CRYSTAL GROWTH & DESIGN
Solid Liquid Equilibrium, Metastable Zone, and Nucleation Parameters of the Oxalic Acid-Water System Waid
Omar†
and Joachim
2006 VOL. 6, NO. 8 1927-1930
Ulrich*,‡
Tafila Technical UniVersity, Department of Natural Resources and Chemical Engineering, P.O. Box 179, 66110-Tafila, Jordan, and Martin-Luther-UniVersita¨t Halle-Wittenberg, FB Ingenieurwissenschaften, Institut fu¨r Verfahrenstechnik/TVT, D-06099 Halle, Germany ReceiVed March 1, 2006; ReVised Manuscript ReceiVed April 20, 2006
ABSTRACT: Measurements of the solubility and metastable zone for the oxalic acid-water system were obtained. The solubility was measured within the temperature range from 284.19 to 352.02 K. The mole fraction solubility was correlated satisfactorily with the temperature by the equation: xeq ) 4 × 10-7 e0.0368T. The values of enthalpy of dissolution, enthalpy of fusion, and enthalpy of mixing were determined to be 30.80, 58.158, and -27.358 kJ mol-1, respectively. The high value of enthalpy of mixing indicates a strong interaction between the solute and the solvent molecules. The width of the metastable zone was measured by an ultrasonic method and was correlated with the cooling rate and the equilibrium temperature by the equation: ∆Tmax ) 7.2206 × 1015b0.266Teq-6.17. The nucleation parameters of oxalic acid in water were determined from the metastable zone data. Over the equilibrium temperature range from 294.75 to 320.75 K, the nucleation rate constant was varied from 0.0084 to 0.0628 #/m2‚min, whereas the nucleation order was varied from 3.2419 to 2.8292. The obtained higher values of nucleation rate constant indicate a higher rate of nucleation. The role of the presence of small amounts of sulfuric acid on the metastable zone width was also investigated. The widest metastable zone was measured due to the presence of sulfuric acid at a concentration of 2.3 × 10-9 g/g of solution. Introduction Oxalic acid is a simple dibasic organic acid, which has several industrial applications. It is used as a rust and scale remover, as a bleaching agent, as an electrolyte in the anodic oxidation of aluminum, and in the manufacture of several miscellaneous chemical derivatives.1 The synthesized solid oxalic acid, which comes from different industrial processes, does not meet the market requirements concerning quality and purity. However, further seeded recrystallization steps are used in a selected solvent to improve the product specifications. One of the most important quantities that is determined in the recrystallization step is the crystal size distribution (CSD) of the product. Controlling the CSD is an important aspect for the production of a high-quality product and for determining the efficiency of the downstream processes. Marketing and meeting of customer acceptance require a product of large crystals that are uniform in size, strong, nonagglomerated, and noncaking in the package. In industrial crystallization processes, the required product specifications are achieved by allowing seed crystals to grow in a supersaturated solution. Supersaturated solutions exhibit a metastable zone in which nucleation is slow or unlikely to occur. The width of the metastable zone is the region between the solubility (saturation) line and the supersaturation (metastable) limit, beyond which spontaneous nucleation takes place. All industrial crystallization processes take place in the metastable zone. Therefore, design and operation of any industrial cooling crystallizer under controlled CSD require the knowledge of the solubility, the metastable zone width, and the nucleation parameters. The quantitative determination of the width of the metastable zone and the nucleation rate as a function of the cooling rate and temperature are important in terms of controlling the supersaturation level at an optimum level to achieve the required CSD and quality of the final product.2 In the case * To whom correspondence should be addressed. Phone: ++ 49/(0) 34 5-55 28 401. Fax: ++ 49/(0) 34 5-55 27 358. E-mail: joachim.ulrich@ iw.uni-halle.de. † Tafila Technical University. ‡ Martin-Luther-Universita ¨ t Halle-Wittenberg.
