Solubility, Metastable Zone Width, and Nucleation Kinetics of Sodium

Article pubs.acs.org/jced

Solubility, Metastable Zone Width, and Nucleation Kinetics of Sodium Dichromate Dihydrate Liping Wang,†,‡ Haitao Feng,† Jiaoyu Peng,†,‡ Naijin Dong,†,‡ Wu Li,† and Yaping Dong*,† †

Qinghai Institute of Salt Lakes, Chinese Academy of Sciences, 810008 Xining, China University of Chinese Academy of Sciences, 100049 Beijing, China

‡

ABSTRACT: The experiment data on the solubility and metastable zone width (MSZW) of sodium dichromate dihydrate have been determined in the temperature range from (290.45 to 319.76) K using the conventional polythermal method by turbidity monitoring technique. Based on the solubility data, the dissolution enthalpy and entropy of sodium dichromate dihydrate were calculated by the van’t Hoff equation. Two approaches were used to estimate the nucleation kinetics of sodium dichromate dihydrate from the MSZW data, the self-consistent Nývlt-like equation and the novel equation of three-dimensional nucleation theory. The notable factors affecting MSZW of sodium dichromate dihydrate such as cooling rate, initial composition, stirring rate, and presence of seed particles have been evaluated in this paper. It was observed that the MSZW of sodium dichromate dihydrate has an obvious decrease with the increase of initial composition, rotation frequency of stirring, and the mass of seed particles, respectively. Nevertheless, the MSZW becomes wider by enhancing the cooling rate and the diameter of seed particles.

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INTRODUCTION Sodium dichromate dihydrate, one of the most important chromate compounds, can be widely used in wood preservation, leather tanning, metal finishing, and refractory.1−3 As a raw material, sodium dichromate dihydrate can be also used for the manufacture of both hexavalent and trivalent chromium products.4,5 The quality of these downstream products depends largely on the purity of sodium dichromate dihydrate. The high quality of sodium dichromate dihydrate can be produced from industrial crystallization by operating crystallization conditions within the metastable zone throughout the crystallization process.6 Therefore, the investigation of MSZW in terms of the separation and purification of sodium dichromate dihydrate is of theoretical and technological importance. The MSZW was usually considered as the difference between the saturation temperature and the nucleation temperature, at which the mass fraction of crystals can be detected when the solution temperature is lowered at a constant rate.7,8 Generally, there is a variety of factors affecting the MSZW data such as solvent, initial composition, cooling rate, stirring rate, presence of impurities and crystalline seeds, etc.9−14 The determined MSZW value under various conditions has strong implications industrially as well as scientifically.7 Industrially, the value of MSZW under various conditions is an essential requirement for the crystallization process to avoid shape nucleation and particle aggregation. Ultimately, the high purity, optimum particle size distribution and crystal shape product was obtained during industrial crystallization.8,15 Scientifically, the MSZW for a substance can be used to reveal the nucleation kinetics by Nývlt’s equation.16,17 However, some drawbacks of the Nývlt’s © 2014 American Chemical Society

equation have been discovered. Recently, Sangwal has postulated two new approaches, the self-consistent Nývlt-like equation and the novel equation of three-dimensional nucleation theory, to explain the nucleation kinetics based on the MSZW data.18,19 These approaches have been used to analyze the experimental MSZW data on nucleation kinetics.6,20,21 In this work, the polythermal method was used to determine the solubility and MSZW of sodium dichromate dihydrate, and thus the effects of cooling rate, initial composition, stirring rate, and presence of seed particles on the MSZW has been investigated. The experiment data was used to evaluate some critical nucleation parameters including the nucleation order (m), nucleation constant (K), interfacial energy (γ), and the activation energy (Esat) by the self-consistent Nývlt-like equation and the novel equation of three-dimensional nucleation theory.

