 Meanwhile, the commonly used electrolyte activity coefficient models such as the Pitzer’s model,10 the electrolyte Wilson model,11,12 NRTL model,13 and UNIQUAC models,14 which account for both the long-range electrostatic forces and the short-range intermolecular forces, can also be applied for modeling the phase equilibrium and other thermodynamic properties of nonaqueous electrolyte solutions. Therefore, a novel thermodynamic frame to model the solubility of inorganic electrolyte in organic solvent and mixed aqueous solvents is studied by independently estimating the thermodynamics functions of transfer from water to organic solvent and the mean activity coefficient of the electrolyte solute. The solubility of alkali iodides in several organic solvents has great importance for the industrial purification of the solvents or precipitation of the salt. Previous studies15−24 show that solvents such as ethanol and butanol can be successfully and economically purified with inorganic salts by operating at the optimal conditions obtained from the respective solubility curves.15,23 However, most available solubility measurements were carried out only at one or two temperatures, and thus the construction of a solubility curve versus temperature becomes impossible. Because of the limited data available and the very large discrepancies among them, it is desirable to experReceived: Revised: Accepted: Published: 9456

April 17, 2012 June 10, 2012 June 19, 2012 June 19, 2012 dx.doi.org/10.1021/ie301000b | Ind. Eng. Chem. Res. 2012, 51, 9456−9467

Industrial & Engineering Chemistry Research

Article

ments. After enough time of solid−liquid mixing and gravitational settling, around 15 mL of clear solution was quickly taken out to another previously weighed measuring vial by a suitably prewarmed syringe with a long tip protected by a microscreen. The vial was then quickly and tightly closed and weighed again to determine the mass of the sample. Then the vial was put into a temperature controllable drying oven (type: STED-01, Wujiang Shentai Oven Instrument Co.) with the cap half-closed to allow the complete evaporation of the solvent. After at least 12 h, the vial was taken out and placed in a desiccator with silica gel for another 2 h in order to reach the ambient temperature. After that, the vial together with the solutes remaining was weighed again to obtain the weight of dry solute. Then the equilibrium solubility could be calculated accordingly. An analytical balance (type: Adventurer AR2140, OHAUS Co.) with precision of ±0.0001 g was used for all the mass measurements. An average value was taken from at least five independent measurements for each temperature. The solubility data was measured at around 5 K increments from 277 to 343 K. The estimated uncertainty of the solubility values based on the error analysis and repeated observations was within 2.7%.

imentally obtain accurate and useful solubility data as a basis for industrial development and theoretical studies. In this work, the solubility phenomena of potassium iodide in three organic solvents of acetone, ethanol, and 1-propanol is studied. The experimental work is conducted in the temperature range of 278 to 343 K at around 5 K increments. New solubility data are obtained, and a detailed comparison has been made with the literature data. Following this, the solubility product of potassium iodide in each solvent is estimated based on that in water. Electrolyte activity coefficient models of the Pitzer, eNRTL, and e-Wilson equations are employed to model the experimental data. The binary interaction parameters of each model are obtained, and the accuracy of the models is compared. The solubility of potassium iodide in binary solvents of ethanol and water is also investigated with a new mixing rule.

2. EXPERIMENTAL SECTION 2.1. Materials. All the Chemicals used this work were of analytical grade and purchased from Beijing Chemical Reagent Co. with stated purity greater than 99.5%. Densities and refractive indices of the solvents at 298.15 K have been measured and the results are listed in Table 1 together with

3. EXPERIMENTAL RESULTS The measured solubility (molality, mol·kg−1) of potassium iodide in ethanol, 1-propanol, and acetone at different temperatures is summarized in Table 2 and shown in Figure 1 and 2. The measurements show that ethanol exhibits the highest solubility to potassium iodide at most temperatures, while 1-propanol always shows the lowest solubility. However, at lower temperature (99.5% >99.5% >99.8%

this work 0.7840 0.7857 0.8002

lit

nD a

0.7845 0.7852 0.7996

this work 1.3592 1.3591 1.3833

b

lita 1.3588b 1.3593 1.3830

Data from Lide25 bData are measured at 293.15 K.

literature data25 for comparison. Densities were measured using an oscillating U-tube densimeter (type: DMA 35, Anton Parr) and refractive indices were measured with an Abbe-3 L refractometer (type: WYA-2W, Shanghai Optical Instrument, Co.). The devices were carefully precalibrated and temperature controlled. All the chemicals were used as received. 2.2. Solubility Measurements. The solubility of potassium iodide in different solvents was measured using the static analytical method, and the compositions of the saturated solutions were determined using the gravimetric method.26−32 The solid−liquid equilibrium was obtained by fully mixing excessive amounts of solutes and solvents in a double layer jacket glass equilibrium cell with a magnetic stirrer. The temperature of the equilibrium cell was controlled by circulating water from a thermostat (type: DTY-15A, Beijing DeTianYou Co.) through the jacket of the cell. The equilibrium temperature was measured using a calibrated 4-wire platinum resistance probe (Pt-100). The temperature data was recorded every 3 s by a computer after the equilibrium temperature was initially reached, and an average value of all the recorded temperature data is reported as the final equilibrium temperature. The experimental records show that the temperature variations never exceeded 0.1 K during all the runs, and the uncertainty of the equilibrium temperature is less than 0.05 K. The stirring was kept for at least 6 h, and then the solution was kept still for another 2 h to allow the undissolved solids to settle down in the lower portion of the equilibrium cell. The attainment of equilibrium was checked by successive measure9457

dx.doi.org/10.1021/ie301000b | Ind. Eng. Chem. Res. 2012, 51, 9456−9467


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Table 2. Solubility of Potassium Iodide in Acetone, Ethanol and 1-Propanol at Different Temperatures T (K)

m (mol·kg−1)