of the oxalic acid-water system, little data are available in the literature on the metastable zone and the nucleation parameters. In this contribution, solubility, metastable zone, and nucleation parameters for the oxalic acid-water system were obtained experimentally by an ultrasonic technique over a wide range of temperatures at different cooling rates. Experimental Section The materials used for preparing all aqueous oxalic acid solutions were distilled water and oxalic acid dihydrate (C2H2O4‚2H2O) crystals of analytical grade (p.a.) manufactured by Merck, Germany. The solubility and the width of the metastable zone were measured in a 0.5 L closed and jacketed glass vessel connected to a programmable thermostatic bath ((0.01 °C). The vessel was agitated using a magnetic stirrer. The vessel was equipped with an immersed probe (LiquiSonic 30) developed by SensoTech GmbH, Magdeburg, Germany. This technique enables detection of the change of ultrasonic velocity ((0.01 m/s) and temperature ((0.01 °C) of the solution. For the solubility measurements, known amounts of oxalic and water were weighed using a balance with an accuracy of ((0.00001 g) and added to the vessel and kept at a temperature about 3 °C lower than the equilibrium temperature to keep a certain observable amount of undissolved crystals. The mixture was agitated at 350 rpm. The temperature was then raised slowly (0.5 °C/h), and the temperature at which the last crystal disappears was observed optically and considered as the equilibrium temperature. The nucleation temperature was determined using the ultrasonic methods described by Omar and Ulrich3-5 and Benecke et al.6 The variation of the ultrasonic velocity and temperature during the cooling of the saturated solution with a constant cooling rate was analyzed to find exactly the nucleation temperature. As the nucleation starts, a change in the relation between the ultrasonic velocity data and the temperature occurs during the cooling. A typical measurement of the nucleation temperature of a solution saturated at 313.25 K and cooled with a rate of 25 K/h is shown in Figure 1. The onset of nucleation is taken as the point at which the linear relation between the ultrasonic velocity and temperature starts to change during the cooling of the supersaturated solution as presented in Figure 1.
Results and Discussion Solubility. The solid-liquid equilibrium of the oxalic acidwater system over the temperature range from 284.19 to 352.02
10.1021/cg060112n CCC: $33.50 © 2006 American Chemical Society Published on Web 07/06/2006
1928 Crystal Growth & Design, Vol. 6, No. 8, 2006
Omar and Ulrich
Figure 3. Fitting of the experimental solubility data to eq 2. Figure 1. The measured change of ultrasonic velocity with temperature during the cooling of a saturated oxalic solution. (Equilibrium temperature 313.25 K; solubility in mole fraction 0.04138019, cooling rate 25 K/h).
Figure 2. Plots of the experimental solubility in mole fraction of oxalic acid in water versus the absolute temperature. Table 1. Measured Solubility Expressed in Mole Fraction of Oxalic Acid in Water over the Temperature Range 284.19-352.02 K xeq
T/K
xeq
T/K
0.01184860 0.01863151 0.02816142 0.04138019
284.19 294.75 303.75 313.25
0.05485156 0.08133083 0.10821429 0.14432559
320.75 332.88 342.23 352.02
experimental solubility data by implementing the following basic thermodynamic relationship:
ln xeq )
K is determined experimentally. The oxalic acid in equilibrium with the saturated solution is a dihydrate crystals of monoclinic prism shape.1 The measured values of the equilibrium concentration (solubility) expressed in mole fraction of oxalic acid in water (xeq) versus the absolute temperature (T) are listed in Table 1 and depicted in Figure 2. An interesting aspect observed in Figure 2 is that the solubility in mole fraction increases exponentially with the absolute temperature. On the basis of the solubility data obtained in this work, the dependency of the solubility in mole fraction on the absolute temperature can be satisfactorily described, within the temperature range studied, by the following exponential equation:
xeq ) AeBT
Figure 4. DSC analysis of oxalic acid dihydrate crystals for a 13.060 mg sample with a heating rate of 3 K/min.