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THEORY Self-Consistent Nývlt-Like Equation. For crystal nucleation theory, Nývlt yielded a relationship between the MSZW and cooling rate R. The Nývlt’s equation can be expressed:19 lgΔTmax =

lgkn 1 − m ⎛⎜ dc ⎞⎟ 1 lg − + lgR ⎝ ⎠ dT m m m

(1)

Received: October 5, 2014 Accepted: December 2, 2014 Published: December 12, 2014 185

dx.doi.org/10.1021/je5009069 | J. Chem. Eng. Data 2015, 60, 185−191

Journal of Chemical & Engineering Data

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where c is the initial composition, kn is a nucleation constant, and m is the apparent nucleation order. The equation reveals a linear dependence of lg ΔTmax and lg R, frequently used to predict the nucleation kinetics by the polythermal method. However, the Nývlt’s equation has some drawbacks: The nucleation constant kn has undefined physical significance and complicated units. Moreover, the parameters the Nývlt’s equation reproduced have an unsatisfactory relationship of the classical 3D nucleation theory.20 To remove these problems, a new approach called as the self-consistent Nývltlike equation has been proposed.19 It predicts a relationship between maximum supercooling ratio (ΔTmax/T0) and cooling rate R: ⎛ f ⎞1/ m⎛ ΔHd ⎞(1 − m)/ m 1/ m ΔTmax =⎜ R ⎟ ⎜ ⎟ T0 ⎝ KT0 ⎠ ⎝ R GTnuc ⎠

According to the classical 3D nucleation theory, the parameters A and B are contained in the dependence of nucleation rate J on supersaturation ln Smax: J = A exp[−B /(ln Smax )2 ]

where the parameter A is a constant associated with the kinetics of formation of nuclei in the growth medium, and the spherical nuclei parameter B can be expressed by 16π ⎛ γ Ω2/3 ⎞ B= ⎟ ⎜ 3 ⎝ kB Tnuc ⎠

ΔHd ΔSd + R GT0 RG

(2)

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(3)

ln(ΔTmax /T0) = Φ′ − β ln T0 + β ln R = Φ + β ln R (4)

where β = 1/m, and

Φ′ =

1 − m ⎛ ΔHd ⎞ 1 ⎛f⎞ ln⎜ ln⎜ ⎟ ⎟+ m m ⎝K⎠ ⎝ R GTnuc ⎠

(5)

(6)

In eq 6, RG is a constant, and Tnuc, ΔHd, and f can be obtained or calculated from the experiment data. Thus, according to eqs 5 and 6, the apparent nucleation order m and the new nucleation constant K can be calculated by the slope and intercept, respectively. Approach Based On Classical Three-Dimensional Nucleation Theory.18 The classical 3D nucleation theory is also used for the calculation of MSZW and the revelation of nucleation kinetics. It predicts a linear relationship between (T0/ΔTmax)2 and ln R: (T0/ΔTmax )2 = F − F1 ln R = F(1 − Z ln R )

(7)

where F = 1/(ZB)((ΔHd)/(RGTnuc))2 2 1 ⎛ ΔHd ⎞ F1 = ⎜ ⎟ B ⎝ R GTnuc ⎠

Z=

⎛ f ΔHd ⎞ F1 = ln⎜ ⎟ F ⎝ AT0 R GTnuc ⎠

(11)

EXPERIMENTAL SECTION

Materials and Apparatus. Sodium dichromate dihydrate with a purity ≥ 0.995 supplied from Tianjin Paisen Technology Corporation was recrystallized twice from aqueous solution. Deionized water (resistivity: 18.25 MΩ·cm) obtained from a water purification system (UPT - II- 20T, Chengdu Ultrapure Technology Co., Ltd.) was used in all cases. Solubility and MSZW measurements were carried out by a CrystalSCAN with 4 parallel reactors (E1061, United Kingdom He., Ltd.). Its schematic diagram has been reported in our previous literature.22 The accuracy of the temperature sensor was 0.1 K. The products containing hydrates crystallized from sodium dichromate solution were identified by X-ray diffractometer (X′Pert PRO, 2006 PANalytical). Solubility and Metastable Zone Width Measurements. The polythermal method has been used in our experiment to determine the solubility and metastable zone width of sodium dichromate dihydrate. At first, a certain amount of sodium dichromate solid and deionized water was mixed to a 100 mL crystallizer. Then the crystal mush was heated/cooled circularly at five different heating/cooling rates of 55 K·h−1, 45 K·h−1, 35 K·h−1, 25 K·h−1, and 15 K·h−1 with a fixed stirring rate of 450 rpm. The laser turbidity sensor was used to monitor the dissolution and nucleation of sodium dichromate dihydrate during all the heating/cooling process. The temperature at the point of crystal disappear and appear was recorded as Tdis and Tnuc, respectively. According to much literature,8,14 the saturation temperature T0 is the temperature that the crystal dissolute in a slower heating rate closer to zero. In this paper, T0 was determined by extrapolating the curve of dissolution temperature and heating rate to zero. The metastable zone width (ΔTmax), the difference between saturation temperature and nucleation temperature, can be given by the format: ΔTmax= T0 − Tnuc. The estimated uncertainties and primary experimental data were summarized in Table 1, respectively.

