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Solubility and solution thermodynamics of ammonium dihydrogen phosphate in the water–methanol system
CJChE-01405; No of Pages 8 Chinese Journal of Chemical Engineering xxx (xxxx) xxx
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Article
Solubility and solution thermodynamics of ammonium dihydrogen phosphate in the water–methanol system☆ Dejun Xu, Dehua Xu, Yanjun Zhong, Tao Luo, Xiushan Yang, Zhiye Zhang, Lin Yang, Xinlong Wang ⁎ School of Chemical Engineering, Sichuan University, Chengdu 610065, China
a r t i c l e
i n f o
Article history: Received 15 September 2018 Received in revised form 29 December 2018 Accepted 9 February 2019 Available online xxxx Keywords: Ammonium dihydrogen phosphate Solubility Water–methanol system
a b s t r a c t The solubility of ammonium dihydrogen phosphate (MAP) in the water–methanol system is essential for antisolvent crystallization studies. To investigate the effect of methanol on the solubility of MAP in water, the solubility of MAP in the water–methanol system was determined by dynamic method and static equilibrium method at temperatures ranging from 293.2 to 343.2 K at atmospheric pressure. Results showed that the solubility of MAP increased with the increase of temperature and the increase of water mole fraction in the water–methanol system. The experimental solubility data were correlated with the modified Apelblat equation, the combined nearly ideal binary solvent/Redlich–Kister (CNIBS/R–K) model and the Jouyban–Acree model. The calculated results based on these three models were in very good agreement with the experimental data with the average relative deviations of 0.65%, 0.97%, and 5.38%, respectively. Simultaneously, the thermodynamic properties of the MAP dissolution process in the water–methanol system, including Gibbs energy change, enthalpy, and entropy were obtained by the Van't Hoff equation, which can be used to assess the crystallization process. © 2019 The Chemical Industry and Engineering Society of China, and Chemical Industry Press. All rights reserved.
1. Introduction Ammonium dihydrogen phosphate (MAP, NH4H2PO4) is an important product in the phosphorus chemical industry and has a wide range of applications in various fields, such as fertilizers, nonlinear optical materials, flame retardants, wastewater treatment [1–5]. The MAP production process comprises the reaction between phosphate and ammonia, crystallization, drying, and so on [6,7]. Among them, the crystallization of MAP is a key step and the traditional crystallization route is in aqueous solution, leading to high energy consumption and production costs. Generally, solubility is a basic thermodynamic parameter in crystallization process. Mullin et al. measured the solubility of MAP over the temperature range 20–40 °C, and investigated the growth kinetic of MAP crystal [8,9]. Yang et al. researched the solid–liquid phase equilibrium for urea phosphate + MAP + water to prepare the urea phosphate in the ternary system [10]. Eysseltová et al. provided an overview of solubility of ammonium phosphates [11]. In recent years, the antisolvent crystallization is proposed as a promising way to save energy and improve the crystal quality, because a suitable antisolvent can decrease the solubility of salt in water [12–15]. In our previous study, a process to produce MAP using ethanol as ☆ Supported by the National Key Research and Development Program of China (2016YFD0200404) and the Sichuan Science and Technology Program (2018RZ0145). ⁎ Corresponding author. E-mail address: [email protected] (X. Wang).
the antisolvent was proposed and this has an important guiding significance on the production of MAP [16]. However, it was difficult to recycle the ethanol by conventional distillation, because the water–ethanol system generates an azeotrope (89.5% of ethanol) at the temperature of 78.1 °C and under atmospheric pressure. Methanol is the simplest alcohol and shares many similarities with ethanol. It can also be used as an antisolvent. Importantly, there exists no azeotrope in the methanol–water system. It is also well known that methanol is cheaper than ethanol due to the methanol overproduction in China. Besides, methanol is a byproduct in some enterprises that produce MAP. Hence, it would be a good choice to use methanol as an antisolvent in the crystallization of MAP. The process is schematically shown in Fig. 1, and an amount of recycled methanol is added to the MAP water solution to lower the solubility of MAP and the MAP product is produced by the antisolvent crystallization. The residual fluid obtained is distillated to recycle methanol. The solubility plays a crucial role in the crystallization process, but relevant data about the solubility in the water–methanol system are not available in any publications. Therefore, we report here the solubility of MAP in the water–methanol system. In this work, the solubility of MAP in the water–methanol system is determined at temperatures ranging from 293.2 to 343.2 K and the experimental data were correlated with the modified Apelblat equation, combined nearly ideal binary solvent/Redlich–Kister (CNIBS/R–K) model and the Jouyban–Acree model. Besides, the thermodynamic properties of the MAP dissolution process in the water–methanol
https://doi.org/10.1016/j.cjche.2019.02.010 1004-9541/© 2019 The Chemical Industry and Engineering Society of China, and Chemical Industry Press. All rights reserved.
Please cite this article as: D. Xu, D. Xu, Y. Zhong, et al., Solubility and solution thermodynamics of ammonium dihydrogen phosphate in the water– methanol system, Chinese Journal of Chemical Engineering, https://doi.org/10.1016/j.cjche.2019.02.010
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D. Xu et al. / Chinese Journal of Chemical Engineering xxx (xxxx) xxx
Fig. 1. A flow-diagram of the antisolvent crystallization process in the water–methanol system for the production of ammonium dihydrogen phosphate (MAP).
system, including Gibbs energy, enthalpy, and entropy were obtained by the Van't Hoff equation. 2. Experimental 2.1. Materials
where m1, m2, M1, and M2 represented the mass of water and methanol and the mole mass of water and methanol, respectively. When x1 ranged from 0 to 0.6, the solubility was determined by the static equilibrium method. For each determination, an excessive amount of MAP was added to the water–methanol system with a known composition. The mixed solution in the sublayer of the jacketed-glass bottle, was stirred for 3.5 h until it reached the equilibrium state. Then, the solution was left static for 1 h, allowing the undissolved MAP to settle down. The supernatant liquid sample obtained was analyzed by the gravimetric method of quinoline phosphomolybdate. When x1 ranged from 0.6 to 1.0, the determination method was switched to the dynamic method. The water–methanol solution of known composition was added to the jacketed-glass bottle and kept at a desired temperature; then MAP with known weight was added sequently. When the last small addition was not completely dissolved, the solid liquid phase equilibrium was established. The total addition amount before the last addition was the solubility of MAP in this water–methanol solution. The solubility of MAP expressed as MAP mole fraction in the water–methanol system, xA, was calculated as follows,
MAP (analytical grade) with a purity greater than 99.0% was from the Sinopharm Chemical Reagent Co., Ltd. Methanol (analytical grade) was from the Chengdu Kelong Chemical Co., Ltd. and its purity was greater than 99.5%. Deionized water was used in the experiments.
xA ¼
2.2. Apparatus and procedure
where mA, and MA represent the mass and the mole mass of MAP, respectively.
In order to ensure the accuracy of measurement, the solubility was relatively low with mole fraction of water from 0 to 0.6 and it was determined by a static equilibrium method [17–20]; the solubility was relatively high with mole fraction of water from 0.6 to 1 and it was determined by a dynamic method [21–23]. The experimental apparatus, as shown in Fig. 2, was presented in detail in previous publications [16]. It consisted of a jacketed-glass bottle (about 500 ml effective volume), a magnetic stirrer, a thermostatic water bath and a mercury thermometer. The temperature was controlled by a thermostatic water bath and determined by a mercury thermometer with an accuracy of 0.1 K. The magnetic stirrer was used to provide an agitation to accelerate the dissolution and the equilibration process. To accurately weigh the mass of a chemical reagent, an electronic balance with a precision of 0.0001 g was used.
mA =MA mA =MA þ m1 =M1 þ m2 =M2
ð2Þ
3. Results and Discussion 3.1. Solubility of MAP in the water–methanol system The mole fraction of MAP in the water–methanol system at temperatures from 293.2 to 343.2 K were listed in Table 1, and dotted in Fig. 3. It was obvious that the solubility of MAP was related to the concentration and temperature of the water–methanol system. The solubility of MAP increased with the increase of temperature and the increase of the water mole fraction in the water–methanol system. At a constant temperature, the solubility increased slowly first, and then increased rapidly when the mole fraction of water (x1) was more than 0.6. It can be seen that the mole fraction of MAP was very small and its variability with the change of temperature was not obvious when the mole fraction of water was less than 0.6. When the binary solvent has a low mole fraction of water (x1 = 0–0.6), the solubility of MAP increased slowly with the increase of temperature, however it increased dramatically at a higher water content (x1 = 0.6–1). Compared with the solubility in pure water (x1 = 1), the MAP solubility was greatly reduced as the amount of methanol increased in the water–methanol system. Therefore, methanol can be used as an effective antisolvent in the MAP crystallization process. 3.2. Solubility model and parameterization
Fig. 2. Experimental device for solubility measurement: 1, thermostatic water (inlet); 2, jacketed-glass bottle; 3, mercury thermometer; 4, magnetic rotor; 5, thermostatic water (outlet).
