Article pubs.acs.org/jced
Solubility of Ibuprofen Sodium Dihydrate in Acetone + Water Mixtures: Experimental Measurement and Thermodynamic Modeling Weiqiang Dun,† Songgu Wu,† Weiwei Tang,† Xuemei Wang,† Dengqiong Sun,† Shichao Du,† and Junbo Gong*,†,‡,§ †
State Key Laboratory of Chemical Engineering, ‡The Co-Innovation Center of Chemistry and Chemical Engineering of Tianjin and Tianjin Key Laboratory for Modern Drug Delivery and High Efficiency, Tianjin University, Tianjin, 300072, China
§
ABSTRACT: The solubility of ibuprofen sodium dihydrate (ISD) in acetone + water mixtures was measured by the gravimetric method at temperatures ranging from (279.55 to 312.05) K. The measured solubilities were correlated by the modified Apelblat equation, the λh (Buchowski) equation, the van’t Hoff model, the combined nearly ideal binary solvent/Redlich−Kister (CNIBS/R-K) equation, and the general single model. The modified Apelblat equation was the best model for correlating the solubility of ISD, while the general single model fits the best for mixed solvents. The standard enthalpy, entropy, and Gibbs energy of the dissociation process of ISD were calculated by the van’t Hoff equation and the modified Apelblat model. In addition, there was a maximum value of solubility at a certain acetone mole fraction in the acetone + water mixture. The modified Apelblat equation, the λh (Buchowski) equation, the van’t Hoff model, the combined nearly ideal binary solvent/ Redlich−Kister (CNIBS/R-K) equation, and the general single model were used to correlate the experimental data. The standard enthalpy, entropy, and Gibbs energy for the dissolution of ISD were calculated from the solubility data.
1. INTRODUCTION Ibuprofen sodium dihydrate (ISD) (C13H21NaO4, 2-(4isobutylphenyl)propionate sodium salt dihydrate) is the stable sodium salt hydrate of ibuprofen with improved absorption characteristics. Ibuprofen sodium belongs to a class of drugs known as nonsteroidal anti-inflammatory drugs used in the therapy of rheumatism, arthritis, fever, headache, and dysmenorrhea.1 The chemical structure is given in Figure 1. ISD can dissolve quickly
2. EXPERIMENTAL SECTION 2.1. Materials. ISD, with the purity of the mass fraction higher than 0.998, was supplied by Shandong Xinhua Pharmaceutical Co., Ltd., China. Acetone was analytical-grade (purchased from Tianjin Kewei Chemical Co., China) with mass fraction purity > 0.995 without further purification. Doubledistilled water was used for preparation of the acetone + water mixtures. Properties of materials used in this paper were presented in Table 1.
Figure 1. Chemical structure of ISD.
Table 1. Properties of Materials Used in This Paper
in water at room temperature in vitro experiments, has the same extent of absorption as other fast-acting ibuprofen formulations, and can be absorbed into plasma more rapidly than conventional ibuprofen.2 In addition, ISD provides faster and greater pain relief than ibuprofen acid.2 Therefore, this compound has received increasing attention. In pharmaceutical industries, the dilution crystallization is one of the most effective way to purify and separate the heat-sensitive drugs.3 The solubility of ISD in pure and mixed solvents is important for solution crystallization.4,5After a thorough literature search, we found some descriptions about the solubility for ibuprofen sodium dihydrate dissolved in water;6 however, there was no solubility data for ISD in solvent mixtures reported until now. In this paper, the solubility of ISD in acetone, water, and acetone + water was measured by the gravimetric method at temperatures ranging from (279.55 to 312.05) K.7−9 © XXXX American Chemical Society
component ibuprofen sodium dihydrate ibuprofen sodium anhydrate water acetone
mass purity > > > >
0.998 0.998 0.995 0.995
molar mass (g·mol−1) 264.296 228.26 18.016 58.08
2.2. Apparatus and Procedure. On the basis of the literature data,6 as ISD loses water far below the melting point, the measured values of melting temperature (Tm1) and enthalpy of fusion (ΔfusH1) are for the anhydrous form of ISD. As shown in Figure 2, ISD loses water at T = 100 °C and becomes Received: May 7, 2014 Accepted: October 1, 2014
A
dx.doi.org/10.1021/je5004093 | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Figure 2. DSC curves of ISD at a heating rate of 10 °C·min−1. Solid line: (25 to 250) °C. Dotted line: (250 to 25) °C. Chain line: (25 to 250) °C.