(1)
where A and B are the solubility parameters. The values of A and B obtained from the exponential regression of the solubility data are 4 × 10-7 and 0.0368 K-1, respectively. The correlation coefficient (R-squared) is 0.9927. The values of the relative standard deviation (σ) and the absolute average deviations (∆) between the data calculated using eq 1 and the measured solubility data are 0.1005 and 5.41 × 10-3, respectively. Enthalpy of Dissolution. The enthalpy of dissolution (∆dissH) for the oxalic acid-water system can be determined from the
-∆dissH +C RT
(2)
where C is a constant. Thus, fitting the solubility data of oxalic acid dihydrate (monoclinic prism shape) in water to eq 2 (ln xeq against 1/T) will result in a straight line approximation, as shown in Figure 3. The enthalpy of dissolution (∆dissH) can then be calculated from the slope. As shown in Figure 2, the experimental solubility data fit very well a straight line with a correlation coefficient (R-squared) equal to 0.9993 and a standard error of 0.025. The value of the slope determined by implementing the least-squares method is calculated to be -3704.7 with the standard error equal to 40.65. Consequently, the enthalpy of dissolution is determined to be 30.80 kJ mol-1. Enthalpy of Fusion. The enthalpy of fusion (∆fusH) is determined experimentally by differential scanning calorimetry (DSC) using the equipment NETZSCH-DSC 204. The DSC analysis of a crystalline sample of oxalic acid dihydrate (monoclinic prism shape) is shown in Figure 4. The first peak at 378.35 K represents a phase transformation from dihydrate to anhydrous crystals (rhombic bipyramid shape).1 The onset of the second peak of Figure 4 at 465.26 K is considered as the melting temperature of anhydrous oxalic acid. The amount of enthalpy of fusion estimated using the measured DSC data is 58.158 kJ mol-1 with an accuracy of (0.04 kJ mol-1. Figure 4 shows, however, that partial decomposition takes place before the acid melts.
Oxalic Acid-Water System
Crystal Growth & Design, Vol. 6, No. 8, 2006 1929 Table 2. Nucleation Kinetic Parameters Evaluated by Fitting the Experimental Data of Figure 5 to Equation 5 and the Corresponding Regression Statistics
Figure 5. Cooling rate against the measured width of metastable zone for oxalic acid-water solutions at the different equilibrium temperatures: ([) Teq ) 294.75 K, (9) Teq ) 303.75 K, (2) Teq) 313.25 K, (×) Teq ) 320.25 K.
Enthalpy of Mixing. The enthalpy of mixing (∆mixH) is an important thermodynamic quantity, which reflects the degree of the interaction of the solvent and solute molecules. It has a significant meaning in describing many crystallization aspects such as relative growth rate of the different phases (i.e., morphology), growth kinetics, and nucleation kinetics. The degree of solvent solute interaction has an impact on the solidliquid interfacial energy, which is an important physical property affecting growth and nucleation processes as discussed by Walton,7 Davey,8 Ohara and Reid,9 and Mersmann.10 The enthalpy of mixing (∆mixH) for nonideal systems is related to the enthalpy of dissolution (∆dissH) and enthalpy of fusion (∆fusH) by the following thermodynamic relation:
∆dissH ) ∆mixH + ∆fusH
(3)
The temperature range of the values in eq 3 must be the same as the temperature range over which the enthalpy of dissolution (∆dissH) is determined by implementing the experimental solubility data within the range from 284.19 to 352.02 K. Using the ∆fusH and ∆dissH values measured in this work, the enthalpy of mixing (∆mixH) of the oxalic acid-water system can be calculated to be -27.358 kJ mol-1. Such large enthalpy of mixing indicates strong solute-solvent interactions. Metastable Zone Width. The width of the metastable zone at different cooling rates is measured to determine the kinetic parameters of the nucleation rate in the oxalic acid-water system. The measurement is based on cooling the saturated solution with a constant cooling rate (d) until homogeneous nucleation takes place at the upper limit of the metastable zone. In the experiments, all measures have be taken such that only homogeneous nucleation is considered, and heterogeneous nucleation will not take place. The solution was filtered to ensure that no nondissolved foreign solid particles exist. The jacketed vessel and the corresponding equipment were washed carefully with filtered deionized water, and the experiments were carried out in the absence of seed crystals. The difference between the saturation or equilibrium temperature (Teq) and the nucleation temperature (Tn) is taken as the metastable zone width (∆Tmax) or the maximum allowable supercooling. Plots of the measured metastable zone width against the cooling rate at different saturation temperatures are presented in Figure 5. The presented results show that the metastable zone increases remarkably with an increase in the cooling rate at all the equilibrium temperatures studied. Also, the width of the metastable zone increases with a decrease in