The solubility of MAP in the water–methanol system was determined as follows. A water–methanol solution with known composition was prepared and the mole fraction of water, x1, was calculated by the equation, m1 =M 1 x1 ¼ m1 =M1 þ m2 =M 2
ð1Þ
3.2.1. Modified Apelblat equation The modified Apelblat equation is a semiempirical model which deduced from the Clausius–Clapeyron equation, and it is widely applied to calculate the solubility of solute in solution. The equation is correlated solubility and temperature in a solvent with known composition [24–26], and it can be expressed as,
ln xA ¼ A þ
B þ C lnT T
ð3Þ
where xA and T are the mole fraction of solute in the solution and the absolute temperature (K), respectively. A, B, and C are the parameters for the model.
Please cite this article as: D. Xu, D. Xu, Y. Zhong, et al., Solubility and solution thermodynamics of ammonium dihydrogen phosphate in the water– methanol system, Chinese Journal of Chemical Engineering, https://doi.org/10.1016/j.cjche.2019.02.010
D. Xu et al. / Chinese Journal of Chemical Engineering xxx (xxxx) xxx
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Table 1 The mole fraction solubility of MAP in experiment (xAexp), the calculated solubility (xAcal), and the relative absolute deviations (RAD) for MAP in the water–methanol system from 293.2 to 343.2 K at p = 0.1 MPa① x1
103xAexp
Apelblat
CNIBS/R–K
3D model
RAD/%
103xAcal
103xAcal
103xAcal
Apelblat
CNIBS/R–K
3D model
T = 293.2 K 0.1650 0.3078 0.4325 0.5425 0.6401 0.7274 0.8058 0.8768 0.9412 1.0000
0.3485 0.7713 1.3979 2.1607 3.6508 6.8532 11.6158 20.0276 34.2949 52.7014
0.3486 0.7686 1.3932 2.2106 3.6730 6.5314 10.8789 19.9344 33.7893 52.6024
0.3471 0.7880 1.3420 2.2057 3.7527 6.5989 11.6995 20.3340 33.8274 52.9234
0.3179 0.7358 1.3287 2.3299 4.1537 7.4056 12.7764 20.6719 30.6288 40.9175
0.03 0.35 0.34 2.31 0.61 4.70 6.34 0.47 1.47 0.19
0.40 2.17 4.00 2.08 2.79 3.71 0.72 1.53 1.36 0.42
8.78 4.60 4.95 7.83 13.78 8.06 9.99 3.22 10.69 22.36
T = 298.2 K 0.1650 0.3078 0.4325 0.5425 0.6401 0.7274 0.8058 0.8768 0.9412 1.0000
0.3658 0.8310 1.5260 2.5003 4.1771 7.7465 13.4705 23.4020 38.6359 58.7484
0.3671 0.8310 1.5270 2.5120 4.2864 7.6789 12.9821 23.1927 38.6734 58.6402
0.3641 0.8486 1.4837 2.4922 4.3039 7.6256 13.5249 23.3597 38.3903 59.0312
0.3428 0.8057 1.4780 2.6259 4.7301 8.5029 14.7719 24.0563 35.8807 48.2806
0.36 0.00 0.07 0.47 2.62 0.87 3.63 0.89 0.10 0.18
0.46 2.12 2.77 0.32 3.04 1.56 0.40 0.18 0.64 0.48
6.29 3.04 3.15 5.02 13.24 9.76 9.66 2.80 7.13 17.82
T = 303.2 K 0.1650 0.3078 0.4325 0.5425 0.6401 0.7274 0.8058 0.8768 0.9412 1.0000
0.3879 0.8933 1.6773 2.8404 4.9751 8.8940 15.5332 27.1650 43.8330 64.4906
0.3863 0.8976 1.6718 2.8454 4.9811 8.9933 15.4268 26.9056 44.1208 65.1286
0.3863 0.9093 1.6419 2.8412 5.0001 8.9176 15.7490 26.8562 43.3119 65.0942
0.3688 0.8796 1.6382 2.9478 5.3635 9.7183 16.9975 27.8551 41.8143 56.6587
0.41 0.48 0.33 0.18 0.12 1.12 0.68 0.95 0.66 0.99
0.41 1.79 2.11 0.03 0.50 0.27 1.39 1.14 1.19 0.94
4.92 1.53 2.33 3.78 7.81 9.27 9.43 2.54 4.61 12.14
T = 308.2 K 0.1650 0.3078 0.4325 0.5425 0.6401 0.7274 0.8058 0.8768 0.9412 1.0000
0.4076 0.9663 1.8170 3.2070 5.8138 10.3599 17.9873 31.1966 49.7643 71.9834
0.4063 0.9687 1.8285 3.2134 5.7651 10.4942 18.2582 31.1260 50.1803 72.0798
0.4071 0.9713 1.8075 3.2161 5.7677 10.3749 18.3058 30.9460 49.1804 72.5209
0.3958 0.9576 1.8098 3.2969 6.0569 11.0594 19.4695 32.1008 48.4877 66.1462
0.32 0.25 0.63 0.20 0.84 1.30 1.51 0.23 0.84 0.13
0.12 0.52 0.52 0.28 0.79 0.14 1.77 0.80 1.17 0.75
2.89 0.90 0.40 2.80 4.18 6.75 8.24 2.90 2.57 8.11
T = 313.2 K 0.1650 0.3078 0.4325 0.5425 0.6401 0.7274 0.8058 0.8768 0.9412 1.0000
0.4255 1.0470 2.0007 3.6479 6.7764 12.0938 21.2793 35.8034 56.7722 80.0918
0.4269 1.0445 1.9979 3.6185 6.6468 12.2025 21.5261 35.9117 56.9034 79.5052
0.4256 1.0456 2.0054 3.6620 6.6900 12.1489 21.4372 35.9073 56.0518 80.5457
0.4238 1.0396 1.9930 3.6741 6.8134 12.5337 22.2047 36.8263 55.9610 76.8417
0.33 0.24 0.14 0.81 1.91 0.90 1.16 0.30 0.23 0.73
0.02 0.13 0.23 0.39 1.28 0.46 0.74 0.29 1.27 0.57
0.40 0.71 0.38 0.72 0.55 3.64 4.35 2.86 1.43 4.06
T = 318.2 K 0.1650 0.3078 0.4325 0.5425 0.6401 0.7274 0.8058 0.8768 0.9412 1.0000
0.4488 1.1284 2.1683 4.0823 7.7178 13.8732 24.6905 41.0793 64.4034 87.9756
0.4484 1.1253 2.1807 4.0633 7.6350 14.1410 25.2850 41.3260 64.3445 87.4152
0.4492 1.1222 2.1905 4.0809 7.5979 13.9885 24.8128 41.3373 63.4306 88.5224
0.4528 1.1258 2.1880 4.0805 7.6362 14.1489 25.2196 42.0656 64.2958 88.8470
0.09 0.27 0.57 0.47 1.07 1.93 2.41 0.60 0.09 0.64
0.09 0.55 1.02 0.03 1.55 0.83 0.50 0.63 1.51 0.62
0.89 0.23 0.91 0.04 1.06 1.99 2.14 2.40 0.17 0.99 (continued on next page)
Please cite this article as: D. Xu, D. Xu, Y. Zhong, et al., Solubility and solution thermodynamics of ammonium dihydrogen phosphate in the water– methanol system, Chinese Journal of Chemical Engineering, https://doi.org/10.1016/j.cjche.2019.02.010
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D. Xu et al. / Chinese Journal of Chemical Engineering xxx (xxxx) xxx
Table 1 (continued) 103xAexp
x1
Apelblat
CNIBS/R–K
3D model
RAD/%
103xAcal
103xAcal
103xAcal
Apelblat
CNIBS/R–K
3D model
T = 323.2 K 0.1650 0.3078 0.4325 0.5425 0.6401 0.7274 0.8058 0.8768 0.9412 1.0000
0.4701 1.2139 2.3711 4.5582 8.7240 16.4235 29.3569 47.2810 72.7504 95.1486
0.4706 1.2113 2.3780 4.5507 8.7393 16.3345 29.5949 47.4378 72.5606 95.8194
0.4709 1.2050 2.3929 4.5601 8.7024 16.3383 29.2034 48.2066 71.8517 95.3472
0.4828 1.2161 2.3953 4.5173 8.5281 15.9123 28.5313 47.8529 73.5553 102.2677
0.11 0.21 0.29 0.16 0.18 0.54 0.81 0.33 0.26 0.71
0.17 0.73 0.92 0.04 0.25 0.52 0.52 1.96 1.24 0.21
2.70 0.18 1.02 0.90 2.25 3.11 2.81 1.21 1.11 7.48
T = 328.2 K 0.1650 0.3078 0.4325 0.5425 0.6401 0.7274 0.8058 0.8768 0.9412 1.0000
0.4942 1.3033 2.6210 5.1392 9.9642 19.0547 34.3574 54.0530 81.7114 104.5250
0.4936 1.3028 2.5906 5.0836 9.9696 18.8095 34.5215 54.3222 81.6121 104.7264
0.4950 1.2951 2.6373 5.1443 9.9925 18.9422 33.8679 55.3804 80.9866 104.4894
0.5138 1.3105 2.6149 4.9853 9.4923 17.8317 32.1568 54.2231 83.8041 117.2121
0.12 0.04 1.16 1.08 0.05 1.29 0.48 0.50 0.12 0.19
0.16 0.63 0.62 0.10 0.28 0.59 1.42 2.46 0.89 0.03
3.97 0.55 0.23 2.99 4.74 6.42 6.41 0.31 2.56 12.14
T = 333.2 K 0.1650 0.3078 0.4325 0.5425 0.6401 0.7274 0.8058 0.8768 0.9412 1.0000
0.5155 1.3949 2.8122 5.6840 11.2219 21.6130 40.3538 61.9963 91.6379 114.4169
0.5174 1.4001 2.8195 5.6650 11.3362 21.5948 40.1363 62.0608 91.5624 114.1440
0.5168 1.3799 2.8499 5.6652 11.2423 21.6998 39.1583 63.7939 91.5125 113.8891
0.5458 1.4091 2.8472 5.4855 10.5315 19.9144 36.1131 61.2112 95.1079 133.7915
0.37 0.37 0.26 0.33 1.02 0.08 0.54 0.10 0.08 0.24