Figure 4. XRD patterns of ISD and ibuprofen sodium anhydrate (ISA).
with protection of a nitrogen atmosphere. The mass of samples were (5 to 10) mg, with the heating rate of 10 °C·min−1. As indicated in Figure 4, the XRD patterns of ISD and ISA are different. From general thermodynamic considerations, it can be seen that the sediment in equilibrium with water-rich solution is dihydrate, but it must lose water if the solvent is pure acetone until a certain equilibrium content of water in acetone is reached. To determine that content, the solutions with varied sediment−solvent proportions as presented in Table 2 were stirred for 8 h. Then, the solution was filtered by the 0.2 um pore size syringe filter, and the solid was measured by XRD and TGA. The results are shown in Figures 5 and 6. To reveal the influence of crystalline water on the solubility of ISD in pure acetone, the solubility of ISA was measured, which was presented in Table 3, and compared with the solubility of ISD in pure acetone in Figure 7. In addition, the water mass fraction (we) data of acetone and acetone + water with dissolved dihydrate were measured and shown in Tables 4 and 5. The solubilities of ISD in acetone + water mixtures were experimentally measured by the gravimetric method. In this method, excess solid ISD was added to different solvents and kept at a certain temperature controlled by a thermostatical bath (SW23, Julabo, Germany) with a stability of 0.05 K. To achieve equilibrium, the solutions were stirred for 8 h. Then, the upper saturated solution was filtered by the 0.2 um pore size syringe filter, which was kept in the same temperature with the saturated solution and dried in vacuum drying oven at 353.15 K for 8 h until the solvent can completely evaporate and no solute molecules escaped. After dried, the samples were weighed for several times every 0.5 h until the weight was unaltered. The experiment was repeated three times and used the arithmetic average value as the final result. All of the masses were measured using a balance (model AB204, Mettler-Toledo, Switzerland) with an accuracy of ± 0.0001 g. Because the ISD is not stable during drying, we decided to make it dehydrated completely, and then the mass of ISD was calculated based on the weighted mass of ibuprofen sodium anhydrate (ISA) and stoichiometric ratio of ISA−water in ISD. The mole fraction solubility x1 in pure solvents and mixture solvents was based on the following equation:
ibuprofen sodium anhydrate (ISA) which is melted at about T = 200 °C. By using differential scanning calorimetry (DSC) (Mettler-Toledo, model DSC 1/500, Switzerland), it was found that partial decomposition does happen during the melting through Figures 2 and 3. The weights of samples which were
Figure 3. DSC curves of ISD at a heating rate of 10 °C·min−1. Solid line: (25 to 250) °C. Dotted line: (250 to 25) °C. Chain line: (25 to 250) °C.
placed into pierced aluminum pans were (5 to 10) mg, with the heating rate 10 °C/min. The measurement was performed under protection of the dry nitrogen atmosphere. The uncertainties of the temperature measurements are estimated to be below 2%. To identify whether the solid phase in the saturated solution was ISD, the X-ray diffraction (XRD) spectrum and thermogravimetric analysis (TGA) of the sample were measured. The XRD patterns were obtained by using Cu Kα (1.54) radiation on a D/MAX 2500 X-ray diffractometer. The samples were recorded between 2θ = 2° and 2θ = 40° with a step size of 0.02° and a scan rate of 1 step·s−1 at ambient conditions. The TGA (Mettler-Toledo, Switzerland) of the sample was measured
x1 = B
m1/M1 m1/M1 + m2 /M 2
(1)
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Table 2. Varied Sediment/Acetone Proportionsa m1/g m2/g a
A
B
C
D
E
F
G
H
0.100 4.270
0.213 4.272
0.313 4.612
0.400 4.309
0.510 4.682
0.599 4.274
0.704 4.745
0.817 4.278
m1 is the mass of ISD; m2 is the mass of acetone.