where RG is gas constant, T0 is saturation temperature, and c*is the mole fraction of the investigated compound. ΔHd and ΔSd are dissolution enthalpy and entropy, respectively. A linear dependence of ln(ΔTmax/T0) and ln R can be obtained by taking logarithms on both sides of eq 2:

Φ = Φ′ − β ln T0

3

In eq 11, γ is the solid−liquid interfacial energy, Ω is the volume of the solute molecule, and kB is the Boltzmann (RG/ NA, RG is ideal gas constant, NA is Avogadro’s number). The eq 7 predicts a linear dependence of (T0/ΔTmax)2 on ln R, with slope F1 and intercept F. F1 depends on the parameter B associated with the kinetics of formation of stable nuclei, while the value of F is related to both parameters A and B. According to eq 11, the interfacial energy γ strongly influenced by solute− solvent interactions can be calculated by the value of parameter B.

where m is the apparent nucleation order and K is a new nucleation constant with a same unit as the nucleation rate (nuclei per unit volume per unit time). RG is the gas constant, and the f is a constant calculated by solute concentration with the units as nuclei/volume. ΔHd is the heat of dissolution and can be evaluated from the solubility data by the van’t Hoff equation: ln c* = −

(10)

(8)

(9) 186



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observed that Figure 1a was identical with Figure 1b, which confirms that the crystallized product is sodium dichromate dihydrate. Solubility of Sodium Dichromate Dihydrate. The solubility data of sodium dichromate dihydrate taken in mole fraction has been measured and plotted in Figure 2. The solubility data we obtained sets a well coherence with ref 23 compared with the data reported by ref 24. The experimental data also agrees well with other reported data.25−27

Table 1. Experimental Solubility and MSZW Data of Sodium Dichromate Dihydrate in Aqueous Solution at Temperature T0 and Pressure p = 0.1 MPaa w (Na2Cr2O7·2H2O)

T0

R/K·h−1

Tdis/K

Tnuc/K

ΔTmax/K

0.7285

290.45

0.7341

294.85

0.7533

304.68

0.7636

309.51

0.7866

319.76

15 25 35 45 55 15 25 35 45 55 15 25 35 45 55 15 25 35 45 55 15 25 35 45 55

290.60 290.93 291.13 291.93 293.03 294.91 295.09 295.35 295.72 296.68 304.75 304.83 304.97 305.22 305.65 309.73 309.93 310.16 310.79 311.40 319.85 319.93 320.02 320.19 320.37

280.03 279.19 278.43 277.67 277.09 285.83 284.95 284.30 283.94 283.32 298.43 297.77 297.40 297.10 296.51 303.97 303.27 302.97 302.63 302.20 314.85 314.36 314.07 313.77 313.40

10.42 11.26 12.02 12.78 13.36 9.02 9.90 10.55 10.91 11.53 6.25 6.91 7.28 7.58 8.17 5.54 6.24 6.54 6.88 7.31 4.91 5.40 5.69 5.99 6.36

Figure 2. Solubility of sodium dichromate dihydrate in aqueous solution: ■, ref 23; ●, ref 24; ▲, experiment.

a

Standard uncertainties u are u(T) = 0.06 K, u(ΔTmax) = 0.08 K, ur(p) = 0.05, and ur(w) = 0.004.

The solubility data experimented in this paper and other reports has been used to calculate the enthalpy and entropy of sodium dichromate dihydrate by the van’t Hoff equation. The plots and results are shown in Figure 3 and Table 2, respectively.

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RESULTS AND DISCUSSION XRD Analysis. Powder X-ray diffraction (XRD) was usually used to identify the solid material and its phase purity. The results were shown in Figure 1. Figure 1a shows the pure sodium dichromate dihydrate pattern obtained from the PDF card (reference code: 00-022-1366). Figure 1b shows the XRD spectrum of the solid crystallized from sodium dichromate dihydrate solution in the measurement of MSZW. It may be

Figure 3. van’t Hoff plot of logarithm mole fraction solubility of sodium dichromate dihydrate on temperature: ■, ref 23; ●, ref 24; ▲, experiment.