105KSP,org

KSP, w

35.58 31.26 27.33 24.03 21.06 18.31 16.02 14.04 12.25 10.69 9.24

29.78 35.59 42.16 48.93 56.29 64.53 72.70 81.06 89.83 98.76 108.30

15.44 16.40 17.28 18.04 18.69 19.21 19.64 19.95 20.16 20.26 20.26 20.16 19.99 19.74

29.89 35.81 42.43 49.49 56.99 64.68 73.06 81.42 90.19 99.40 109.31 118.55 126.66 135.13

Acetone 278.15 283.15 288.27 293.11 298.02 303.18 308.05 312.85 317.75 322.65 327.85

0.1133 0.1008 0.08805 0.08060 0.07364 0.06883 0.06344 0.06139 0.06344 0.06577 0.07709

278.25 283.33 288.47 293.50 298.47 303.27 308.26 313.05 317.95 323.00 328.40 333.45 337.95 342.75

0.09360 0.1005 0.1105 0.1241 0.1323 0.1412 0.1516 0.1620 0.1735 0.1750 0.1927 0.2002 0.2214 0.2287

278.55 283.45 288.48 288.60 292.65 297.35 303.39 308.15 312.97 313.05 316.75 323.34 328.55 332.95 333.53 338.23 342.83

0.02547 0.02943 0.03178 0.03225 0.03384 0.03801 0.04408 0.04824 0.05307 0.05206 0.05774 0.06180 0.06957 0.07481 0.07590 0.08224 0.08956

Ethanol

Figure 1. Comparison of solubility of potassium iodide in ethanol, 1propanol at different temperatures: (■) ethanol, this work; (□) ethanol, Pawar;20 (●) ethanol, Larson;23 (○) Thomas;22 (⧫) Turner;24 (▲) 1-propanol, this work; (△) 1-propanol, Pawar.21

1-Propanol 0.7818 0.8158 0.8456 0.8463 0.8662 0.8849 0.9018 0.9097 0.9129 0.9129 0.9122 0.9047 0.8937 0.8812 0.8793 0.8627 0.8439

30.22 35.96 42.44 42.61 48.26 55.26 64.88 72.87 81.27 81.42 88.03 100.02 109.59 117.64 118.69 127.16 135.27

Figure 2. Comparison of solubility of potassium iodide in acetone at different temperatures: (●) this work; (○) Livingston;16 (▲) Walden;19 (■) Lannung;18 (⧫) Lasczynski.17 The smoothed curve is for reference: continuous, this work; dashed, Livingston.

where KI(S) represents the undissovled solid potassium iodide and K+ and I− stand for the ionized potassium cation and iodide anion in the organic solvents, respectively. The thermodynamic equilibrium constant, also known as solubility product, for this dissociation reaction is expressed as α +α − KSP(T ) = K I αKI (2)

minimum solubility perfectly matches the smoothed solubility curve from Livingston’s data.

4. THERMODYNAMIC MODELING OF THE SOLUBILITY Potassium iodide is a 1:1 type strong electrolyte. In this work, it is dissolved with a low saturation concentration in the solvents of ethanol, 1-propanol, and acetone. These solvents are of rather high dielectric constant, so it is reasonable to assume that potassium iodide is completely ionized in these solvents and the dissolution equilibrium reaction can be expressed as KI(S) ↔ K+ + I−

where α is the activity of each specie. Turner24 and Livingston16 have experimentally confirmed that, within our measuring temperature range, there is no formation of crystal solvates and anhydrous potassium iodide is the equilibrium solid phase for all the three solvents. By assuming the equilibrium solid potassium iodide is pure and of activity unity, eq 2 yields:

(1) 9458



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KSP(T ) = αK+αI− = (γm)K+ (γm)I− = m±2 γ±2

solubility product of potassium iodide in water KSP,w at other temperatures can be calculated from eq 6 with ΔGw values estimated from eq 7. The calculated KSP,w at each experimental temperature are listed in Table 2. For the organic solvents used in this work, however, these necessary thermodynamic function data have not been reported and this makes a direct calculation of the solubility product of an electrolyte in nonaqueous solvents problematic. A feasible solution is to treat the Gibbs energy change of the dissolution reaction in an organic solvent, ΔGorg(T), as combination of that in pure water ΔGw(T) and the Gibbs energy of transfer of the electrolyte from pure water to that solvent, ΔGtr,w→org(T):

(3)

with γ± =

γK+γI−

m± =

mK+m I−

(1:1 electrolyte)

(4)

(1:1 electrolyte)

(5)

where m± and γ± are the mean molality and corresponding mean activity coefficient of the ions. For the 1:1 electrolyte like KI, they are related to the individual anion and cation properties as shown in eqs 4 and 5. With the assumption of completely ionization, m± is equal to the real molality of the electrolyte. Hereafter all the thermodynamic functions are on the molality scale in this work unless specially stated. Therefore with knowledge of the solubility product and the mean electrolyte activity coefficient, the solubility can be estimated from eq 3. 4.1. Solubility Product of Potassium Iodide in Organic Solvents. The solubility product KSP can be estimated from the basic thermodynamics relation: ΔG(T ) = −ln KSP(T ) RT