0.25 1.08 1.34 0.33 0.18 0.40 2.96 2.90 0.14 0.46
5.88 1.02 1.24 3.49 6.15 7.86 10.51 1.27 3.79 16.93
T = 338.2 K 0.1650 0.3078 0.4325 0.5425 0.6401 0.7274 0.8058 0.8768 0.9412 1.0000
0.5433 1.5061 3.0651 6.2907 12.7193 24.5788 46.7065 70.8881 102.6762 124.2069
0.5420 1.5035 3.0659 6.2980 12.8502 24.7212 46.5175 70.7420 102.4778 124.0788
0.5448 1.4876 3.1109 6.2803 12.6800 24.8255 45.0801 73.0419 102.7475 123.4820
0.5787 1.5119 3.0924 6.0189 11.6487 22.1678 40.4172 68.8527 107.5333 152.1199
0.24 0.17 0.03 0.12 1.03 0.58 0.40 0.21 0.19 0.10
0.28 1.23 1.49 0.17 0.31 1.00 3.48 3.04 0.07 0.58
6.52 0.39 0.89 4.32 8.42 9.81 13.47 2.87 4.73 22.47
T = 343.2 K 0.4325 0.5425 0.6401 0.7274 0.8058 0.8768 0.9412 1.0000
3.3277 6.9494 14.6603 28.2828 53.8241 80.6188 114.1807 134.4030
3.3307 6.9859 14.5229 28.2221 53.7497 80.4619 114.4281 134.5370
3.3288 6.9473 14.5686 28.9338 52.0654 82.5069 113.3988 134.4598
3.3506 6.5864 12.8466 24.5992 45.0862 77.1831 121.1477 172.3133
0.09 0.53 0.94 0.21 0.14 0.19 0.22 0.10
0.03 0.03 0.63 2.30 3.27 2.34 0.68 0.04
0.69 5.22 12.37 13.02 16.23 4.26 6.10 28.21
①
The standard uncertainties u are u(T) = 0.1 K, ur(p) = 0.05, ur(x1) = 0.0002, and ur(xA) = 0.033.
3.2.2. CNIBS/R–K model The Combined Nearly Ideal Binary-Solvent/Redlich–Kister (CNIBS/R–K) model is one of the theoretical models, and it is a power series equation which associated the solubility with the concentration of one of the solvents in binary solvent systems [27–29]. The model is broadly used to calculate the solubility in binary solvents at constant temperature, and it is described as follows, ln xA ¼ B0 þ B1 x1 þ B2 x21 þ B3 x31 þ B4 x41
ð4Þ
where B0, B1, B2, B3, and B4 are the parameters of the simplified CNIBS/ R–K model in the mixed solvents.
3.2.3. Jouyban–Acree model The Jouyban–Acree model is a 3D model and it is presented for the calculation of solubility in the mixed solvents system [30]. In this model, the binary and ternary interactions have all been included. According to this model the solubility can be calculated as, B1 B2 ln xA ¼ x1 A1 þ þ ð1−x1 Þ A2 þ T T i x1 ð1−x1 Þ h J 0 þ J 1 ð2x1 −1Þ þ J 2 ð2x1 −1Þ2 þ T
ð5Þ
Please cite this article as: D. Xu, D. Xu, Y. Zhong, et al., Solubility and solution thermodynamics of ammonium dihydrogen phosphate in the water– methanol system, Chinese Journal of Chemical Engineering, https://doi.org/10.1016/j.cjche.2019.02.010
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Table 4 Parameters of the 3D Jouyban−Acree model for the MAP solubility in the water–methanol system Parameters
Value
A1 A2 B1×10−3 B2×10−3 J0×10−2 J1×10−2 J2×10−3 Adj. R2 Overall RAD
6.673 ± 0.266 5.571 ± 0.343 −2.893 ± 0.084 −1.238 ± 0.120 2.415 ± 1.011 −8.333 ± 1.475 1.303 ± 0.187 0.9981 5.38
3.3. Relative absolute deviations
Fig. 3. The solubility of MAP (expressed as MAP mole fraction xA) in the water–methanol system as a function of the mole fraction of water in the solvent (x1) at different temperatures.
To evaluate the deviation between the experimental data and the model calculation values, the relative average deviations (RAD) are calculated as follows,
RAD ¼
where A1, A2, B1, B2, J0, J1, and J2 are the parameters of the Jouyban– Acree model for the mixed solvent system.
3.2.4. Model parameterization The solubility of MAP in the water–methanol system at different temperatures was fitted by the three models mentioned above and the corresponding parameters were obtained as listed in Tables 2–4. In addition, the solubility curves calculated by the three models were represented in Figs. 4–6, respectively.
exp ! 1 X xA −xcal A 100% exp N xA
ð6Þ
where N is the number of experimental points. xAexp and xAcal are the experimental and calculated solubility of MAP in the water–methanol system, respectively. The values of RAD are calculated for the three different models and listed in Tables 1–4. It can be seen clearly that the RAD values are very small for all the three solubility models. The RAD values are 0.65%, 0.97%, and 5.38% for the modified Apelblat equation, for the CNIBS/R–K model, and for the Jouyban–Acree model, respectively. The coefficient of determination (R2) is very good and all of them reach 0.999 for the model of modified Apelblat equation and CNIBS/R–K. For the Jouyban–Acree model, the R2 is 0.9981. The results
Table 2 Parameters of the modified Apelblat equation for the MAP solubility in the water–methanol system x1
A
B
C
Adj. R2
RAD
0.1650 0.3078 0.4325 0.5425 0.6401 0.7274 0.8058 0.8768 0.9412 1.0000 Overall
−29.107 ± 6.646 −42.882 ± 6.200 −48.680 ± 8.884 −24.012 ± 13.671 −17.224 ± 23.668 −31.691 ± 22.539 −33.227 ± 27.013 −45.627 ± 7.590 −25.026 ± 7.539 6.738 ± 9.580
167.042 ± 349.020 419.974 ± 346.659 499.509 ± 514.810 −1106.723 ± 710.972 −1780.000 ± 1191.078 −1225.093 ± 1220.853 −1355.809 ± 1476.112 −404.429 ± 441.930 −1048.375 ± 396.646 −2041.605 ± 450.741
3.622 ± 0.997 6.034 ± 0.925 7.112 ± 1.319 3.815 ± 2.014 3.114 ± 3.469 5.428 ± 3.294 5.867 ± 3.933 7.585 ± 1.107 4.438 ± 1.102 −0.479 ± 1.431
0.9995 0.9998 0.9996 0.9996 0.9992 0.9992 0.9991 0.9999 0.9999 0.9997
0.22 0.26 0.43 0.58 0.87 1.23 1.65 0.43 0.40 0.41 0.65
Table 3 Parameters of the simplified CNIBS/R–K Model for the MAP solubility in the water–methanol system T/K
B0×10−2
B1×10−2
B2×10−2
B3×10−2
B4×10−2
Adj. R2
RAD
293.2 298.2 303.2 308.2 313.2 318.2 323.2 328.2 333.2 338.2 343.2 Overall
−0.098 ± 0.002 −0.097 ± 0.002 −0.096 ± 0.001 −0.095 ± 0.001 −0.095 ± 0.001 −0.095 ± 0.001 −0.095 ± 0.001 −0.095 ± 0.001 −0.095 ± 0.001 −0.095 ± 0.002 −0.076 ± 0.035
0.153 ± 0.022 0.153 ± 0.015 0.145 ± 0.011 0.139 ± 0.008 0.139 ± 0.007 0.143 ± 0.009 0.152 ± 0.008 0.153 ± 0.010 0.160 ± 0.014 0.169 ± 0.016 0.043 ± 0.212
−0.328 ± 0.068 −0.323 ± 0.047 −0.294 ± 0.035 −0.272 ± 0.025 −0.269 ± 0.020 −0.279 ± 0.026 −0.310 ± 0.025 −0.309 ± 0.030 −0.335 ± 0.043 −0.362 ± 0.048 −0.065 ± 0.466
0.397 ± 0.083 0.394 ± 0.057 0.363 ± 0.042 0.341 ± 0.030 0.341 ± 0.025 0.361 ± 0.032 0.411 ± 0.031 0.415 ± 0.036 0.456 ± 0.052 0.496 ± 0.059 0.207 ± 0.443
−0.154 ± 0.035 −0.154 ± 0.024 −0.145 ± 0.018 −0.139 ± 0.013 −0.142 ± 0.011 −0.154 ± 0.014 −0.181 ± 0.013 −0.186 ± 0.015 −0.208 ± 0.022 −0.229 ± 0.025 −0.129 ± 0.154
0.9996 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9996
1.92 1.20 0.98 0.69 0.54 0.73 0.66 0.72 1.00 1.17 1.17 0.97
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D. Xu et al. / Chinese Journal of Chemical Engineering xxx (xxxx) xxx
Fig. 4. The solubility of MAP (expressed as mole fraction xA) in the water–methanol system: x1 represented the mole fraction of water in the binary solvent, the solid lines were calculated with the modified Apelblat equation.