From Table 2, we can find that the values calculated by our experiment are closer to those of ref 23, while it has more deviations than those of ref 24. The dissolution enthalpy of sodium dichromate dihydrate is greater than zero. It reveals the dissolution of sodium dichromate dihydrate is an endothermic process.

Figure 1. XRD pattern of sodium dichromate dihydrate: (a) pure; (b) crystallized products. 187



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Table 2. Dissolution Enthalpy and Entropy Values of Sodium Dichromate Dihydrate

a

data

ΔHd/J·mol−1

ΔSd/J·mol−1·K−1

RCa

ref 23 ref 24 expt’l

7831.68 8223.46 7727.49

10.50 12.02 10.05

0.9665 0.9551 0.9743

Regression coefficient.

Solubility and Supersolubility of Sodium Dichromate Dihydrate. The solubility and supersolubility curves at different cooling rates were constructed in Figure 4. It may

Figure 5. Effects of different initial compositions on the MSZW of sodium dichromate dihydrate, cooling rate: ■, 55 K·h−1; ●, 45 K·h−1; ▲, 35 K·h−1; ▼, 25 K·h−1; ⧫, 15 K·h−1.

Figure 4. Solubility and supersolubility data of sodium dichromate dihydrate: ■, Solubility curve; Supersolubility data at different cooling rates: ○, 55 K·h−1; ●, 45 K·h−1; △, 35 K·h−1; ▲, 25 K·h−1; ▽, 15 K· h−1.

be seen from Figure 4 that the MSZW broadens with the enhancement of cooling rate. It is easy to explain that a higher cooling rate will supply a higher supercooling, which enhances the MSZW of sodium dichromate dihydrate. Effects of Different Initial Compositions on the MSZW of Sodium Dichromate Dihydrate. In our paper, five initial compositions of sodium dichromate dihydrate have been prepared and crystallized in constant cooling rates (55 K·h−1, 45 K·h−1, 35 K·h−1, 25 K·h−1, and 15 K·h−1) with a fixed stirring rate of 450 rpm. The experimental MSZW data is shown in Figure 5. Both Figures 4 and 5 show the MSZW of sodium dichromate dihydrate narrows with the increase of initial composition. The reason is that the saturation temperature increases with the increase of initial composition, which improves the diffusion and collision probabilities of solute. As a result, the crystallization point goes ahead, thus the MSZW becomes narrow. Effects of Different Stirring Rates on the MSZW of Sodium Dichromate Dihydrate. To investigate the effects of stirring rates on the MSZW of sodium dichromate dihydrate, stationary mass fraction [w(Na2Cr2O7·2H2O) = 0.7614)] has been prepared and heated/cooled at five series of stirring rates ((250 to 650) rpm) with constant heating/cooling rate. The measured data has been presented in Figure 6. It shows that the MSZW of sodium dichromate dihydrate narrows with the improvement of the stirring rate at a fixed cooling rate. It is mainly because that the increase of the stirring rate accelerates the diffusion and collision chances of solute, causing a higher

Figure 6. Effects of different stirring rates on the MSZW of sodium dichromate dihydrate, stirring rate: ■, 250 rpm;●, 350 rpm;▲, 450 rpm;▼, 550 rpm;⧫, 650 rpm.

second nucleation rate and an earlier detection of crystal, which consequently reduces the MSZW. MSZW of Sodium Dichromate Dihydrate Added Seeds. In industrial crystallization, the presence of seeds was an effective way to control the crystallization process in the metastable zone, facilitating secondary nucleation and improving the purity of crystallized products. In order to reveal the effects of seed particles on the MSZW, different masses and sizes of seed particles were added to an increasing supercooling solution. The seed particles were obtained by recrystallization from sodium dichromate solution, and thus were sieved by series of different standard sieves. To investigate the effects of mass of seed crystals on the MSZW of sodium dichromate dihydrate, six series (0 mg, 10 mg, 20 mg, 50 mg, 100 mg, and 200 mg) of seed with settled diameter (180 μm to 250 μm) were added to an identical supersaturated solution [w(Na2Cr2O7·2H2O) = 0.7641], after which was cooled at the temperature below 2 K of the average dissolution temperature. The stirring rate (450 rpm) and cooling rate (45 K·h−1) were constant and invariable in experimental procedure. The results were presented in Figure 7. In order to 188



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Nucleation Kinetics of Sodium Dichromate Dihydrate. The dependence of ln(ΔTmax/T0) and (T0/ΔTmax)2 on ln R for sodium dichromate dihydrate at different saturation temperatures in aqueous solution were plotted in Figures 8 and 9. A

Figure 7. Effects of different masses of seed particles on the MSZW of sodium dichromate dihydrate.

investigate the effects of different sizes of seed crystals on the MSZW of sodium dichromate dihydrate, 20 mg different diameter of seed (180 μm to 250 μm) were prepared and added to an identical supersaturated solution, which composition and added temperature was discussed above. All experimental data were showed in Table 3.