ΔGorg (T ) = ΔGw (T ) + ΔGtr ,w → org (T )

in which the subscript org means organic solvent and w means water. As discussed above, ΔGw(T) is estimated through eqs 7−10. On the other hand, single-ion transfer properties can be obtained from electrochemical measurements of the temperature dependence of reversible electrode processes or calorimetric studies. Marcus has systematically reviewed the experimental data of thermodynamic functions of transfer of ions and salts from water to nonaqueous solvents from the literature of 1930 up to 2007. He critically evaluated the literature data and compiled his recommended values of the thermodynamic functions, such as Gibbs free energy, enthalpy, and entropy of transfer of ions from water to nonaqueous solvents in a series of articles.35−39 The suggested values are supposed to be fairly reliable and therefore the thermodynamic functions of transfer of potassium cation and iodide anion from water to the organic solvents are adopted in this work. It should be noted that the tabulated data from Marcus was reported on the molarity scale (c, mol·L−1), so it was converted into molality scale following the method described in Marcus’ paper.35,36 The converted values are listed in Table 4. The ΔGtr,w→org(T) of potassium iodide should be

(6)

where ΔG(T) is the Gibbs energy change of the dissolution reaction (eq 1) at temperature T. The temperature dependent ΔG(T) can be calculated by the following expression:33,34 ΔG(T ) ΔG(T 0) ΔH(T 0) ⎛ 1 1⎞ ⎜ = − − ⎟ 0 0 ⎝T RT R T⎠ RT 0 ⎛ 0 ⎞ ΔCP(T ) ⎛ T ⎞ T − − 1⎟ ⎜ln⎜ 0 ⎟ + R T ⎝ ⎝T ⎠ ⎠

(7)

Where ΔG(T ), ΔH(T ), and ΔCP(T ) are the Gibbs energy, enthalpy, and mole heat capacity changes, respectively, of the reaction represented by eq 1 at the reference temperature T0, and they can be calculated from the formation energy of each specie: 0

0

0

Table 4. Thermodynamic Properties of Transfer from Water to Organic Solvent on Molality Scale at 298.15 K

ΔG KI(T 0) = ΔGf,K+(T 0) + ΔGf,I−(T 0) − ΔGf,KI,S(T 0) 0

0

ΔG0tr

(kJ mol−1)

0

ΔHKI(T ) = ΔHf,K (T ) + ΔHf,I (T ) − ΔHf,KI,S(T ) +

−

acetone ethanol 1-propanol

(9)

ΔCP,KI(T 0) = C P,K+(T 0) + C P,I−(T 0) − C P,KI,S(T 0)

(10)

where ΔGf, ΔHf, and CP are the Gibbs energy of formation, enthalpy of formation, and heat capacity of the species, respectively. For most ions and salts, such thermodynamics functions are well determined at 298.15 K in aqueous solution and the data are readily available in many handbooks.25 So the reference temperature T0 is taken as 298.15 K for convenience’s sake and the thermodynamic function values for the species relevant to this work are listed in Table 3. Furthermore, the

K+ I− KI

ΔG0f (kJ mol−1)

c0P (J mol−1 K−1)

−252.40 −55.20 −327.90

−283.30 −51.60 −324.90

21.80 −142.30 52.90

6.0 18.4 19.8

ΔS0tr −1

(J mol

K−1)

−120.0 −111.0 −119.2

ΔG0tr

(kJ mol−1)

ΔS0tr (J mol−1 K−1)

27.0 14.9 20.8

−117.0 −44.0 −68.2

the sum of that of each ion. Most thermodynamic data recommended by Marcus are only at 298.15 K and the Gibbs energy of transfer at other temperatures ΔGtr,w→org(T) can be calculated from the expression suggested by Kamps:34,40 ΔGtr,w→org (T ) = ΔGtr,w→org,298.15K − ΔStr,w→org,298.15K (T − 298.15)

(12)

Therefore, the Gibbs energy change of the dissolution reaction in the organic solvents can be calculated from eqs 11 and 12. And then, the solubility product of potassium iodide in different organic solvents, KSP,org, at different temperatures can be determined from eq 6 or it directly relates KSP,w as

Table 3. Standard Thermodynamic Functions of Potassium Iodide Crystal Salts and Corresponding Ions in Water at 298.15 K ΔH0f (kJ mol−1)

I−

K+

(8) 0

(11)

⎛ ΔGtr,w→org ⎞ KSP,org = KSP,w exp⎜ − ⎟ RT ⎝ ⎠ 9459

(13)



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The comparisons of KSP,w and KSP,org for the organic solvents are shown in Figure 3. The solubility products of potassium iodide in the organic solvents are much smaller than that in water and follow the order of water > acetone > ethanol > 1-propanol. Also, the solubility product shows quite different temperature dependency in different solvent. In Figure 3, the solubility product of

potassium iodide in water increases with temperature while that in acetone decreases with temperature and the solubility product in ethanol and 1-propanol present a maximum at around 325 and 315 K, respectively. The maximum solubility product effect is also observed for the dissolution of sodium chloride in water.33 The temperature dependence of the solubility product of an electrolyte is examined by differentiating eq 6 with respect to T ΔG

(

d − RT dKSP = KSP dT dT

) (14)

Putting eqs 7−10 into eq 14, we obtain the derivative of the solubility product of electrolyte in water: dKSP,w dT

=

KSP,w RT 2

[ΔH(T 0) + ΔC P(T 0)(T − T 0)]

(15)

It is clear that the temperature dependence of the solubility product is determined by the basic thermodynamic functions (eq 8−10) at the reference temperature T0. For potassium iodide, ΔH(298.15) = 20300 (J·mol−1) and ΔCP (298.15) = −173.4 (J·mol−1·K−1),25 which gives a maximum KSP,w of 203.5 at T = 415.22 K obtained by letting eq 15 equal zero and T0 = 298.15 K. Therefore, within our experimental range, we only see that the solubility product of potassium iodide in water increases with temperature. Putting eq 11 and 12 into eq 14, we obtain the derivative of the solubility product of electrolyte in organic solvent: dKSP,org dT