Fig. 6. 3D scatter plot of the MAP solubility (expressed as mole fraction xA) versus T and x1 in the water–methanol system: x1 represented the mole fraction of water in the binary solvent, the 3D surface was calculated with the Jouyban–Acree model.
show that the solubility of MAP in the water–methanol system can be predicted by the three solubility models, the values of RAD and R2 indicate that the predicted values are reliable. By comparing the three models, the accuracy of the modified Apelblat equation is the highest, the Jouyban–Acree model is the lowest, and the CNIBS/R–K model is intermediate. The modified Apelblat equation is used to predict the solubility of MAP in the same binary solvent system of identical composition but at different temperatures, while the CNIBS/R–K model is used to predict the solubility at a certain temperature at different concentrations of solvents. For the modified Apelblat equation and the CNIBS/R– K model, it requires a lot of model parameters to describe the solubility of MAP in the water–methanol system. For the Jouyban–Acree model, although it has a larger RAD and a lower R2, the Jouyban–Acree model considers the combined impact of the temperature and the composition of the binary solvent, and the needed model parameters are much less than the model parameters of the modified Apelblat equation and the CNIBS/R–K model. Therefore, the Jouyban–Acree model is considered sufficient to predict the solubility of MAP at different temperatures and component concentrations in the water–methanol system.
⊖ where the ΔsolHm is the standard molar dissolution enthalpy and the ⊖ ΔsolSm is the standard molar dissolution entropy. The Van't Hoff plot of the MAP solubility in the water–methanol sys⊖ ⊖ tem is presented in Fig. 7 and the values of ΔsolHm and ΔsolSm obtained are listed in Table 5. From Table 5, it can be obviously seen that the ⊖ ⊖ values of ΔsolHm are positive, and the values of ΔsolSm are mostly pos⊖ itive and while some are negative. Because the values of Δ solHm are
Fig. 5. Natural logarithm mole fraction solubility of MAP in the water–methanol system: x1 represented the mole fraction of water in the binary solvent, the solid lines were calculated with the CNIBS/R–K model.
Fig. 7. Natural logarithm of the MAP solubility versus 1/T for the Van't Hoff plots in the water–methanol system: ■ x1 = 1.0000; ○ x1 = 0.9412; ▲ x1 = 0.8768; ▽ x1 = 0.8058; ◆ x1 = 0.7274; ◇ x1 = 0.6401; ▼ x1 = 0.5425; △ x1 = 0.4325; ● x1 = 0.3078; □ x1 = 0.1650; x1 represented the mole fraction of water in the binary solvent.
3.4. Thermodynamic properties of the solution According to the thermodynamic principles of solid–liquid equilibrium, the Van't Hoff equation can be used to describe the relationship between the absolute temperature and logarithm of mole fraction solubility. The equation is expressed as follows [31,32], ln xA ¼ −
ΔsolH⊖ ΔsolS⊖ m m þ RT R
ð7Þ
Please cite this article as: D. Xu, D. Xu, Y. Zhong, et al., Solubility and solution thermodynamics of ammonium dihydrogen phosphate in the water– methanol system, Chinese Journal of Chemical Engineering, https://doi.org/10.1016/j.cjche.2019.02.010
D. Xu et al. / Chinese Journal of Chemical Engineering xxx (xxxx) xxx Table 5 Standard molar dissolution enthalpy and entropy for the MAP in the water–methanol system x1
⊖ ΔsolHm /J ∙ mol−1 ∙ K−1
⊖ ΔsolSm /J ∙ mol−1 ∙ K−1
Adj. R2
8.09 12.29 14.58 19.48 23.13 24.18 26.03 23.21 20.37 15.72
−38.65 −17.77 −5.06 15.47 32.18 40.66 51.33 46.54 41.24 29.13
0.9992 0.9991 0.9987 0.9999 0.9994 0.9979 0.9972 0.9993 0.9995 0.9997
0.1650 0.3078 0.4325 0.5425 0.6401 0.7274 0.8058 0.8768 0.9412 1.0000
7
temperature and the increase of the mole fraction of water in the binary solvent. The modified Apelblat equation, CNIBS/R–K model and Jouyban–Acree model were successfully applied to fit the experimental solubility data with the average RAD of 0.65%, 0.97%, and 5.38%, respectively. On the basis of these results, it can be concluded that methanol can be used as an effective antisolvent in the crystallization process of MAP. Furthermore, the thermodynamic properties such as enthalpy, entropy and Gibbs energy change associated with the MAP dissolution process were calculated by the Van't Hoff equation; results indicated that the dissolution process of MAP in the water–methanol system was endothermic and nonspontaneous.
References positive, it can be proved that the MAP dissolution process is endothermic, which confirms that the solubility of MAP increases with the increase of temperature in the water–methanol system. The value of ⊖ ΔsolHm is maximum when the molar fraction of water is 0.8058 at the investigated experimental points. It can be speculated that the solubility of MAP is mainly affected by temperature at a particular concentration ⊖ of water. When the values of Δ solSm were negative, the contribution ⊖ of ΔsolSm to the Gibbs energy is positive, which substantiate the very low solubility of MAP in methanol-rich binary solvents. The solubleness ⊖ of MAP increases when the values of Δ solSm become more and more positive, with the increase of water content in the water–methanol system. ⊖ ⊖ Through the ΔsolHm and ΔsolSm , the molar Gibbs energy change associated with the MAP dissolution process can be calculated by Eq. (8). By introduction of Eq. (8) to Eq. (7), then Eq. (9) is obtained. The values ⊖ of the ΔsolGm are listed in Table 6. ⊖ ⊖ ΔsolG⊖ m ¼ ΔsolHm −TΔsolSm
ð8Þ
ΔsolG⊖ m ¼ −RT lnxA
ð9Þ
⊖ Obviously, Eq. (9) shows that the ΔsolGm is a linear function of the natural logarithm of the MAP solubility at a constant temperature. ⊖ From Table 6, it can be seen clearly that the value of ΔsolGm decreased with the increase of the mole fraction of water in the water–methanol ⊖ system at a constant temperature. It reveals that a smaller Δ solGm ⊖ value means better solubleness and a larger solubility. All the ΔsolGm values are positive, which indicates that the MAP dissolution process is not spontaneous in the water–methanol system.