Figure 5. TGA of sediments obtained from A to H experiments.
Figure 7. Solubilities of ISD and ISA in acetone: ■, ISA; ●, ISD.
that the solubility of ISD in all of the systems studied increases with the increase of temperature. At a certain temperature, the solubility of ISD has a maximum value in the acetone + water system, as shown in Figure 9. 3.2. Data Correlation. 3.2.1. Modified Apelblat Model. Used to describe the relationship between mole fraction of the solubility and temperature,10 the modified Apelblat equation is presented as follows: B ln x1 = A + + C ln(T /K) (3) T /K where x1 presents the mole fraction solubility of the solute in the solution, and T presents the absolute temperature. A, B, and C, which are listed in Table 7 are the empirical parameters. The average percent deviation (APD %) and the root-mean-square deviations (RMSD) are also listed in Table 7, which is shown as Figure 6. XRD of sediments obtained from A to H experiments.
APD% = x1 =
m1/M1 m1/M1 + m2 /M 2 + m3 /M3
(2)
1 N
N
∑
x1, i − x1,cali x1, i
i=1
(4)
The root-mean-square deviations (RMSD) are presented as follows:
where m1, m2, and m3 represent the mass of the ISD and solvents, respectively; M1, M2, and M3 are, respectively, the molecular weights of the ISD and the solvents.
N
∑i = 1 (xic − xie)2
RMSD =
3. RESULTS AND DISCUSSION 3.1. Solubility Data. The experimental mole fraction solubilities of ISD in acetone, water, and acetone + water solvent mixtures at the temperature arranging from (279.55 to 312.05) K are presented in Tables 4, 5, and 6 and Figure 5, respectively. From Tables 5 and 6 and Figure 8, it can conclude
N
(5)
The relative deviations (RD) between the experimental values and the calculated values are shown in Tables 4, 5, and 6. The RD is shown below: RD =
xe − xc xe
(6)
Table 3. Mole Fraction Solubilities (xe) of ISA in Acetone (p = 0.1 MPa) T/K xe·10−4
278.15 0.377
283.15 0.407
288.15 0.458
293.15 0.489 C
298.15 0.559
303.15 0.619
308.15 0.752
313.15 0.830
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Table 4. Mole Fraction Solubilities (xe) of ISD in Acetone (w) + Water (1 − w), Where w Is the Mass Fraction (p = 0.1 MPa)a 102 RD T/K
−2
xe·10
we
eq 3
eq 7
102 RD T/K
eq 8
xe·10
−2
w = 0.10 279.55 282.35 287.35 292.35 297.25 302.25 307.25 312.05
0.9364 1.2316 1.427 1.7901 2.3238 3.2987 4.0052 4.7728
0.902 0.902 0.903 0.903 0.904 0.906 0.907 0.908
279.55 282.35 287.35 292.35 297.25 302.25 307.25 312.05
1.2116 1.5089 1.8318 2.4461 2.9426 3.9989 4.7927 5.4013