=

KSP,org RT

2

[ΔHtr(T 0) + ΔH(T 0)

+ ΔC P(T − T 0)]

(16)

So the temperature dependence of the solubility product of an electrolyte in organic solvent is determined not only by the basic thermodynamic functions for aqueous solution but also by the enthalpy of transfer at the reference temperature T0. Again, by letting eq 16 equal zero, we can solve the temperature that gives the maximum solubility product. For potassium iodide, the enthalpies of transfer from water to acetone, ethanol, and 1propanol are −40270, −15530, and −17570 (J·mol−1), respectively,39 which gives the maxima as KSP,acetone = 1.757 × 10−3 at T = 184.0 K; KSP,ethanol = 2.03 × 10−4 at T = 325.7 K; and KSP,1‑propanol = 9.13 × 10−6 at T = 313.9 K. In addition, the enthalpy of transfer from water to acetone is so negative as to make the overall enthalpy change in eq 16 negative, which means the solubility product should decrease with temperature until the temperature is lower than 184 K. Therefore, within our experimental temperature range, the two maxima are observed in Figure 3 for ethanol and 1-propanol, respectively, while the solubility product of potassium iodide in acetone is observed to be decreasing with temperature. On the other hand, the solubility product of an electrolyte is the product of molality solubility and the mean activity coefficient as eq 3 shows. Since we observe the solubilities of potassium iodide increase with temperature in ethanol and 1propanol, the mean activity coefficients of potassium iodide in the solvents are supposed to decrease with temperature. In summary, the basic thermodynamic functions such as the overall enthalpy changes have great impact on the solubility product and the apparent solubility and how they vary with temperature. The temperature dependencies of the solubility product and the apparent solubility are not always consistent.

Figure 3. Solubility products of potassium iodide in ethanol, 1propanol, and acetone at different temperatures in comparison with those in water. 9460



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Table 5. Correlation Results of the Pizter’s, e-NRTL, and e-Wilson Equations: Parameter Values and the Average Percentage Relative Deviation ARD% e-NRTL

Pizter’s acetone ethanol 1-propanol

β1

ARD%

Δgem

Δgme

ARD%

Δλem

Δλme

ARD%

8.858 7.303 70.06

−13.25 −17.01 −118.9

6.99 1.07 5.14

4445.55 1740.56 −2032.54

−8455.18 −3301.46 4234.12

5.07 16.66 44.16

47350.8 −2036.08 −4332.51

3893.81 6701.71 10587.4

15.53 0.75 4.10

4.2. Modeling the Activity Coefficients. 4.2.1. Activity Coefficient Models for Electrolyte Solutions. In comparison with the modeling of phase equilibrium of nonelectrolyte solutions, three additional limits of ionization, electric neutrality, and the long-range interactions should be carefully considered in describing the electrolyte solutions’ excess Gibbs free energy with conventional activity coefficient models.2,5−7,41 At present, the activity coefficient models that are commonly employed for aqueous electrolytes can be divided into two groups. The first one contains the models of empirical extensions of the Debye−Hückel law, such as the Pitzer’s model10 which mends the deviation from the Debye− Hückel law by additional terms to account for the ionic strength dependence of the long-range forces among ions. The other group of models assumes contributions of the mole excess Gibbs free energy are a combination of long-range electrostatic forces described by a medication form of the Debye−Hückel law, and short-range intermolecular forces described by local composition activity coefficient models such as the Wilson model,11,12 NRTL model,13 and UNIQUAC model.14 These electrolyte models have been successfully employed for modeling the phase equilibrium and other thermodynamic properties of diverse aqueous electrolyte solutions. In principle, they can also be applicable to other types of electrolyte solutions such as organic solvent or mixed solvents as well. In this wok, the Pitzer,10 e-Wilson,11,12 and eNRTL13 models are employed to model the mean activity coefficient of potassium iodide in the organic solvent. The mean activity coefficient is calculated as an unsymmetrical convention on the molality scale, and the reference state is the pure solute infinitely diluted in the solvent at equilibrium temperature and pressure. The exact mathematical forms and the meaning of various variables for these models are described in detail in the Appendix. 4.2.2. Model Parameter Optimization. The Pizter, e-NRT,L and e-Wilson models all have two solute−solvent interaction energy parameters to be determined by fitting the experimental data. So the following objective function is used for the fitting:

potassium iodide in the organic solvents at different temperatures and their correlations with the Pitzer equation are shown in Figure 4. Potassium iodide shows higher solubility but a

Figure 4. Mean activity coefficients of potassium iodide in ethanol, 1propanol and acetone at different temperatures: (◆) acetone; (▲) ethanol; (●) 1-propanol. The lines are calculated by the Pitzer’s equation.

lower mean activity coefficient in ethanol than in acetone. As expected, the mean activity coefficient of potassium iodide in ethanol and 1-propanol decreases with temperature while that in acetone shows a maximum around 308 K at which the minimum solubility shows up. The Pitzer’s equation presents very good correlations for the experimental mean activity coefficients of ethanol and 1-propanol but a bit worse results for acetone as shown in Figure 4. The goodness of the fit of the models to the experimental data can be expressed by the average percentage relative deviations (ARD%), which is calculated according to the following definition:

NP

Min f2 =

− ln γi,calc )2 ∑ (ln γi,expt ± ± i=1

e-Wilson

β0

1 ARD % = NP

(17)

where the superscripts expt and calc stand for the experimental and the calculated mean activity coefficient of potassium iodide, respectively. Np is the number of data points for each system. The natural logarithm of experimental mean activity coefficient is determined from eq 3 with the experimental molality solubility and the calculated solubility product of the potassium iodide in the organic solvents. Only the solubility data measured in this work are used for the parameter optimization, and the Levenberg−Marquardt method is used as the optimization algorithm for minimizing eq 17. The optimized parameters for the Pitzer, e-NRTL, and e-Wilson models are presented in Table 5. The mean activity coefficient of