4. Conclusions The solubility of MAP in the water–methanol system at atmospheric pressure and at the temperatures from 293.2 to 343.2 K was determined with the static equilibrium method and the dynamic method. Results show that the solubility of MAP increased with the increase of
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Table 6 The molar Gibbs energy change ΔsolGm⊖/kJ ∙ mol−1 for the MAP dissolution at different temperatures in the water–methanol system x1
0.1650 0.3078 0.4325 0.5425 0.6401 0.7274 0.8058 0.8768 0.9412 1.0000
T/K 293.2
298.2
303.2
308.2
313.2
318.2
323.2
328.2
333.2
338.2
343.2
19.41 17.47 16.02 14.96 13.68 12.15 10.86 9.53 8.22 7.17
19.62 17.59 16.08 14.85 13.58 12.05 10.68 9.31 8.07 7.03
19.80 17.70 16.11 14.78 13.37 11.90 10.50 9.09 7.88 6.91
20.00 17.79 16.17 14.71 13.19 11.71 10.30 8.88 7.69 6.74
20.21 17.87 16.18 14.62 13.00 11.50 10.03 8.67 7.47 6.57
20.39 17.96 16.23 14.55 12.87 11.32 9.79 8.45 7.26 6.43
20.59 18.04 16.24 14.49 12.74 11.04 9.48 8.20 7.04 6.32
20.77 18.13 16.22 14.38 12.58 10.81 9.20 7.96 6.83 6.16
20.97 18.21 16.27 14.32 12.44 10.62 8.89 7.70 6.62 6.01
21.14 18.27 16.27 14.25 12.27 10.42 8.61 7.44 6.40 5.86
/ / 16.28 14.18 12.05 10.17 8.34 7.18 6.19 5.73
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Article
Solubility and solution thermodynamics of ammonium dihydrogen phosphate in the water–methanol system☆ Dejun Xu, Dehua Xu, Yanjun Zhong, Tao Luo, Xiushan Yang, Zhiye Zhang, Lin Yang, Xinlong Wang ⁎ School of Chemical Engineering, Sichuan University, Chengdu 610065, China
a r t i c l e
i n f o
Article history: Received 15 September 2018 Received in revised form 29 December 2018 Accepted 9 February 2019 Available online xxxx Keywords: Ammonium dihydrogen phosphate Solubility Water–methanol system
a b s t r a c t The solubility of ammonium dihydrogen phosphate (MAP) in the water–methanol system is essential for antisolvent crystallization studies. To investigate the effect of methanol on the solubility of MAP in water, the solubility of MAP in the water–methanol system was determined by dynamic method and static equilibrium method at temperatures ranging from 293.2 to 343.2 K at atmospheric pressure. Results showed that the solubility of MAP increased with the increase of temperature and the increase of water mole fraction in the water–methanol system. The experimental solubility data were correlated with the modified Apelblat equation, the combined nearly ideal binary solvent/Redlich–Kister (CNIBS/R–K) model and the Jouyban–Acree model. The calculated results based on these three models were in very good agreement with the experimental data with the average relative deviations of 0.65%, 0.97%, and 5.38%, respectively. Simultaneously, the thermodynamic properties of the MAP dissolution process in the water–methanol system, including Gibbs energy change, enthalpy, and entropy were obtained by the Van't Hoff equation, which can be used to assess the crystallization process. © 2019 The Chemical Industry and Engineering Society of China, and Chemical Industry Press. All rights reserved.
1. Introduction Ammonium dihydrogen phosphate (MAP, NH4H2PO4) is an important product in the phosphorus chemical industry and has a wide range of applications in various fields, such as fertilizers, nonlinear optical materials, flame retardants, wastewater treatment [1–5]. The MAP production process comprises the reaction between phosphate and ammonia, crystallization, drying, and so on [6,7]. Among them, the crystallization of MAP is a key step and the traditional crystallization route is in aqueous solution, leading to high energy consumption and production costs. Generally, solubility is a basic thermodynamic parameter in crystallization process. Mullin et al. measured the solubility of MAP over the temperature range 20–40 °C, and investigated the growth kinetic of MAP crystal [8,9]. Yang et al. researched the solid–liquid phase equilibrium for urea phosphate + MAP + water to prepare the urea phosphate in the ternary system [10]. Eysseltová et al. provided an overview of solubility of ammonium phosphates [11]. In recent years, the antisolvent crystallization is proposed as a promising way to save energy and improve the crystal quality, because a suitable antisolvent can decrease the solubility of salt in water [12–15]. In our previous study, a process to produce MAP using ethanol as ☆ Supported by the National Key Research and Development Program of China (2016YFD0200404) and the Sichuan Science and Technology Program (2018RZ0145). ⁎ Corresponding author. E-mail address: [email protected] (X. Wang).
the antisolvent was proposed and this has an important guiding significance on the production of MAP [16]. However, it was difficult to recycle the ethanol by conventional distillation, because the water–ethanol system generates an azeotrope (89.5% of ethanol) at the temperature of 78.1 °C and under atmospheric pressure. Methanol is the simplest alcohol and shares many similarities with ethanol. It can also be used as an antisolvent. Importantly, there exists no azeotrope in the methanol–water system. It is also well known that methanol is cheaper than ethanol due to the methanol overproduction in China. Besides, methanol is a byproduct in some enterprises that produce MAP. Hence, it would be a good choice to use methanol as an antisolvent in the crystallization of MAP. The process is schematically shown in Fig. 1, and an amount of recycled methanol is added to the MAP water solution to lower the solubility of MAP and the MAP product is produced by the antisolvent crystallization. The residual fluid obtained is distillated to recycle methanol. The solubility plays a crucial role in the crystallization process, but relevant data about the solubility in the water–methanol system are not available in any publications. Therefore, we report here the solubility of MAP in the water–methanol system. In this work, the solubility of MAP in the water–methanol system is determined at temperatures ranging from 293.2 to 343.2 K and the experimental data were correlated with the modified Apelblat equation, combined nearly ideal binary solvent/Redlich–Kister (CNIBS/R–K) model and the Jouyban–Acree model. Besides, the thermodynamic properties of the MAP dissolution process in the water–methanol
https://doi.org/10.1016/j.cjche.2019.02.010 1004-9541/© 2019 The Chemical Industry and Engineering Society of China, and Chemical Industry Press. All rights reserved.
Please cite this article as: D. Xu, D. Xu, Y. Zhong, et al., Solubility and solution thermodynamics of ammonium dihydrogen phosphate in the water– methanol system, Chinese Journal of Chemical Engineering, https://doi.org/10.1016/j.cjche.2019.02.010
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D. Xu et al. / Chinese Journal of Chemical Engineering xxx (xxxx) xxx
Fig. 1. A flow-diagram of the antisolvent crystallization process in the water–methanol system for the production of ammonium dihydrogen phosphate (MAP).
system, including Gibbs energy, enthalpy, and entropy were obtained by the Van't Hoff equation. 2. Experimental 2.1. Materials
where m1, m2, M1, and M2 represented the mass of water and methanol and the mole mass of water and methanol, respectively. When x1 ranged from 0 to 0.6, the solubility was determined by the static equilibrium method. For each determination, an excessive amount of MAP was added to the water–methanol system with a known composition. The mixed solution in the sublayer of the jacketed-glass bottle, was stirred for 3.5 h until it reached the equilibrium state. Then, the solution was left static for 1 h, allowing the undissolved MAP to settle down. The supernatant liquid sample obtained was analyzed by the gravimetric method of quinoline phosphomolybdate. When x1 ranged from 0.6 to 1.0, the determination method was switched to the dynamic method. The water–methanol solution of known composition was added to the jacketed-glass bottle and kept at a desired temperature; then MAP with known weight was added sequently. When the last small addition was not completely dissolved, the solid liquid phase equilibrium was established. The total addition amount before the last addition was the solubility of MAP in this water–methanol solution. The solubility of MAP expressed as MAP mole fraction in the water–methanol system, xA, was calculated as follows,
MAP (analytical grade) with a purity greater than 99.0% was from the Sinopharm Chemical Reagent Co., Ltd. Methanol (analytical grade) was from the Chengdu Kelong Chemical Co., Ltd. and its purity was greater than 99.5%. Deionized water was used in the experiments.
xA ¼
2.2. Apparatus and procedure
where mA, and MA represent the mass and the mole mass of MAP, respectively.
In order to ensure the accuracy of measurement, the solubility was relatively low with mole fraction of water from 0 to 0.6 and it was determined by a static equilibrium method [17–20]; the solubility was relatively high with mole fraction of water from 0.6 to 1 and it was determined by a dynamic method [21–23]. The experimental apparatus, as shown in Fig. 2, was presented in detail in previous publications [16]. It consisted of a jacketed-glass bottle (about 500 ml effective volume), a magnetic stirrer, a thermostatic water bath and a mercury thermometer. The temperature was controlled by a thermostatic water bath and determined by a mercury thermometer with an accuracy of 0.1 K. The magnetic stirrer was used to provide an agitation to accelerate the dissolution and the equilibration process. To accurately weigh the mass of a chemical reagent, an electronic balance with a precision of 0.0001 g was used.
mA =MA mA =MA þ m1 =M1 þ m2 =M2
ð2Þ
3. Results and Discussion 3.1. Solubility of MAP in the water–methanol system The mole fraction of MAP in the water–methanol system at temperatures from 293.2 to 343.2 K were listed in Table 1, and dotted in Fig. 3. It was obvious that the solubility of MAP was related to the concentration and temperature of the water–methanol system. The solubility of MAP increased with the increase of temperature and the increase of the water mole fraction in the water–methanol system. At a constant temperature, the solubility increased slowly first, and then increased rapidly when the mole fraction of water (x1) was more than 0.6. It can be seen that the mole fraction of MAP was very small and its variability with the change of temperature was not obvious when the mole fraction of water was less than 0.6. When the binary solvent has a low mole fraction of water (x1 = 0–0.6), the solubility of MAP increased slowly with the increase of temperature, however it increased dramatically at a higher water content (x1 = 0.6–1). Compared with the solubility in pure water (x1 = 1), the MAP solubility was greatly reduced as the amount of methanol increased in the water–methanol system. Therefore, methanol can be used as an effective antisolvent in the MAP crystallization process. 3.2. Solubility model and parameterization
Fig. 2. Experimental device for solubility measurement: 1, thermostatic water (inlet); 2, jacketed-glass bottle; 3, mercury thermometer; 4, magnetic rotor; 5, thermostatic water (outlet).