Figure 8. Plots of ln(ΔTmax/T0) against ln R for sodium dichromate dihydrate at various saturation temperature in aqueous solution, Saturation temperature: ■, 290.45 K;●, 294.85 K;▲, 304.68 K;▼, 309.51 K;⧫, 319.76 K.

Table 3. Effect of Different Sizes of Seed Particles on the MSZW of Sodium Dichromate Dihydrate mesh no.

diameter/μm

ΔTmax/K

20−30 60−80 100−120 180−200 300−320

600−850 180−250 125−150 75−80 45−48

7.56 6.58 4.46 2.76 2.37

As observed from Figure 7, the MSZW decreases rapidly with the increased mass of added seed crystals. The possible reason is that the larger number of seed particles generates more nucleation center and enhances the collision nucleation rate. As a result, the MSZW of sodium dichromate dihydrate reduces with the improving addition of seed particles. It may be seen from Table 3 that the smaller seeds have more effective reduction on the MSZW of sodium dichromate dihydrate. It is incompatible with some earlier observations by other authors.28−30 They stated that only larger seeds could be effective in reducing MSZW, since small seeds consumed more supercooling to grow up and huge seeds were easy to hit the impeller blades and produce new nuclei. In our experiment, a great quantity of seed particles was added to an increasing supersaturated solution. As the cooling rate (45 K·h−1) was persistent and large enough, the supercooling consumed by the growth of added seeds can be ignored. When a certain degree of the supersaturation has been achieved, the secondary nucleation occurs. At a same mass, there is larger number of smaller seed particles, higher collision chance with glass, stirring impeller and each other. This generates secondary nucleation easily and causes the crystal temperature in advance, so that the MSZW reduces with the decrease diameter of added seed crystals.

Figure 9. Plots of (T0/ΔTmax)2 against ln R for sodium dichromate dihydrate at various saturation temperature in aqueous solution, Saturation temperature: ■, 290.45 K;●, 294.85 K;▲, 304.68 K;▼, 309.51 K;⧫, 319.76 K.

best fit of the measured data has been represented in Figures 8 and 9. The values of −Φ, m, and K have been listed in Table 4 according to eq 2. As seen from Table 4, the values of −Φ and K increase with the increase of T0, while the nucleation order m Table 4. Calculated m and K According to eq 2 for Sodium Dichromate Dihydrate at Different Saturation Temperatures

a

189

T0/K

m

−Φ

K (×1028 m−3·h−1)

RCa

290.45 294.85 304.68 309.51 319.76

5.20 5.45 5.15 4.90 5.21

3.86 3.98 4.41 4.57 4.70

6.97 7.97 12.58 14.94 17.47

0.9864 0.9933 0.9751 0.9867 0.9869

Regression coefficient. dx.doi.org/10.1021/je5009069 | J. Chem. Eng. Data 2015, 60, 185−191


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Table 6. Intercepts −Φ and ln(F1/2) and Activation Energy Esat According to eq 13 for Sodium Dichromate Dihydrate

has little dependence on T0. The average value of m is about 5.18, which suggests that the nuclei born subsequently by instantaneous nucleation mechanism.10 Table 5 shows the

plot

Table 5. Calculated A and γ According to eq 7 for Sodium Dichromate Dihydrate at Different Saturation Temperatures

a

T0/K

F

Z

A (×1027 m−3·h−1)

γ/mJ·m−2

RCa

290.45 294.85 304.68 309.51 319.76

1421.93 1899.09 4310.41 5736.27 7680.41

0.1664 0.1634 0.1674 0.1717 0.1667

6.80 7.25 6.09 5.14 5.91

1.54 1.42 1.08 0.98 0.91

0.9983 0.9918 0.9860 0.9803 0.9949

a

RCa

13.36 13.73

23.43 23.79

0.9551 0.9451


the value of Esat calculated by both plot of ln(F1/2) and −Φ against 1/T0 was much higher than the activation energy of pure water. The high Esat of sodium dichromate dihydrate suggests strong solute−solvent interactions, leading to more solute dissolving into the pure water. Ultimately, it causes the high solubility of sodium dichromate dihydrate in water, which has been also confirmed in Figure 2 and Figure 4.