NP

∑ i=1

|γi,expt − γi,calc | ± ± γi,expt ±

100 (18)

The calculated ARD% for each electrolyte activity coefficient model is also summarized in Table 5 and the overall ARD% is shown in Figure 5. Among these three two-parameter electrolyte models, the Pitzer equation gives the best results with respect to the overall ARD%. For an individual potassium iodide−solvent system, the e-Wilson model presents the best correlation for the alcohol solvents but the worst for acetone. In the case of the e-NRTL model, it gives completely converse results to the e-Wilson model. This may be due to the local composition assumption difference for the short-range energy parameters between the two models as mentioned by Macedo11 and Zhao.12 9461



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Figure 5. Scheme of average percentage relative deviations (ARD%) of different electrolyte activity coefficient models.

In their paper, Xu and Macedo11 also tried to improve the accuracy of the e-Wilson model by considering the nonrandom factor α in the model as an additional adjustable parameter. Their calculation results show that the model accuracy can be greatly improved especially for the 1−1 type electrolyte when α is adjusted simultaneously with the other two parameters. Therefore the attempt of adjusting α to increase the accuracy of the e-Wilson and e-NRTL equations is made then. In this case, both models are three-parameter models and are named as Wilson2 and NRTL2, respectively. The newly optimized parameters of the e-Wilson2 and e-NRTL2 models together with the calculated ARD% for each salt are listed in Table 6. The overall ARD% for the two models are shown in Figure 4 for comparison as well. As expected, the accuracy of the eNRTL2 model is significantly improved and it gives even smaller overall ARD% than the Pitzer model. The threeparameter e-Wilson2 model exhibits the best results with an overall ARD% of 1.36%. For the solvent of acetone, the eNRTL2 model still shows the best results while the e-Wilson2 model is more advantageous for the alcohol solvents. 4.2.3. Temperature Extrapolation. In Livingston’s work,16 the measurements of the solubility of potassium iodide in acetone were carried out at temperature down to 195 K. Using their data (temperature down to 215 K, below which the solvate KI·5C3H6O or KI·6C3H6O will be formed), we investigated the prediction ability of different electrolyte solution models. Figure 6 shows the prediction results using different models with our regressed parameters at higher temperature. As expected, the e-NTRL2 model still presents the best prediction power for acetone. The average percentage relative deviation for the five extrapolated data points is 21.5%. On the other hand, the Pitzer, e-NTRL, and e-Wilson and eWilson2 equations all underpredict the solubility and the e-

Figure 6. Extrapolation results of different electrolyte activity coefficient models for the solubility of potassium iodide in acetone. Points stand for the experimental values; the lines denote the calculated values using different models.

Wilson equation even predicts a maximum solubility at around 277 K. 4.2.4. Prediction of the Solubility in Mixed Solvents. When the methodology is extended to mixed solvents, the same procedure as that for pure organic solvent can be applied. In this case, the solvent mixtures are considered to be equivalent to the one-component solvent and the Gibbs energy of transfer of the electrolyte from pure water to the desired solvent mixture is calculated. The interactions between the solvent components would be embodied in the experimental thermodynamic functions of transfer and the mixing rule proposed in this work. Pawar et al.20 reported their measurements on the solubility of potassium iodide in a binary mixture of ethanol and water at different temperatures. So their data are employed to verify our methodology to calculate the solubility of salt in a mixed aqueous organic solvent. As discussed above, the e-Wilson equation has obvious advantages on modeling the solubility of potassium iodide in alcohol solvents and therefore is chosen to calculate the solubility of potassium iodide in aqueous ethanol solutions. To reduce the adjustable parameters in the model, the original e-Wilson equation is employed for the modeling work and thus the nonrandom factor α is fixed as 0.1. The thermodynamic functions such as Gibbs energy and entropy of transfer of the ions from water to aqueous ethanol solvents at different ethanol compositions were reviewed and summarized in Marcus’ series articles.35,36,38,39,42 To estimate

Table 6. Correlation Results of the Three-Parameter e-NRTL and e-Wilson Equations: Parameter Values and the Average Percentage Relative Deviation ARD% e-NRTL2 acetone ethanol 1-propanol

e-Wilson2

α

Δgem

Δgme

ARD%

α

Δλem

Δλme

ARD%

1.306 2.592 −7150.3

5033.6 405.6 0.9050

−14.25 −1894.6 578.8

1.63 3.46 4.62

2.976 × 10−4 4.304 × 10−2 3.022 × 10−3

5026.9 −1752.8 −1524.6

13.03 5386.8 4173.95

2.44 0.66 1.24

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such functions at Pawar’s experimental solvent compositions, the tabulated thermodynamic function values from Marcus’s papers are correlated with polynomials first. The results for the ions are shown in Figure 7. Since no thermodynamic function

Δλme,mix = Δλme,E[xE0 + k me(x E0x w0 )n ] = Δλme,E(x E0 + k me[x E0(1 − x E0)]n )

(21)

in which Δλem,E and Δλme,E are the temperature-independent energy parameters for pure ethanol, which have already been determined as −2036.08 and 6701.71 (Table 5), respectively. x0E is the mole fraction of ethanol in the mixed solvent (salt free basis). kem and kme are two composition-independent but temperature-dependent parameters. n is a constant, which is determined as 1.25 for the water and ethanol mixtures by a trial and error method. kem and kme are optimized by fitting the experimental solubility from Pawar et al.,20 and the calculation results are listed in Table 7. The predictions at 298.15 K are Table 7. Optimized Parameters in the Proposed Mixing Rule (eqs 20 and 21)