The solubility of MAP in the water–methanol system was determined as follows. A water–methanol solution with known composition was prepared and the mole fraction of water, x1, was calculated by the equation, m1 =M 1 x1 ¼ m1 =M1 þ m2 =M 2
ð1Þ
3.2.1. Modified Apelblat equation The modified Apelblat equation is a semiempirical model which deduced from the Clausius–Clapeyron equation, and it is widely applied to calculate the solubility of solute in solution. The equation is correlated solubility and temperature in a solvent with known composition [24–26], and it can be expressed as,
ln xA ¼ A þ
B þ C lnT T
ð3Þ
where xA and T are the mole fraction of solute in the solution and the absolute temperature (K), respectively. A, B, and C are the parameters for the model.
Please cite this article as: D. Xu, D. Xu, Y. Zhong, et al., Solubility and solution thermodynamics of ammonium dihydrogen phosphate in the water– methanol system, Chinese Journal of Chemical Engineering, https://doi.org/10.1016/j.cjche.2019.02.010
D. Xu et al. / Chinese Journal of Chemical Engineering xxx (xxxx) xxx
3
Table 1 The mole fraction solubility of MAP in experiment (xAexp), the calculated solubility (xAcal), and the relative absolute deviations (RAD) for MAP in the water–methanol system from 293.2 to 343.2 K at p = 0.1 MPa① x1
103xAexp
Apelblat
CNIBS/R–K
3D model
RAD/%
103xAcal
103xAcal
103xAcal
Apelblat
CNIBS/R–K
3D model
T = 293.2 K 0.1650 0.3078 0.4325 0.5425 0.6401 0.7274 0.8058 0.8768 0.9412 1.0000
0.3485 0.7713 1.3979 2.1607 3.6508 6.8532 11.6158 20.0276 34.2949 52.7014
0.3486 0.7686 1.3932 2.2106 3.6730 6.5314 10.8789 19.9344 33.7893 52.6024
0.3471 0.7880 1.3420 2.2057 3.7527 6.5989 11.6995 20.3340 33.8274 52.9234
0.3179 0.7358 1.3287 2.3299 4.1537 7.4056 12.7764 20.6719 30.6288 40.9175
0.03 0.35 0.34 2.31 0.61 4.70 6.34 0.47 1.47 0.19
0.40 2.17 4.00 2.08 2.79 3.71 0.72 1.53 1.36 0.42
8.78 4.60 4.95 7.83 13.78 8.06 9.99 3.22 10.69 22.36
T = 298.2 K 0.1650 0.3078 0.4325 0.5425 0.6401 0.7274 0.8058 0.8768 0.9412 1.0000
0.3658 0.8310 1.5260 2.5003 4.1771 7.7465 13.4705 23.4020 38.6359 58.7484
0.3671 0.8310 1.5270 2.5120 4.2864 7.6789 12.9821 23.1927 38.6734 58.6402
0.3641 0.8486 1.4837 2.4922 4.3039 7.6256 13.5249 23.3597 38.3903 59.0312
0.3428 0.8057 1.4780 2.6259 4.7301 8.5029 14.7719 24.0563 35.8807 48.2806
0.36 0.00 0.07 0.47 2.62 0.87 3.63 0.89 0.10 0.18
0.46 2.12 2.77 0.32 3.04 1.56 0.40 0.18 0.64 0.48
6.29 3.04 3.15 5.02 13.24 9.76 9.66 2.80 7.13 17.82
T = 303.2 K 0.1650 0.3078 0.4325 0.5425 0.6401 0.7274 0.8058 0.8768 0.9412 1.0000
0.3879 0.8933 1.6773 2.8404 4.9751 8.8940 15.5332 27.1650 43.8330 64.4906
0.3863 0.8976 1.6718 2.8454 4.9811 8.9933 15.4268 26.9056 44.1208 65.1286
0.3863 0.9093 1.6419 2.8412 5.0001 8.9176 15.7490 26.8562 43.3119 65.0942
0.3688 0.8796 1.6382 2.9478 5.3635 9.7183 16.9975 27.8551 41.8143 56.6587
0.41 0.48 0.33 0.18 0.12 1.12 0.68 0.95 0.66 0.99
0.41 1.79 2.11 0.03 0.50 0.27 1.39 1.14 1.19 0.94
4.92 1.53 2.33 3.78 7.81 9.27 9.43 2.54 4.61 12.14
T = 308.2 K 0.1650 0.3078 0.4325 0.5425 0.6401 0.7274 0.8058 0.8768 0.9412 1.0000
0.4076 0.9663 1.8170 3.2070 5.8138 10.3599 17.9873 31.1966 49.7643 71.9834
0.4063 0.9687 1.8285 3.2134 5.7651 10.4942 18.2582 31.1260 50.1803 72.0798
0.4071 0.9713 1.8075 3.2161 5.7677 10.3749 18.3058 30.9460 49.1804 72.5209
0.3958 0.9576 1.8098 3.2969 6.0569 11.0594 19.4695 32.1008 48.4877 66.1462
0.32 0.25 0.63 0.20 0.84 1.30 1.51 0.23 0.84 0.13
0.12 0.52 0.52 0.28 0.79 0.14 1.77 0.80 1.17 0.75
2.89 0.90 0.40 2.80 4.18 6.75 8.24 2.90 2.57 8.11
T = 313.2 K 0.1650 0.3078 0.4325 0.5425 0.6401 0.7274 0.8058 0.8768 0.9412 1.0000
0.4255 1.0470 2.0007 3.6479 6.7764 12.0938 21.2793 35.8034 56.7722 80.0918
0.4269 1.0445 1.9979 3.6185 6.6468 12.2025 21.5261 35.9117 56.9034 79.5052
0.4256 1.0456 2.0054 3.6620 6.6900 12.1489 21.4372 35.9073 56.0518 80.5457
0.4238 1.0396 1.9930 3.6741 6.8134 12.5337 22.2047 36.8263 55.9610 76.8417
0.33 0.24 0.14 0.81 1.91 0.90 1.16 0.30 0.23 0.73
0.02 0.13 0.23 0.39 1.28 0.46 0.74 0.29 1.27 0.57
0.40 0.71 0.38 0.72 0.55 3.64 4.35 2.86 1.43 4.06
T = 318.2 K 0.1650 0.3078 0.4325 0.5425 0.6401 0.7274 0.8058 0.8768 0.9412 1.0000
0.4488 1.1284 2.1683 4.0823 7.7178 13.8732 24.6905 41.0793 64.4034 87.9756
0.4484 1.1253 2.1807 4.0633 7.6350 14.1410 25.2850 41.3260 64.3445 87.4152
0.4492 1.1222 2.1905 4.0809 7.5979 13.9885 24.8128 41.3373 63.4306 88.5224
0.4528 1.1258 2.1880 4.0805 7.6362 14.1489 25.2196 42.0656 64.2958 88.8470
0.09 0.27 0.57 0.47 1.07 1.93 2.41 0.60 0.09 0.64
0.09 0.55 1.02 0.03 1.55 0.83 0.50 0.63 1.51 0.62
0.89 0.23 0.91 0.04 1.06 1.99 2.14 2.40 0.17 0.99 (continued on next page)
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D. Xu et al. / Chinese Journal of Chemical Engineering xxx (xxxx) xxx
Table 1 (continued) 103xAexp
x1
Apelblat
CNIBS/R–K
3D model
RAD/%
103xAcal
103xAcal
103xAcal
Apelblat
CNIBS/R–K
3D model
T = 323.2 K 0.1650 0.3078 0.4325 0.5425 0.6401 0.7274 0.8058 0.8768 0.9412 1.0000
0.4701 1.2139 2.3711 4.5582 8.7240 16.4235 29.3569 47.2810 72.7504 95.1486
0.4706 1.2113 2.3780 4.5507 8.7393 16.3345 29.5949 47.4378 72.5606 95.8194
0.4709 1.2050 2.3929 4.5601 8.7024 16.3383 29.2034 48.2066 71.8517 95.3472
0.4828 1.2161 2.3953 4.5173 8.5281 15.9123 28.5313 47.8529 73.5553 102.2677
0.11 0.21 0.29 0.16 0.18 0.54 0.81 0.33 0.26 0.71
0.17 0.73 0.92 0.04 0.25 0.52 0.52 1.96 1.24 0.21
2.70 0.18 1.02 0.90 2.25 3.11 2.81 1.21 1.11 7.48
T = 328.2 K 0.1650 0.3078 0.4325 0.5425 0.6401 0.7274 0.8058 0.8768 0.9412 1.0000
0.4942 1.3033 2.6210 5.1392 9.9642 19.0547 34.3574 54.0530 81.7114 104.5250
0.4936 1.3028 2.5906 5.0836 9.9696 18.8095 34.5215 54.3222 81.6121 104.7264
0.4950 1.2951 2.6373 5.1443 9.9925 18.9422 33.8679 55.3804 80.9866 104.4894
0.5138 1.3105 2.6149 4.9853 9.4923 17.8317 32.1568 54.2231 83.8041 117.2121
0.12 0.04 1.16 1.08 0.05 1.29 0.48 0.50 0.12 0.19
0.16 0.63 0.62 0.10 0.28 0.59 1.42 2.46 0.89 0.03
3.97 0.55 0.23 2.99 4.74 6.42 6.41 0.31 2.56 12.14
T = 333.2 K 0.1650 0.3078 0.4325 0.5425 0.6401 0.7274 0.8058 0.8768 0.9412 1.0000
0.5155 1.3949 2.8122 5.6840 11.2219 21.6130 40.3538 61.9963 91.6379 114.4169
0.5174 1.4001 2.8195 5.6650 11.3362 21.5948 40.1363 62.0608 91.5624 114.1440
0.5168 1.3799 2.8499 5.6652 11.2423 21.6998 39.1583 63.7939 91.5125 113.8891
0.5458 1.4091 2.8472 5.4855 10.5315 19.9144 36.1131 61.2112 95.1079 133.7915
0.37 0.37 0.26 0.33 1.02 0.08 0.54 0.10 0.08 0.24
0.25 1.08 1.34 0.33 0.18 0.40 2.96 2.90 0.14 0.46
5.88 1.02 1.24 3.49 6.15 7.86 10.51 1.27 3.79 16.93
T = 338.2 K 0.1650 0.3078 0.4325 0.5425 0.6401 0.7274 0.8058 0.8768 0.9412 1.0000