Teq/K
kN/(#/m2‚min)
n
R-squared
standard error
294.75 303.75 313.25 320.75
0.0084 0.0115 0.0180 0.0628
3.2419 3.5048 3.4199 2.8292
0.93854 0.94501 0.80829 0.75966
0.11212 0.10605 0.19802 0.22171
the saturation temperature. In this work, the data shown in Figure 5 are analyzed by implementing the nucleation model devised by Nyvlt.11 This model relies on the fact that the rate of nucleation (Bn), which is described by the power relationship (eq 4), can be approximated as the rate of supersaturation at the metastable limit. Consequently, the cooling rate (d) is related to the maximum allowable supercooling (∆Tmax) by eq 5.
Bn ) kN∆Cn
(4)
d ) kN(∆Tmax)n
(5)
where kN and n are the nucleation rate constant and the nucleation order, respectively. The nucleation rate constant (kn) is strongly temperature dependent and depends on many other parameters such as fluid dynamics, the presence of additives, and type of solvent. The nucleation rate order (n) reflects the role of supersaturation and the mechanism of nucleation. The experimental measurements of the metastable zone width can be satisfactorily fitted to eq 5 as can be viewed by the solid lines in Figure 5. The values of the nucleation rate constant and the nucleation order are evaluated by the logarithmic straight-line regression analysis of the data points presented in Figure 5. The results of the regression analysis at the different equilibrium temperatures studied are listed in Table 2. There is an obvious increase in the value of the nucleation rate constant with an increase in the equilibrium temperature, whereas the order of nucleation is slightly influenced by the equilibrium temperature. It is sometimes very useful for the practical crystallizer design, control, or operation to have a correlation by which the metastable zone width (∆Tmax) can be calculated as a function of the cooling rate (d) and equilibrium temperature (Teq). It was found that the best formula, which fits the experimental data shown in Figure 4, has the form:
∆Tmax ) kdgTheq where k, g, and h are constants with their values, obtained by the multiple linear regression analysis of the logarithmic form of eq 6, are 7.2206 × 1015 K1-g-h ming, 0.266 and -6.17, respectively. Figure 6 shows the degree by which eq 6 can be used to determine the metastable zone width compared to the real experimental measurements. The relative standard deviation and the average absolute deviation between the calculated from eq 6 and the measured experimentally are 0.0758 and 0.1155, respectively. Effect of H2SO4 on the Metastable Zone. The metastable boundaries, i.e., nucleation and saturation temperatures are significantly influenced by the addition of small amounts of additives. In this work, the effect of the presence of traces of sulfuric acid in a saturated oxalic acid solution with its equilibrium temperature chosen to be 313.65 K was investigated. The variation of the equilibrium and nucleation temperatures due to the addition of sulfuric acid is shown in Figure 7.
1930 Crystal Growth & Design, Vol. 6, No. 8, 2006
Figure 6. The calculated values of the width of the metastable zone by eq 6 versus the measured values.
Omar and Ulrich
crystallization or recrystallization of oxalic acid from water can be carried out with high separation efficiency by cooling. The determined enthalpy of dissolution of oxalic acid in water is relatively high, indicating strong solvent solute interactions. The width of the metastable zone of oxalic acid in water is rather small compared with other organic substances, which means difficulties in controlling the crystal size distribution due to unavoidable nucleation. Therefore, successful seeded crystallization will require control of the supersaturation within the metastable region by applying the appropriate cooling profile, which maintains optimum levels of supersaturations to achieve the crystal growth in the absence of nucleation. The values of nucleation rate constant are very high compared to other organic materials. This means higher homogeneous nucleation rates or smaller values of solid liquid interfacial energy. The increased width of the metastable zone due to the addition of small amounts of sulfuric acid is of importance in controlling the metastability. Acknowledgment. The authors gratefully acknowledge the financial support from the Deutsche Forschungsgemeinschaft (DFG). References
Figure 7. The effect of the presence of sulfuric acid on the nucleation and equilibrium temperatures of a saturated aqueous oxalic acid solution.