0.804 0.805 0.806 0.808 0.810 0.813 0.815 0.817
279.55 282.35 287.35 292.35 297.25 302.25 307.25 312.05
1.2979 1.5715 1.8796 2.5926 3.0056 4.1286 4.8922 5.8234
0.706 0.707 0.709 0.712 0.714 0.718 0.722 0.725
279.55 282.35 287.35 292.35 297.25 302.25 307.25 312.05
1.375 1.6412 1.9077 2.6496 3.1829 4.2208 4.9787 5.9575
0.608 0.609 0.611 0.615 0.618 0.623 0.627 0.632
279.55 282.35 287.35 292.35
1.2047 1.4387 1.8045 2.2633
0.508 0.509 0.512 0.514
w=
w=
w=
w=
a
0.88 10.87 −2.45 −7.04 −5.91 5.02 1.75 −1.38 0.20 2.53 6.43 −3.52 −1.12 −6.22 3.25 2.47 −1.58 0.30 1.31 4.39 −4.74 2.28 −6.17 3.73 0.31 −0.57 0.40 2.70 4.60 −7.10 1.14 −3.29 3.30 −0.28 −0.35 0.50 5.05 5.08 −1.58 −5.85
−2.25 9.08 −2.94 −6.57 −5.04 5.74 2.03 −1.91
−3.12 8.53 −3.17 −6.51 −4.82 5.97 2.15 −2.06
−8.20 0.05 −4.96 0.72 −2.88 6.01 3.44 −3.81
−9.07 −0.51 −5.18 0.76 −2.68 6.22 3.56 −3.93
−3.05 1.77 −5.29 3.05 −4.76 4.86 0.71 −1.46
−3.91 1.21 −5.49 3.14 −4.51 5.11 0.84 −1.62
−1.50 2.06 −7.63 1.93 −1.93 4.43 0.11 −1.24
−2.32 1.52 −7.82 2.02 −1.69 4.67 0.24 −1.40
−4.08 −0.62 −2.90 −4.25
−4.96 −1.21 −3.13 −4.20
297.25 302.25 307.25 312.05
2.9341 3.9079 4.7226 5.378
279.55 282.35 287.35 292.35 297.25 302.25 307.25 312.05
1.1194 1.3129 1.5373 1.9667 2.5621 3.4914 4.3609 4.7925
279.55 282.35 287.35 292.35 297.25 302.25 307.25 312.05
0.8241 1.0599 1.2628 1.5402 2.0324 2.7533 3.5573 4.188
279.55 282.35 287.35 292.35 297.25 302.25 307.25 312.05
0.3733 0.4656 0.7658 0.9246 1.2248 1.6605 2.2007 2.8035
279.55 282.35 287.35 292.35 297.25 302.25 307.25 312.05
0.1171 0.1636 0.1843 0.2205 0.2979 0.4013 0.4803 0.7661
we
eq 3
w = 0.50 0.519 −3.58 0.524 3.14 0.529 2.38 0.533 −1.58 w = 0.60 0.408 9.61 0.409 8.03 0.411 −5.48 0.414 −7.94 0.417 −5.44 0.424 3.23 0.429 5.12 0.432 −2.94 w = 0.70 0.306 0.38 0.308 9.22 0.309 −0.30 0.311 −7.12 0.314 −4.16 0.319 1.76 0.325 3.71 0.329 −1.77 w = 0.80 0.203 −8.06 0.204 −5.09 0.206 11.00 0.208 −1.03 0.210 −2.32 0.214 −0.42 0.218 0.58 0.223 −0.07 w = 0.90 0.102 −19.39 0.103 8.01 0.104 3.31 0.105 −0.09 0.107 4.87 0.109 5.31 0.110 −9.99 0.111 2.32
eq 8
−0.81 5.51 3.24 −3.45
−0.60 5.74 3.36 −3.57
1.46 2.80 −6.88 −6.56 −2.90 5.38 5.90 −4.61
0.69 2.26 −7.11 −6.52 −2.72 5.59 6.02 −4.72
0.39 9.26 −0.24 −7.08 −4.16 1.73 3.68 −1.75
−0.34 8.79 −0.43 −7.02 −3.97 1.94 3.79 −1.89
−11.12 −7.07 10.49 −0.80 −1.71 0.17 0.82 −0.42
−11.87 −7.58 10.30 −0.79 −1.58 0.35 0.92 −0.52
14.77 26.41 9.55 −3.58 −3.29 −2.87 −14.18 6.79
14.77 26.47 9.55 −3.54 −3.22 −2.82 −14.18 6.74
Standard uncertainties u are u(T) = 0.05 K; ur(xe) = 0.02.