0.5433 1.5061 3.0651 6.2907 12.7193 24.5788 46.7065 70.8881 102.6762 124.2069
0.5420 1.5035 3.0659 6.2980 12.8502 24.7212 46.5175 70.7420 102.4778 124.0788
0.5448 1.4876 3.1109 6.2803 12.6800 24.8255 45.0801 73.0419 102.7475 123.4820
0.5787 1.5119 3.0924 6.0189 11.6487 22.1678 40.4172 68.8527 107.5333 152.1199
0.24 0.17 0.03 0.12 1.03 0.58 0.40 0.21 0.19 0.10
0.28 1.23 1.49 0.17 0.31 1.00 3.48 3.04 0.07 0.58
6.52 0.39 0.89 4.32 8.42 9.81 13.47 2.87 4.73 22.47
T = 343.2 K 0.4325 0.5425 0.6401 0.7274 0.8058 0.8768 0.9412 1.0000
3.3277 6.9494 14.6603 28.2828 53.8241 80.6188 114.1807 134.4030
3.3307 6.9859 14.5229 28.2221 53.7497 80.4619 114.4281 134.5370
3.3288 6.9473 14.5686 28.9338 52.0654 82.5069 113.3988 134.4598
3.3506 6.5864 12.8466 24.5992 45.0862 77.1831 121.1477 172.3133
0.09 0.53 0.94 0.21 0.14 0.19 0.22 0.10
0.03 0.03 0.63 2.30 3.27 2.34 0.68 0.04
0.69 5.22 12.37 13.02 16.23 4.26 6.10 28.21
①
The standard uncertainties u are u(T) = 0.1 K, ur(p) = 0.05, ur(x1) = 0.0002, and ur(xA) = 0.033.
3.2.2. CNIBS/R–K model The Combined Nearly Ideal Binary-Solvent/Redlich–Kister (CNIBS/R–K) model is one of the theoretical models, and it is a power series equation which associated the solubility with the concentration of one of the solvents in binary solvent systems [27–29]. The model is broadly used to calculate the solubility in binary solvents at constant temperature, and it is described as follows, ln xA ¼ B0 þ B1 x1 þ B2 x21 þ B3 x31 þ B4 x41
ð4Þ
where B0, B1, B2, B3, and B4 are the parameters of the simplified CNIBS/ R–K model in the mixed solvents.
3.2.3. Jouyban–Acree model The Jouyban–Acree model is a 3D model and it is presented for the calculation of solubility in the mixed solvents system [30]. In this model, the binary and ternary interactions have all been included. According to this model the solubility can be calculated as, B1 B2 ln xA ¼ x1 A1 þ þ ð1−x1 Þ A2 þ T T i x1 ð1−x1 Þ h J 0 þ J 1 ð2x1 −1Þ þ J 2 ð2x1 −1Þ2 þ T
ð5Þ
Please cite this article as: D. Xu, D. Xu, Y. Zhong, et al., Solubility and solution thermodynamics of ammonium dihydrogen phosphate in the water– methanol system, Chinese Journal of Chemical Engineering, https://doi.org/10.1016/j.cjche.2019.02.010
D. Xu et al. / Chinese Journal of Chemical Engineering xxx (xxxx) xxx
5
Table 4 Parameters of the 3D Jouyban−Acree model for the MAP solubility in the water–methanol system Parameters
Value
A1 A2 B1×10−3 B2×10−3 J0×10−2 J1×10−2 J2×10−3 Adj. R2 Overall RAD
6.673 ± 0.266 5.571 ± 0.343 −2.893 ± 0.084 −1.238 ± 0.120 2.415 ± 1.011 −8.333 ± 1.475 1.303 ± 0.187 0.9981 5.38
3.3. Relative absolute deviations
Fig. 3. The solubility of MAP (expressed as MAP mole fraction xA) in the water–methanol system as a function of the mole fraction of water in the solvent (x1) at different temperatures.
To evaluate the deviation between the experimental data and the model calculation values, the relative average deviations (RAD) are calculated as follows,
RAD ¼
where A1, A2, B1, B2, J0, J1, and J2 are the parameters of the Jouyban– Acree model for the mixed solvent system.
3.2.4. Model parameterization The solubility of MAP in the water–methanol system at different temperatures was fitted by the three models mentioned above and the corresponding parameters were obtained as listed in Tables 2–4. In addition, the solubility curves calculated by the three models were represented in Figs. 4–6, respectively.
exp ! 1 X xA −xcal A 100% exp N xA
ð6Þ
where N is the number of experimental points. xAexp and xAcal are the experimental and calculated solubility of MAP in the water–methanol system, respectively. The values of RAD are calculated for the three different models and listed in Tables 1–4. It can be seen clearly that the RAD values are very small for all the three solubility models. The RAD values are 0.65%, 0.97%, and 5.38% for the modified Apelblat equation, for the CNIBS/R–K model, and for the Jouyban–Acree model, respectively. The coefficient of determination (R2) is very good and all of them reach 0.999 for the model of modified Apelblat equation and CNIBS/R–K. For the Jouyban–Acree model, the R2 is 0.9981. The results
Table 2 Parameters of the modified Apelblat equation for the MAP solubility in the water–methanol system x1
A
B
C
Adj. R2
RAD
0.1650 0.3078 0.4325 0.5425 0.6401 0.7274 0.8058 0.8768 0.9412 1.0000 Overall
−29.107 ± 6.646 −42.882 ± 6.200 −48.680 ± 8.884 −24.012 ± 13.671 −17.224 ± 23.668 −31.691 ± 22.539 −33.227 ± 27.013 −45.627 ± 7.590 −25.026 ± 7.539 6.738 ± 9.580
167.042 ± 349.020 419.974 ± 346.659 499.509 ± 514.810 −1106.723 ± 710.972 −1780.000 ± 1191.078 −1225.093 ± 1220.853 −1355.809 ± 1476.112 −404.429 ± 441.930 −1048.375 ± 396.646 −2041.605 ± 450.741
3.622 ± 0.997 6.034 ± 0.925 7.112 ± 1.319 3.815 ± 2.014 3.114 ± 3.469 5.428 ± 3.294 5.867 ± 3.933 7.585 ± 1.107 4.438 ± 1.102 −0.479 ± 1.431
0.9995 0.9998 0.9996 0.9996 0.9992 0.9992 0.9991 0.9999 0.9999 0.9997
0.22 0.26 0.43 0.58 0.87 1.23 1.65 0.43 0.40 0.41 0.65
Table 3 Parameters of the simplified CNIBS/R–K Model for the MAP solubility in the water–methanol system T/K
B0×10−2
B1×10−2
B2×10−2
B3×10−2
B4×10−2
Adj. R2
RAD
293.2 298.2 303.2 308.2 313.2 318.2 323.2 328.2 333.2 338.2 343.2 Overall
−0.098 ± 0.002 −0.097 ± 0.002 −0.096 ± 0.001 −0.095 ± 0.001 −0.095 ± 0.001 −0.095 ± 0.001 −0.095 ± 0.001 −0.095 ± 0.001 −0.095 ± 0.001 −0.095 ± 0.002 −0.076 ± 0.035
0.153 ± 0.022 0.153 ± 0.015 0.145 ± 0.011 0.139 ± 0.008 0.139 ± 0.007 0.143 ± 0.009 0.152 ± 0.008 0.153 ± 0.010 0.160 ± 0.014 0.169 ± 0.016 0.043 ± 0.212
−0.328 ± 0.068 −0.323 ± 0.047 −0.294 ± 0.035 −0.272 ± 0.025 −0.269 ± 0.020 −0.279 ± 0.026 −0.310 ± 0.025 −0.309 ± 0.030 −0.335 ± 0.043 −0.362 ± 0.048 −0.065 ± 0.466
0.397 ± 0.083 0.394 ± 0.057 0.363 ± 0.042 0.341 ± 0.030 0.341 ± 0.025 0.361 ± 0.032 0.411 ± 0.031 0.415 ± 0.036 0.456 ± 0.052 0.496 ± 0.059 0.207 ± 0.443
−0.154 ± 0.035 −0.154 ± 0.024 −0.145 ± 0.018 −0.139 ± 0.013 −0.142 ± 0.011 −0.154 ± 0.014 −0.181 ± 0.013 −0.186 ± 0.015 −0.208 ± 0.022 −0.229 ± 0.025 −0.129 ± 0.154
0.9996 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9996
1.92 1.20 0.98 0.69 0.54 0.73 0.66 0.72 1.00 1.17 1.17 0.97
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D. Xu et al. / Chinese Journal of Chemical Engineering xxx (xxxx) xxx
Fig. 4. The solubility of MAP (expressed as mole fraction xA) in the water–methanol system: x1 represented the mole fraction of water in the binary solvent, the solid lines were calculated with the modified Apelblat equation.