Figure 7. Thermodynamic functions of transfer of the ions from water to aqueous ethanol binary mixtures at 298.15 K. Points are data from Marcus:35,36,38,39,42 solid, I−; hollow, K+; lines are polynomial correlations.

data are available at very dilute regions of ethanol mole fractions less than 0.05, the fittings were not extrapolated to zero concentration with the purpose of smoothing the available literature data only. Thus the solubility product of potassium iodide in a mixed solvent of water and ethanol at different solvent compositions and temperatures can be calculated in the same way as that applied for pure organic solvents. In the e-Wilson equation, the long-range and short-range contributions are calculated separately. For the long-range contribution (calculated by the Pizter−Debye−Hückel equation13), the specific density and the relative dielectric constant of the solvent mixture are required. The density of the aqueous ethanol mixtures at different compositions and temperatures are empirically correlated as polynomials from the handbook data.25 The Oster’s rule43 is used for correlating the relative dielectric constants of the solvent mixtures:

(

) +( ) (x ) + (x )

M Dx 0 ρ

Dmix =

0M ρ

w

w

M Dx 0 ρ 0M ρ

kme

ARD%

−3.445 −3.525 −3.622 −3.706

6.27 7.13 7.87 7.99

compared with experimental data in Figure 8. It can be seen that the predictions from this simple mixing rule agree well with the experimental observations. However, when the ethanol mole fraction exceeds 0.5, the predictions tend to overestimate the solubility (around 30% higher). That may be due to the uncertainties of the thermodynamic functions of I− in that range. As can be seen from Figure 7, we actually lack those functions for I− when the ethanol mole fraction exceeds 0.5. Therefore if we just consider the results where the ethanol mole fraction is below 0.5, the ARD% of the solubility predictions for the four temperatures are only 3.04%, 3.04%, 4.22%, and 4.27%, respectively. The obtained kem and kme at different temperatures are plotted in Figure 9. A strong linear relation is observed from the figure. So the generalized equations for kem and kme is determined as

(19)

in which x0 is the compound mole concentration in the solvent mixture (salt free). The subscripts w and E denote water and ethanol, respectively. The temperature-dependent relative dielectric constant and density (kg·m−3) of water are calculated by the empirical expressions in the handbook of Zemaitis et al.5 For the short-range contributions, the mixed solvents are treated as a single solvent, and the following new predictive mixing rules for the interaction energy parameter (Δλem and Δλme) are proposed: Δλem,mix = Δλem,E[x E0 + kem(x E0x w0 )n ] = Δλem,E(x E0 + kem[x E0(1 − x E0)]n )

kem −114.9 −100.7 −91.95 −87.73

Figure 8. Solubility of potassium iodide in binary mixed solvents of water and ethanol at 298.15 K. Points are experimental data from Pawar et al.20, and the line is calculated by the proposed mixing rule.

E

E

T (K) 298.15 303.15 308.15 313.15

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terms of the calculated overall ARD%. However, when the nonrandomness parameter α in the e-NRTL and e-Wilson equations are set as the third adjustable parameter, both models can better reproduce the experimental data. The e-NRTL model shows the best calculation results for acetone and the eWilson equation shows the highest accuracy for ethanol and 1propanol. Among all the models investigated, the e-NRTL2 model can give the most reliable predictions of the solubility of potassium iodide in acetone in a wide temperature from the transition point of potassium iodide until the normal boiling point of acetone. A simple predictive mixing rule is proposed to estimate the solubility of potassium iodide in a binary mixed solvents. Only two adjustable parameters are needed for the whole composition range at each temperature. The predictions agree quite well with the experimental observations and the optimized parameters show strong linear dependence on temperature.

■

Figure 9. Temperature dependence of the parameter kem and kme in the proposed mixing rule for mixed solvents of water and ethanol.

kem = 1.8014 − 0.0176T

k me = −651.32 + 1.8076T

2

(R = 0.9989) 2

(R = 0.9426)

The Pitzer’s Model

(22)

The Pitzer’s model is an empirical extensions of the Debye− Hückel equation with a viral type polynomial to represent the long-range electrostatic forces, which depend on temperature, solvent property, and ionic strength.10 The Pitzer’s model for the Gibbs excess energy is based on the molality scale. For the 1:1 electrolyte, the equation is given as,

(23)

Better correlation for kme can be obtained if second order polynomial regression is applied: k me = −9961.6 + 62.749T − 0.0997T 2

APPENDIX

(R2 = 0.9999)

ln γ± = f γ + mBγ + m2C γ

(24)

This assumption, however, needs more experimental data to verify.

(A.1)

with ⎡ I1/2 ⎤ 2 1/2 ⎥ f γ = − Aφ ⎢ + ln(1 + bI ) b ⎣ 1 + bI1/2 ⎦

5. CONCLUSIONS New equilibrium solubility data of potassium iodide in selected organic solvents of acetone, ethanol, and 1-propanol are determined by a gravimetric method over the temperature range of 278−343 K. The experimental results show ethanol has the highest solubility to potassium iodide followed by acetone and 1-propanol, but at lower temperature (2 mol·kg−1).41 Therefore to reduce the model parameters, we set C0 as 0 in this work and regressed β0 and β1 for each salt from our experimental mean activity coefficient data.

ln γ±* = ln γ±*,LR + ln γ±*,SR

(A.12)