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values of F, Z, A, and γ calculated by eq 7. It may be observed from Table 5 that the enhancement of saturation temperature T0 increases the values of F; however, it has an adverse effect on the results of A and γ. The values of Z listed in Table 5 depend less on the saturation temperature T0. The dependence of −Φ, F1/2, and T0 may be related by an Arrhenius-type equation:18,19,21

CONCLUSIONS The determination of the solubility and MSZW of sodium dichromate dihydrate was performed by polythermal method. The experimental data was analyzed by the self-consistent Nývlt-like equation and the novel equation of three-dimensional nucleation theory to reveal the nucleation kinetics of sodium dichromate dihydrate. Some critical nucleation parameters such as the nucleation order (m), nucleation constant (K), interfacial energy (γ), and the activation energy (Esat) have been evaluated in this work. The effects of cooling rate, initial composition, stirring rate and presence of seed particles on the MSZW have been studied. The results indicate that all the parameters have a profound influence on the MSZW date. In order to avoid uncontrollable spontaneous nucleation and obtain high purity products, the investigation may help us select an optimum condition to control the industrial crystallization process in the metastable zone.

(12)

A linear dependence can be obtained by taking logarithms on both sides of eq 12: ln y = ln y0 − Esat /R GT0

Esat/kJ·mol−1

[ln(F )](1/T0) −Φ(1/T0)


y = y0 e−Esat / R GT0

intercept

1/2

(13)

where RG is the gas constant, T0 denotes the saturation temperature, ln y is equal to the value of −Φ and ln(F1/2), and ln y0 can be extrapolated by the intercept of the straight line. In eq 13, the activation energy Esat associated with the diffusion of solute in the solution can be calculated by the slope of the straight line. The relationship of ln(F1/2), −Φ against 1/T0 and the calculated value of Esat for sodium dichromate dihydrate according to eq 13 have been showed in Figure 10 and Table 6,

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 86-971-6302023. Fax: 86-971-6310402. Funding

This work is financially supported in part by the National Natural Science Foundation of China (No. 41273032) and Trust Foundation of Qinghai Province (No. 2012-J-215). Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Barnhart, J. Chromium chemistry and implications for environmental fate and toxicity. Soil Sediment Contam. 1997, 6, 561−568. (2) Barnhart, J. Occurrences, uses, and properties of chromium. Regul. Toxicol. Pharmacol. 1997, 26, S3−S7. (3) Ceprini, M. Q.; Gottesman, R. T. Chromium salt compositions and a process for their production. U.S. Patents, 3932285, 1976. (4) Young, J. A. Sodium dichromate dihydrate. J. Chem. Educ. 2003, 80, 1251−1251. (5) Ding, Y. Production and Application of Chrome Compounds; Chemical Industry Press: Beijing, 2003. (6) Zhang, X. Y.; Wang, X. F.; Hao, L.; Yang, X. W.; Dang, L. p.; Wei, H. Y. Solubility and metastable zone width of DL-tartaric acid in aqueous solution. Cryst. Res. Technol. 2012, 47, 1153−1163. (7) Kadam, S. S.; Kulkarni, S. A.; Ribera, R. C.; Stankiewicz, A. I.; ter Horst, J. H.; Kramer, H. J. M. A new view on the metastable zone width during cooling crystallization. Chem. Eng. Sci. 2012, 72, 10−19. (8) Mullin, J. W. Crystallization, 4th ed.; Butterworth-Heinemann: London, 2001.

Figure 10. Plots of ln(F1/2) and −Φ against 1/T0 for sodium dichromate dihydrate according to eq 13, plot: ■, ln(F1/2);●, −Φ.

respectively. In Figure 10, the straight lines were approximately parallel to each other. It causes that the value of −Φ0 and Esat obtained by the plot of −Φ against 1/T0 was nearly equal to ln(F1/2)0 and Esat obtained by the plot of ln(F1/2) against 1/T0. As reported,21 the value of the activation energy ED for selfdiffusion in pure water is 8.4 kJ·mol−1. As seen from Table 6, 190