Table 5. Mole Fraction Solubilities (xe) of ISD in Acetone (p = 0.1 MPa)a
Table 6. Mole Fraction Solubilities (xe) of ISD in Water (p = 0.1 MPa)
102 RD
a
eq 7
T/K
xe·10−3
279.55 282.35 287.35 292.35 297.25 302.25 307.25 312.05
0.253 0.273 0.305 0.349 0.389 0.450 0.504 0.620
we·10−3
102 RD
eq 3
eq 7
eq 8
T/K
xe·10−2
eq 3
eq 7
eq 8
Acetone 0.459 −1.98 0.962 0.33 1.567 0.82 1.970 2.32 2.372 0.31 4.084 0.60 5.091 −3.49 6.400 1.60
4.51 3.77 0.30 −0.46 −3.21 −2.11 −4.03 4.31
5.02 4.10 0.33 −0.60 −3.44 −2.33 −4.09 4.48
279.55 282.35 287.35 292.35 297.25 302.25 307.25 312.05
0.3831 0.4752 0.7753 1.2189 1.7443 2.5214 3.4323 4.1253
Water 13.31 3.24 −0.26 −0.75 −3.65 −0.31 2.53 −0.97
−28.30 −27.50 −12.33 −1.32 1.55 5.88 5.66 −4.49
−30.41 −29.08 −13.03 −1.46 1.74 6.19 5.89 −4.61
a
Standard uncertainties u are u(T) = 0.05 K; ur(xe) = 0.02. D
Standard uncertainties u are u(T) = 0.05 K; ur(xe) = 0.02. dx.doi.org/10.1021/je5004093 | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 7. Parameters of eq 2 for ISD in Acetone, Water, and Acetone (w) + Water (1 − w) Mixed Solvents at Temperatures from (279.55 to 312.05) K w
A·102
0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90
1.513 4.381 2.069 2.039 3.847 3.533 0.361 1.243 −11.260 −3.806 11.360
Figure 8. Mole fraction solubilities of ISD in acetone (w) + water (1 − w), acetone, and water, where w is the acetone mass fraction. ■, w = 0.1; □, w = 0.2; +, w = 0.3; ×, w = 0.4; ▽, w = 0.5; △, w = 0.6; ⧫, w = 0.7; ▲, w = 0.8; ▼,w = 0.9; ★, w = 1.0; ●, w = 0.0.
w
λ
0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90
6.290 4.416 5.193 4.980 4.895 4.655 5.757 8.013 2.206
27.590
3.2.2. λh Model. The experimental solubility can also be correlated by the λh equation,11 which was first developed by Buchowski et al., and is expressed as
RMSD·10−4
4.413 3.389 2.938 2.846 3.530 5.972 3.549 3.570 6.656
10.644 10.425 9.737 8.467 9.575 13.959 8.216 3.477 2.240
1.413
0.080
3.127
6.040
h·102
RMSD·10−3
APD%
Acetone + Water 7.079 4.443 9.040 3.758 7.875 3.120 8.095 2.604 8.363 3.108 8.912 4.562 7.814 3.534 6.486 4.076 23.990 10.173 Acetone 3.575·103 2.801 Water 2.149 10.876
1.078 1.383 1.047 0.933 1.220 1.522 0.817 0.358 0.355 0.014 1.326
N
(7)
ln x1 =
where λ and h are two model parameters, T is the absolute temperature, x1 is the mole fraction solubility of ISD, and Tm1 is the melting temperature. The two parameters λ and h together with the average percent deviation (APD%) and the root-meansquare deviations (RMSD) are shown in Table 8. 3.2.3. van’t Hoff Model. The relationship between the mole fraction solubility of a solute and the temperature in a solution can be expressed by the van’t Hoff equation,12 which is given as follows: ΔH ° ΔS° + RT R
Acetone + Water −1.062 −0.209 −2.300 −0.639 −1.276 −0.294 −1.257 −0.290 −2.071 −0.599 −1.938 −0.512 −0.553 −0.037 −1.011 −0.166 4.562 1.698 Acetone 1.449 0.569 Water −5.608 −1.670
APD%
where x1 is the mole fraction solubility of solute in the solution, T is the corresponding absolute temperature, and R is the gas constant; ΔH0 and ΔS0 donate the standard enthalpy and entropy of dissolution, respectively.13 The standard enthalpy and entropy along with the root-mean-square deviations (RMSD) and the average percent deviation (APD%) are shown in Table 9. 3.2.4. The CNIBS/R-K Equation and the General Single Model. To describe the solubility of the solute in the binary solvent system, the combined nearly ideal binary solvent/ Redlich−Kister (CNIBS/R-K) model14 was proposed as follows:
Figure 9. Mole fraction solubilities of ISD in acetone (w) + water (1 − w), acetone, and water at different temperatures: ■, T = 279.55 K; ●, T = 282.35 K; ▲, T = 287.35 K; ▼, T = 292.35 K; ⧫, T = 297.25 K; ★, T = 302.25 K; □, T = 307.25 K; ○, T = 312.05 K. w is the acetone mass fraction.