Similar to the Chen’s idea of using local composition concept to account for the contribution of the short-range excess Gibbs energy, Xu and Macedo11 extended the Wilson equation model to describe the activity coefficients of electrolytes. In their eWilson model, the excess Gibbs energy of an electrolyte solution is also expressed as a sum of contributions of a longrange and a short-range excess Gibbs energy term as described by eq A.9. The same equations (eq A.10 and A.11) are employed to describe the long-range contribution. A modified Wilson equation, however, was used to describe the short-range unsymmetric activity coefficients of the different species in the electrolyte solution. The main difference between this model and the e-NRTL model lies in the assumption that the shortrange energy parameter between species in a local cell has an

(A.11)

xi is the true mole fraction of species i based on all the molecular and ionic species in the solution. For KI, xK+ = xI‑ = m/(2m + 1000/MW) and therefore Ix = xK+. In eq A.9, ln γ*± ,SR represents the short-range contribution. For the reaction represented by eq 1, its relation to the individual ionic activity coefficients is expressed as 9465



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enthalpic rather than Gibbs energy nature.11,12 For the cation the e-Wilson model gives:

Literature, 4th ed.; Vol. I. American Chemical Society: Washington, D.C., 1958. (4) Stephen, H.; Stephen, T. Solubilities of Inorganic and Organic Compounds. Vol. 1, Pergamon Press: Oxford, 1963. (5) Zemaitis, J. J. F.; Clark, D. M.; Rafal, M.; Scrivner, N. C. Handbook of Aqueous Electrolyte Thermodynamics, Wiley-AICHE: New York, 1986. (6) Pitzer, K. S. Activity Coefficients in Electrolyte Solutions, 2nd ed.; CRC Press: Boca Raton, FL, 1991. (7) Anderko, A.; Wang, P.; Rafal, M. Electrolyte solutions: From thermodynamic and transport property models to the simulation of industrial processes. Fluid Phase Equilib. 2002, 194−197, 123−142. (8) Hefter, G.; Marcus, Y.; Waghorne, W. E. Enthalpies and entropies of transfer of electrolytes and ions from water to mixed aqueous organic solvents. Chem. Rev. 2002, 102, 2773−2836. (9) Marcus, Y. Gibbs energies of transfer of anions from water to mixed aqueous organic solvents. Chem. Rev. 2007, 107, 3880−3897. (10) Pitzer, K. S. Thermodynamics of electrolytes. 1. Theoretical basis and general equations. J. Phys. Chem. 1973, 77, 268−277. (11) Xu, X.; Macedo, E. A. New modified wilson model for electrolyte solutions. Ind. Eng. Chem. Res. 2003, 42, 5702−5707. (12) Zhao, E. S.; Yu, M.; Sauve, R. E.; Khoshkbarchi, M. K. Extension of the Wilson model to electrolyte solutions. Fluid Phase Equilib. 2000, 173, 161−175. (13) Chen, C. C. Representation of solid−liquid equilibrium of aqueous-electrolyte systems with the electrolyte NRTL model. Fluid Phase Equilib. 1986, 27, 457−474. (14) Thomsen, K.; Rasmussen, P.; Gani, R. Simulation and optimization of fractional crystallization processes. Chem. Eng. Sci. 1998, 53, 1551−1564. (15) Evertz, C. R.; Livingston, R. Solubilities of some alkali iodides in acetone. J. Phys. Colloid. Chem. 1949, 53, 1330−1333. (16) Livingston, R.; Halverson, R. R. Solubility of potassium iodide in acetone. J. Phys. Chem. 1946, 50, 1−6. (17) Laszczynsk, S. V. Ueber die loslichkeit einiger anorganischer salze in organischen fliissigkeiten. Ber. Landwirtsch. 1894, 27, 2285− 2288. (18) Lannung, A. The solubility of alkali halogenides in acetone. Z. Phys. Chem.-Abteilung a 1932, 161, 255−268. (19) Walden, P. T. On the dissociation pressures of ferric oxide. J. Am. Chem. Soc. 1908, 30, 1350−1355. (20) Pawar, R. R.; Nahire, S. B.; Hasan, M. Solubility and density of potassium iodide in binary ethanol−water solvent mixture at (298.15, 303.15, 308.15 and 313.15) K. J. Chem. Eng. Data 2010, 55, 1073− 1073. (21) Pawar, R. R.; Golait, S. M.; Hasan, M.; Sawant, A. B. Solubility and density of potassium iodide in a binary propan-1-ol-water solvent mixture at (298.15, 303.15, 308.15, and 313.15) K. J. Chem. Eng. Data 2010, 55, 1314−1316. (22) Thomas, J. D. R. The solubilities of alkali metal iodides in ethanol. J. Inorg. Nucl. Chem. 1962, 24, 1477−1478. (23) Larson, R. G.; Hunt, H. Molecular forces and solvent power. J. Phys. Chem. 1939, 43, 417−423. (24) Turner, W. E. S.; Bissett, C. C. The solubilities of alkali haloids in methyl, ethyl, propyl, and isoamyl alcohols. J. Chem. Soc. 1913, 103, 1904−1910. (25) Lide, D. R. CRC Handbook of Chemistry and Physics, 90 ed.; Taylor & Francis: Boca Raton, FL, 2009. (26) Long, B. W.; Wang, L. S.; Wu, J. S. Solubilities of 1,3benzenedicarboxylic acid in water + acetic acid solutions. J. Chem. Eng. Data 2005, 50, 136−137. (27) Long, B.; Yang, Z. Measurements of the solubilties of m-phthalic acid in acetone, ethanol and acetic ether. Fluid Phase Equilib. 2008, 266, 38−41. (28) Long, B.; Wang, Y.; Yang, Z. Partition behaviour of benzoic acid in (water + n-dodecane) solutions at t = (293.15 and 298.15) K. J. Chem. Thermodyn. 2008, 40, 1565−1568.