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(9) Zhang, Y.; Li, Z. Effects of Cooling Rate, Saturation Temperature, and Solvent on the Metastable Zone Width of Triethanolamine Hydrochloride. Ind. Eng. Chem. Res. 2011, 50, 6375−6381. (10) Kashchiev, D.; Borissova, A.; Hammond, R. B.; Roberts, K. J. Effect of cooling rate on the critical undercooling for crystallization. J. Cryst. Growth 2010, 312, 698−704. (11) Titiz-Sargut, S.; Ulrich, J. Influence of additives on the width of the metastable zone. Cryst. Growth Des. 2002, 2, 371−374. (12) Rauls, M.; Bartosch, K.; Kind, M.; Kuch, S.; Lacmann, R.; Mersmann, A. The influence of impurities on crystallization kinetics−a case study on ammonium sulfate. J. Cryst. Growth 2000, 213, 116−128. (13) Black, S.; Muller, F. On the Effect of Temperature on Aqueous Solubility of Organic Solids. Org. Process Res. Dev. 2010, 14, 661−665. (14) Peng, J. Y.; Dong, Y. P.; Nie, Z.; Kong, F. Z.; Meng, Q. F.; Li, W. Solubility and Metastable Zone Width Measurement of Borax Decahydrate in Potassium Chloride Solution. J. Chem. Eng. Data 2012, 57, 890−895. (15) Kulkarni, S. A.; Kadam, S. S.; Meekes, H.; Stankiewicz, A. I.; ter Horst, J. H. Crystal Nucleation Kinetics from Induction Times and Metastable Zone Widths. Cryst. Growth Des. 2013, 13, 2435−2440. (16) Nývlt, J. Kinetics of nucleation in solutions. J. Cryst. Growth 1968, 3, 377−383. (17) Nývlt, J.; Soehnel, O.; Matuchova, M. The kinetics of industrial crystallization; Academia: Prague, 1985. (18) Sangwal, K. Novel Approach to Analyze Metastable Zone Width Determined by the Polythermal Method: Physical Interpretation of Various Parameters. Cryst. Growth Des. 2009, 9, 942−950. (19) Sangwal, K. A novel self-consistent Nyvlt-like equation for metastable zone width determined by the polythermal method. Cryst. Res. Technol. 2009, 44, 231−247. (20) Sangwal, K.; Wojcik, K. Investigation of metastable zone width of ammonium oxalate aqueous solutions. Cryst. Res. Technol. 2009, 44, 363−372. (21) Sangwal, K. Some features of metastable zone width of various systems determined by polythermal method. CrystEngComm 2011, 13, 489−501. (22) Wang, L. P.; Peng, J. Y.; Li, L. L.; Feng, H. T.; Dong, Y. P.; Li, W.; Liang, J.; Zheng, Z. L. Solubility and Metastable Zone Width of Sodium Chromate Tetrahydrate. J. Chem. Eng. Data 2013, 58, 3165− 3169. (23) Liu, G. Q.; Ma, L. X.; Liu, J. Data Book of Chemical Engineering Properties of Matter: Inorganic; Chemical Industry Press: Beijing, 2002. (24) Lange, N. A.; Speight, J. Lange’s handbook of chemistry; McGrawHill: New York, 2005. (25) Hartford, W. H. Note on the System Sodium Dichromate Water. J. Am. Chem. Soc. 1941, 63, 1473−1474. (26) Ellingboe, J. J. L. Phase Diagrams for the Na2SO4-Na2Cr2O7H2O System. J. Chem. Eng. Data 1964, 9, 91−93. (27) Korin, E.; Soifer, L. Phase Diagram for the System Na2Cr2O7+ NaNO3+ H2O in the Temperature Range 20 to 40 °C. J. Chem. Eng. Data 1996, 41, 885−887. (28) Kubota, N.; Fujiwara, M. Minimum seed crystal size for secondary nucleation of potassium alum in a stirred-vessel crystallizer. J. Chem. Eng. Jpn. 1990, 23, 691−696. (29) Mayer, C.; Lacmann, R. Secondary nucleation of sodium chlorate studied with the aid of asymmetric crystallization. Chem. Eng. Technol. 1997, 20, 633−640. (30) Threlfall, T. L.; De’Ath, R. W.; Coles, S. J. Metastable Zone Widths, Conformational Multiplicity, and Seeding. Org. Process Res. Dev. 2013, 17, 578−584.

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Solubility, Metastable Zone Width, and Nucleation Kinetics of Sodium

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