Fig. 6. 3D scatter plot of the MAP solubility (expressed as mole fraction xA) versus T and x1 in the water–methanol system: x1 represented the mole fraction of water in the binary solvent, the 3D surface was calculated with the Jouyban–Acree model.
show that the solubility of MAP in the water–methanol system can be predicted by the three solubility models, the values of RAD and R2 indicate that the predicted values are reliable. By comparing the three models, the accuracy of the modified Apelblat equation is the highest, the Jouyban–Acree model is the lowest, and the CNIBS/R–K model is intermediate. The modified Apelblat equation is used to predict the solubility of MAP in the same binary solvent system of identical composition but at different temperatures, while the CNIBS/R–K model is used to predict the solubility at a certain temperature at different concentrations of solvents. For the modified Apelblat equation and the CNIBS/R– K model, it requires a lot of model parameters to describe the solubility of MAP in the water–methanol system. For the Jouyban–Acree model, although it has a larger RAD and a lower R2, the Jouyban–Acree model considers the combined impact of the temperature and the composition of the binary solvent, and the needed model parameters are much less than the model parameters of the modified Apelblat equation and the CNIBS/R–K model. Therefore, the Jouyban–Acree model is considered sufficient to predict the solubility of MAP at different temperatures and component concentrations in the water–methanol system.
⊖ where the ΔsolHm is the standard molar dissolution enthalpy and the ⊖ ΔsolSm is the standard molar dissolution entropy. The Van't Hoff plot of the MAP solubility in the water–methanol sys⊖ ⊖ tem is presented in Fig. 7 and the values of ΔsolHm and ΔsolSm obtained are listed in Table 5. From Table 5, it can be obviously seen that the ⊖ ⊖ values of ΔsolHm are positive, and the values of ΔsolSm are mostly pos⊖ itive and while some are negative. Because the values of Δ solHm are
Fig. 5. Natural logarithm mole fraction solubility of MAP in the water–methanol system: x1 represented the mole fraction of water in the binary solvent, the solid lines were calculated with the CNIBS/R–K model.
Fig. 7. Natural logarithm of the MAP solubility versus 1/T for the Van't Hoff plots in the water–methanol system: ■ x1 = 1.0000; ○ x1 = 0.9412; ▲ x1 = 0.8768; ▽ x1 = 0.8058; ◆ x1 = 0.7274; ◇ x1 = 0.6401; ▼ x1 = 0.5425; △ x1 = 0.4325; ● x1 = 0.3078; □ x1 = 0.1650; x1 represented the mole fraction of water in the binary solvent.
3.4. Thermodynamic properties of the solution According to the thermodynamic principles of solid–liquid equilibrium, the Van't Hoff equation can be used to describe the relationship between the absolute temperature and logarithm of mole fraction solubility. The equation is expressed as follows [31,32], ln xA ¼ −
ΔsolH⊖ ΔsolS⊖ m m þ RT R
ð7Þ
Please cite this article as: D. Xu, D. Xu, Y. Zhong, et al., Solubility and solution thermodynamics of ammonium dihydrogen phosphate in the water– methanol system, Chinese Journal of Chemical Engineering, https://doi.org/10.1016/j.cjche.2019.02.010
D. Xu et al. / Chinese Journal of Chemical Engineering xxx (xxxx) xxx Table 5 Standard molar dissolution enthalpy and entropy for the MAP in the water–methanol system x1
⊖ ΔsolHm /J ∙ mol−1 ∙ K−1
⊖ ΔsolSm /J ∙ mol−1 ∙ K−1
Adj. R2
8.09 12.29 14.58 19.48 23.13 24.18 26.03 23.21 20.37 15.72
−38.65 −17.77 −5.06 15.47 32.18 40.66 51.33 46.54 41.24 29.13
0.9992 0.9991 0.9987 0.9999 0.9994 0.9979 0.9972 0.9993 0.9995 0.9997
0.1650 0.3078 0.4325 0.5425 0.6401 0.7274 0.8058 0.8768 0.9412 1.0000
7
temperature and the increase of the mole fraction of water in the binary solvent. The modified Apelblat equation, CNIBS/R–K model and Jouyban–Acree model were successfully applied to fit the experimental solubility data with the average RAD of 0.65%, 0.97%, and 5.38%, respectively. On the basis of these results, it can be concluded that methanol can be used as an effective antisolvent in the crystallization process of MAP. Furthermore, the thermodynamic properties such as enthalpy, entropy and Gibbs energy change associated with the MAP dissolution process were calculated by the Van't Hoff equation; results indicated that the dissolution process of MAP in the water–methanol system was endothermic and nonspontaneous.
References positive, it can be proved that the MAP dissolution process is endothermic, which confirms that the solubility of MAP increases with the increase of temperature in the water–methanol system. The value of ⊖ ΔsolHm is maximum when the molar fraction of water is 0.8058 at the investigated experimental points. It can be speculated that the solubility of MAP is mainly affected by temperature at a particular concentration ⊖ of water. When the values of Δ solSm were negative, the contribution ⊖ of ΔsolSm to the Gibbs energy is positive, which substantiate the very low solubility of MAP in methanol-rich binary solvents. The solubleness ⊖ of MAP increases when the values of Δ solSm become more and more positive, with the increase of water content in the water–methanol system. ⊖ ⊖ Through the ΔsolHm and ΔsolSm , the molar Gibbs energy change associated with the MAP dissolution process can be calculated by Eq. (8). By introduction of Eq. (8) to Eq. (7), then Eq. (9) is obtained. The values ⊖ of the ΔsolGm are listed in Table 6. ⊖ ⊖ ΔsolG⊖ m ¼ ΔsolHm −TΔsolSm
ð8Þ
ΔsolG⊖ m ¼ −RT lnxA
ð9Þ
⊖ Obviously, Eq. (9) shows that the ΔsolGm is a linear function of the natural logarithm of the MAP solubility at a constant temperature. ⊖ From Table 6, it can be seen clearly that the value of ΔsolGm decreased with the increase of the mole fraction of water in the water–methanol ⊖ system at a constant temperature. It reveals that a smaller Δ solGm ⊖ value means better solubleness and a larger solubility. All the ΔsolGm values are positive, which indicates that the MAP dissolution process is not spontaneous in the water–methanol system.
4. Conclusions The solubility of MAP in the water–methanol system at atmospheric pressure and at the temperatures from 293.2 to 343.2 K was determined with the static equilibrium method and the dynamic method. Results show that the solubility of MAP increased with the increase of
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Table 6 The molar Gibbs energy change ΔsolGm⊖/kJ ∙ mol−1 for the MAP dissolution at different temperatures in the water–methanol system x1
0.1650 0.3078 0.4325 0.5425 0.6401 0.7274 0.8058 0.8768 0.9412 1.0000
T/K 293.2
298.2
303.2
308.2
313.2
318.2
323.2
328.2
333.2
338.2
343.2
19.41 17.47 16.02 14.96 13.68 12.15 10.86 9.53 8.22 7.17
19.62 17.59 16.08 14.85 13.58 12.05 10.68 9.31 8.07 7.03
19.80 17.70 16.11 14.78 13.37 11.90 10.50 9.09 7.88 6.91
20.00 17.79 16.17 14.71 13.19 11.71 10.30 8.88 7.69 6.74
20.21 17.87 16.18 14.62 13.00 11.50 10.03 8.67 7.47 6.57
20.39 17.96 16.23 14.55 12.87 11.32 9.79 8.45 7.26 6.43
20.59 18.04 16.24 14.49 12.74 11.04 9.48 8.20 7.04 6.32
20.77 18.13 16.22 14.38 12.58 10.81 9.20 7.96 6.83 6.16
20.97 18.21 16.27 14.32 12.44 10.62 8.89 7.70 6.62 6.01
21.14 18.27 16.27 14.25 12.27 10.42 8.61 7.44 6.40 5.86
/ / 16.28 14.18 12.05 10.17 8.34 7.18 6.19 5.73
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Please cite this article as: D. Xu, D. Xu, Y. Zhong, et al., Solubility and solution thermodynamics of ammonium dihydrogen phosphate in the water– methanol system, Chinese Journal of Chemical Engineering, https://doi.org/10.1016/j.cjche.2019.02.010