XS ΛES zM ⎡ ⎢ α ⎣ XS + (XM + XX )ΛES XX + XM + XS ΛSE

ln γM*,SR,Wilson = −

⎤ + ln(XX + XS ΛSE) − ΛES − ln ΛSE⎥ ⎦ (A.18)

and for the anion XS ΛES zX ⎡ ⎢ α ⎣ XS + (XM + XX )ΛES XM + + ln(XM + XS ΛSE) XX + XS ΛSE ⎤ − ΛES − ln ΛSE⎥ ⎦ (A.19)

ln γX*,SR,Wilson = −

where Xi is the effective mole fraction, which is defined as the product of mole fraction xi of ion i and the charge zj it carries. Xi = xizi X S = xS

(A.20)

α is the nonrandom factor that was set as 0.1 by Xu and Macedo.11 Λij is the adjustable energy parameter and its temperature dependence is given as ⎛ Δλij ⎞ Λij = exp⎜ − ⎟ ⎝ RT ⎠

(A.21)

Then the unsymmetric short-range mean activity coefficient lnγ±*,SR,Wilson can be obtained from eq A.18, the mean activity coefficient of the solute on mole faction scale ln γ*± is calculated from eq A.9 and the molality ln γ± is calculated by eq A.17. In the e-Wilson model, there are two adjustable energy parameters Δλij to be optimized by fitting the experimental data.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The financial support of the Fundamental Research Funds for the Central Universities, Beijing University of Chemical Technology (ZZ1107) is acknowledged. Prof. John M. Shaw (University of Alberta) is greatly acknowledged for his hospitality and encouragements during the preparation of this paper.

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REFERENCES

(1) Mullin, J. W., Crystallization, 3rd ed.; Butterworth-Heinemann: Oxford, 2000. (2) Robinson, R. A.; Stokes, R. H. Electrolyte solutions, 2nd revised ed.; Dover Publications Inc.: New York, 2002. (3) Linke, W. F. Solubilities of Inorganic and Metal Organic Compounds; A Compilation of Solubility Data from the Periodic 9466



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(29) Long, B.; Wang, Y.; Zhang, R.; Xu, J. Measurement and correlation of the solubilities of m-phthalic acid in monobasic alcohols. J. Chem. Eng. Data 2009, 54, 1764−1766. (30) Ding, Z.; Zhang, R.; Long, B.; Liu, L.; Tu, H. Solubilities of mphthalic acid in petroleum ether and its binary solvent mixture of alcohol + petroleum ether. Fluid Phase Equilib. 2010, 292, 96−103. (31) Long, B.; Li, J.; Zhang, R.; Wan, L. Solubility of benzoic acid in acetone, 2-propanol, acetic acid, and cyclohexane: Experimental measurement and thermodynamic modeling. Fluid Phase Equilib. 2010, 297, 113−120. (32) Long, B.; Li, J.; Song, Y.; Du, J. Temperature-dependent solubility of α-form l-glutamic acid in selected organic solvents: Measurements and thermodynamic modeling. Ind. Eng. Chem. Res. 2011, 50, 8354−8360. (33) Huang, J. Q.; Li, J. D.; Gmehling, J. Prediction of solubilities of salts, osmotic coefficients, and vapor−liquid equilibria for single and mixed solvent electrolyte systems using the liquac model. Fluid Phase Equilib. 2009, 275, 8−20. (34) Long, B. Experimental studies and thermodynamic modeling of the solubilities of potassium nitrate, potassium chloride, potassium bromide, and sodium chloride in dimethyl sulfoxide. Ind. Eng. Chem. Res. 2011, 50, 7019−7026. (35) Marcus, Y. Thermodynamic functions of transfer of single ions from water to nonaqueous and mixed-solvents. 1. Gibbs free-energies of transfer to non-aqueous solvents. Pure Appl. Chem. 1983, 55, 977− 1021. (36) Marcus, Y. Thermodynamic functions of transfer of single ions from water to nonaqueous and mixed-solvents. 2. Enthalpies and entropies of transfer to nonaqueous solvents. Pure Appl. Chem. 1985, 57, 1103−1128. (37) Wohlfarth, C. Landolt-börnstein iv/17: Static Dielectric Constants of Pure Liquids and Binary Liquid Mixtures; Springer: New York, 2008. (38) Kalidas, C.; Hefter, G.; Marcus, Y. Gibbs energies of transfer of cations from water to mixed aqueous organic solvents. Chem. Rev. 2000, 100, 819−852. (39) Hefter, G.; Marcus, Y.; Waghorne, W. E. Enthalpies and entropies of transfer of electrolytes and ions from water to mixed aqueous organic solvents. Chem. Rev. 2002, 102, 2773−2835. (40) Kamps, A. P. S. Model for the gibbs excess energy of mixedsolvent (chemical-reacting and gas-containing) electrolyte systems. Ind. Eng. Chem. Res. 2005, 44, 201−225. (41) Prausnitz, J. M.; Lichtenthaler, R. N.; Azevedo, E. G. Molecular Thermodynamics of Fluid Phase Equilibria, 3ed.; Prentice-Hall: Englewood Cliffs, New York, 1999. (42) Marcus, Y. Thermodynamic functions of transfer of single ions from water to nonaqueous and mixed-solvents. 3. Standard potentials of selected electrodes. Pure Appl. Chem. 1985, 57, 1129−1132. (43) Oster, G. The dielectric properties of liquid mixtures. J. Am. Chem. Soc. 1946, 68, 2036−2041. (44) Yaws, C. L. Chemical Properties Handbook; McGraw-Hill Book Co.: Beijing, 1999.

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Thermodynamics Studies on the Solubility of Inorganic Salt in Organic

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