ln x1 = −
C·102
Table 8. Parameters of eq 6 for ISD in Acetone, Water, and Acetone (w) + Water (1 − w) Mixed Solvents at Temperatures from (279.55 to 312.05) K
0.006
⎛1 ⎛ 1 − x1 ⎞ 1 ⎞ ln⎜1 + λ ⎟ ⎟ = λh⎜ − x1 ⎠ Tm1 ⎠ ⎝T ⎝
B·104
x0B
ln(x1)B , T +
x0C
ln(x1)C , T +
x0Bx0C
∑ Si(x0B i=0
−
x0C)i
(9)
where Si is a constant listed in Table 10 and N is the number of solvents and equals 2 in this paper. xB0 and xC0 are the initial mole solubility of the binary solvents. (x1)B,T and (x1)C,T are the mole fraction composition of the solute in pure solvents B and C, respectively. Equation 12 can be further simplified as eq 13, named the general single model.15 ln x1 = B0 + B1x0 + B2 x02 + B3x03 + B4 x04
(8) E
(10)
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where ΔsolH0, ΔsolS0, and ΔsolG0 are the standard enthalpy, standard entropy, and Gibbs energy change of dissolution of ISD, respectively, A to C are the parameters of the Apelblat model, and T is 298.15 K. The relative contributions of the enthalpy %ζH and entropy %ζTS can be calculated from eqs 14 to 15
Table 9. Parameters of eq 6 for ISD in Acetone, Water, and Acetone (w) + Water (1 − w) Mixed Solvents at Temperatures from (279.55 to 312.05) K w
ΔH0·104
0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90
3.610 3.380 3.368 3.312 3.423 3.409 3.607 4.407 3.797
ΔH0 Acetone + Water 90.549 84.560 84.489 82.868 85.810 84.409 89.269 111.734 79.903 Acetone −0.641 Water 150.424
1.913 5.488
APD%
RMSD·10−3
4.540 3.989 3.228 2.710 3.344 4.452 3.518 4.241 10.155
1.095 1.431 1.082 0.973 1.269 1.550 0.823 0.363 0.355
3.019
0.015
11.552
1.385
%ζH = 100·
|Δsol H °| |Δsol H °| + |T Δsol S°|
(14)
|T Δsol S°| |Δsol H °| + |T Δsol S°|
(15)
%ζTS = 100·
The results are shown in Table 12. From which, it can be seen that the ΔsolH0, ΔsolS0, and ΔsolG0 in solvent mixtures are all Table 12. Standard Enthalpy, Entropy, and Gibbs Energy Change of ISD in Acetone, Water, and Acetone (w) + Water (1 − w) Mixed Solvents ΔsolH0·104
ΔsolS0
ΔsolG0·103
w
(J·mol−1)
(J·mol−1·K−1)
(J·mol−1)
%ζH
%ζTS
0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0.00
3.634 3.271 3.320 3.270 3.352 3.410 3.666 4.287 4.160 2.060 5.235
91.440 81.230 83.053 81.612 83.729 84.694 91.286 107.820 91.155 3.995 142.750
9.073 8.491 8.438 8.366 8.558 8.848 10.730 14.420 9.445 19.410 9.787
57.136 57.458 57.279 57.336 57.315 57.454 57.392 57.147 60.485 94.535 55.167
42.864 42.542 42.721 42.664 42.685 42.546 42.608 42.853 39.515 5.465 44.843
Table 10. Parameters of eq 12 for ISD in Binary Acetone (1) + Water (2) Solvent Mixtures T/K
S0
S1
S2
APD%
279.55 282.35 287.35 292.35 297.25 302.25 307.25 312.05
10.34 10.21 10.03 10.03 9.91 10.01 10.03 9.53
1.91 2.54 4.54 5.44 6.94 7.70 8.72 9.86