As shown in Figure 7, the equilibrium temperature fluctuates around its value of the pure solution, and the variation due to the addition of sulfuric acid is very slight and can be neglected. However, the nucleation temperature is significantly influenced by the addition of sulfuric acid. The maximum width of the metastable zone is measured at a concentration of sulfuric acid of 2.3 × 10-9 g/g of solution. The same phenomenon was observed by Sargurt and Ulrich.12 They measured both suppression or enlargement effects on the width of the metastable zone of both substances potassium alum and potassium chloride depending on the impurity concentration. Such an increase of the width of the metastable zone using additives is of great interest for the design and operation of industrial crystallization. A wider metastable zone facilitates a better control of nucleation and thus the crystal size distribution of the product. Conclusions Data on solid liquid equilibrium and the nucleation parameters of oxalic acid-water system were measured. Also, the measurements of the effect of the presence of small amounts of sulfuric acid on the width of the metastable zone were obtained. The exponential increase in solubility with temperature means that
(1) Katz, E. W.; Hoyer, F. E. Purification of Organic Acids by Recrystallization. In Proceedings of the International Symposium on Industrial Crystallization ISIC ’98, Tianjin, China, September 2125, 1998; pp 277-281. (2) Mullin, J. W. Crystallization, 3rd ed.; Butterworth-Heineman: Oxford, U.K., 1993. (3) Omar, W.; Ulrich, J. Application of Ultrasonics in the Control of Crystallization Processes. In CGOM 4; Ulrich, J., Ed.; Verlag Shaker: Aachen, 1997; pp 294-301. (4) Omar, W.; Ulrich, J. Ultrasonics for in situ Measurement of Supersaturation, Growth Kinetics, Solubility and Metastability. In Proceedings of the International Symposium on Industrial Crystallization ISIC ‘98, Tianjin, China, September 21-25, 1998; pp 322326. (5) Omar, W.; Ulrich, J. Ultrasonic methods for the control and study of batch crystallization processes. In Proceedings of the 14th International Symposium on Industrial Crystallization, Cambridge, UK, September 12-16, 1999; Institution of Chemical Engineers: Rugby, UK, 1999. (6) Benecke, I.; Bay, K.; Ulrich, J. Determination of the metastable zone width and control of batch crystallizers by ultrasonic technique. In Proceedings of the 15th International Symposium on Industrial Crystallization, Sorrento, Italy, September 15-18, 2002; Chianese, A., Ed.; AIDIC Servizi S.r.l: Milan, Italy, 2002. (7) Walton, A. G. Nucleation in Liquids and Solutions. In Nucleation; Zettlemoyer, A. C., Ed.; Marcel Dekker: New York, 1969; pp 225327. (8) Davey, R. J. Solvent effects in crystallization processes. In Current Topics in Materials Science; Kaldis, E., Ed.; North-Holland Publishing Company: Amsterdam, 1982; Vol. 8, pp 429-479. (9) Ohara, M.; Reid, R. C. Modeling Crystal Growth Rates from Solution; Prentice Hall: Englewood Cliffs, NJ, 1973. (10) Mersmann, A. Crystallization Technology Handbook; Marcel Decker Inc.: New York, 1995. (11) Nyvlt, J. Kinetics of nucleation in solutions. J. Cryst. Growth 1968, 3/4, 377-383. (12) Titiz-Sargut, S.; Ulrich, J. Influence of additives on the width of the metastable zone. Cryst. Growth Des. 2002, 2, 371-374.
CG060112N