4.47 7.52 5.79 4.38 5.20 6.12 5.85 8.37
4.09 3.65 3.19 3.35 2.76 2.71 3.62 5.32
where B0, B1, B2, B3, and B4 are the model parameters, and the regression results together with ADP% are listed in Table 11, and x0 is the original mole fraction composition of the binary solvent.
positive, indicating that the dissolution process of ISD in studied systems is endothermic, enthalpy-driven, and non-spontaneous.
Table 11. Parameters of eq 13 for ISD in Binary Acetone (1) + Water (2) Solvent Mixtures T/K
B0
B1
B2
B3
B4
APD%
279.55 282.35 287.35 292.35 297.25 302.25 307.25 312.05
−5.35 −4.81 −5.10 −5.05 −4.53 −4.13 −3.99 −3.76
8.56 5.80 12.31 14.65 11.06 10.53 11.47 10.35
−26.88 −19.32 −46.74 −53.34 −41.62 −40.86 −46.31 −40.91
39.97 30.80 74.47 81.25 66.80 66.75 77.45 66.86
−25.13 −20.82 −43.72 −46.10 −39.95 −40.25 −46.64 −39.64
0.64 0.40 0.81 0.89 0.90 0.88 1.09 1.42
4. CONCLUSIONS The solubility of ISD in acetone + water mixtures was measured by the gravimetric method with the temperature ranging from (279.55 to 312.05) K. The solubility of ISD in binary acetone + water solvent mixtures changes with the temperature and solvent composition. The solubility of ISD increases when the temperature increases. With the increasing concentration of acetone in acetone + water mixtures, the solubility of ISD increases first, then decreases. The solubility reaches the maximum value at 0.40 mass fraction of acetone. Four models were used to correlate the solubility data of ISD in the binary solvent, and the general single model was the best one. In addition, the ΔsolH0, ΔsolS0, and ΔsolG0 of solubility of ISD in solvent mixtures are all positive.
3.3. Standard Enthalpy, Standard Entropy, and Gibbs Energy. The standard enthalpy, standard entropy, and Gibbs free energy change of the solution of ISD in different solvent mixtures can be calculated from eqs 11 to 13, which combine the van’t Hoff equation with the modified Apelblat model.16 ⎛ B⎞ Δsol H ° = RT ⎜C − ⎟ ⎝ T⎠
(11)
Δsol S° = R(A + C + C ln T )
(12)
⎛ ⎞ B Δsol G° = −RT ⎜A + + C ln T ⎟ ⎝ ⎠ T
(13)
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AUTHOR INFORMATION
Corresponding Author
*Tel.: 86-22-27405754. Fax: +86-22-27374971. E-mail: junbo_
[email protected]. Funding
The work was financially supported by National Natural Science Foundation of China (NNSFC 21176173), State Key Laboratory of Chemical Engineering of China (SKL-CHE-11B02), and National High Technology Research and Development Program (863 program, no. 2012AA021202). F
dx.doi.org/10.1021/je5004093 | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
Notes
The authors declare no competing financial interest.
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