CRYSTAL

GROWTH
Solid Liquid Equilibrium, Metastable Zone, and Nucleation & DESIGN
Parameters of the Oxalic Acid-Water System
2006
Waid Omar† and Joachim Ulrich*,‡ VOL. 6, NO. 8
Tafila Technical UniVersity, Department of Natural Resources and Chemical Engineering, 1927-1930
P.O. Box 179, 66110-Tafila, Jordan, and Martin-Luther-UniVersität Halle-Wittenberg,
FB Ingenieurwissenschaften, Institut für 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.
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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
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zone was measured due to the presence of sulfuric acid at a concentration of 2.3 × 10-9 g/g of solution.

Introduction of the oxalic acid-water system, little data are available in the
literature on the metastable zone and the nucleation parameters.
Oxalic acid is a simple dibasic organic acid, which has several In this contribution, solubility, metastable zone, and nucleation
industrial applications. It is used as a rust and scale remover, parameters for the oxalic acid-water system were obtained
as a bleaching agent, as an electrolyte in the anodic oxidation experimentally by an ultrasonic technique over a wide range of
of aluminum, and in the manufacture of several miscellaneous temperatures at different cooling rates.
chemical derivatives.1 The synthesized solid oxalic acid, which
comes from different industrial processes, does not meet the Experimental Section
market requirements concerning quality and purity. However,
further seeded recrystallization steps are used in a selected The materials used for preparing all aqueous oxalic acid solutions
solvent to improve the product specifications. One of the most were distilled water and oxalic acid dihydrate (C2H2O4‚2H2O) crystals
of analytical grade (p.a.) manufactured by Merck, Germany. The
important quantities that is determined in the recrystallization solubility and the width of the metastable zone were measured in a 0.5
step is the crystal size distribution (CSD) of the product. L closed and jacketed glass vessel connected to a programmable
Controlling the CSD is an important aspect for the production thermostatic bath ((0.01 °C). The vessel was agitated using a magnetic
of a high-quality product and for determining the efficiency of stirrer. The vessel was equipped with an immersed probe (LiquiSonic
the downstream processes. Marketing and meeting of customer 30) developed by SensoTech GmbH, Magdeburg, Germany. This
acceptance require a product of large crystals that are uniform technique enables detection of the change of ultrasonic velocity ((0.01
m/s) and temperature ((0.01 °C) of the solution.
in size, strong, nonagglomerated, and noncaking in the package. For the solubility measurements, known amounts of oxalic and water
In industrial crystallization processes, the required product were weighed using a balance with an accuracy of ((0.00001 g) and
specifications are achieved by allowing seed crystals to grow added to the vessel and kept at a temperature about 3 °C lower than
in a supersaturated solution. Supersaturated solutions exhibit a the equilibrium temperature to keep a certain observable amount of
metastable zone in which nucleation is slow or unlikely to occur. undissolved crystals. The mixture was agitated at 350 rpm. The
The width of the metastable zone is the region between the temperature was then raised slowly (0.5 °C/h), and the temperature at
which the last crystal disappears was observed optically and considered
solubility (saturation) line and the supersaturation (metastable) as the equilibrium temperature.
limit, beyond which spontaneous nucleation takes place. All The nucleation temperature was determined using the ultrasonic
industrial crystallization processes take place in the metastable methods described by Omar and Ulrich3-5 and Benecke et al.6 The
zone. Therefore, design and operation of any industrial cooling variation of the ultrasonic velocity and temperature during the cooling
crystallizer under controlled CSD require the knowledge of the of the saturated solution with a constant cooling rate was analyzed to
solubility, the metastable zone width, and the nucleation find exactly the nucleation temperature. As the nucleation starts, a
change in the relation between the ultrasonic velocity data and the
parameters. The quantitative determination of the width of the temperature occurs during the cooling. A typical measurement of the
metastable zone and the nucleation rate as a function of the nucleation temperature of a solution saturated at 313.25 K and cooled
cooling rate and temperature are important in terms of control- with a rate of 25 K/h is shown in Figure 1. The onset of nucleation is
ling the supersaturation level at an optimum level to achieve taken as the point at which the linear relation between the ultrasonic
the required CSD and quality of the final product.2 In the case velocity and temperature starts to change during the cooling of the
supersaturated solution as presented in Figure 1.
* 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@ Results and Discussion
iw.uni-halle.de.
† Tafila Technical University. Solubility. The solid-liquid equilibrium of the oxalic acid-
‡ Martin-Luther-Universität Halle-Wittenberg. water 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 tem-
perature 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. Figure 4. DSC analysis of oxalic acid dihydrate crystals for a 13.060
mg sample with a heating rate of 3 K/min.
Table 1. Measured Solubility Expressed in Mole Fraction of Oxalic
Acid in Water over the Temperature Range 284.19-352.02 K experimental solubility data by implementing the following basic
xeq T/K xeq T/K thermodynamic relationship:
0.01184860 284.19 0.05485156 320.75
0.01863151 294.75 0.08133083 332.88
-∆dissH
0.02816142 303.75 0.10821429 342.23
ln xeq ) +C (2)
RT
0.04138019 313.25 0.14432559 352.02
K is determined experimentally. The oxalic acid in equilibrium where C is a constant. Thus, fitting the solubility data of oxalic
with the saturated solution is a dihydrate crystals of monoclinic acid dihydrate (monoclinic prism shape) in water to eq 2 (ln
prism shape.1 The measured values of the equilibrium concen- xeq against 1/T) will result in a straight line approximation, as
tration (solubility) expressed in mole fraction of oxalic acid in shown in Figure 3. The enthalpy of dissolution (∆dissH) can
water (xeq) versus the absolute temperature (T) are listed in Table then be calculated from the slope. As shown in Figure 2, the
1 and depicted in Figure 2. An interesting aspect observed in experimental solubility data fit very well a straight line with a
Figure 2 is that the solubility in mole fraction increases correlation coefficient (R-squared) equal to 0.9993 and a
exponentially with the absolute temperature. standard error of 0.025. The value of the slope determined by
On the basis of the solubility data obtained in this work, the implementing the least-squares method is calculated to be
dependency of the solubility in mole fraction on the absolute -3704.7 with the standard error equal to 40.65. Consequently,
temperature can be satisfactorily described, within the temper- the enthalpy of dissolution is determined to be 30.80 kJ mol-1.
ature range studied, by the following exponential equation: Enthalpy of Fusion. The enthalpy of fusion (∆fusH) is
determined experimentally by differential scanning calorimetry
xeq ) AeBT (1) (DSC) using the equipment NETZSCH-DSC 204. The DSC
analysis of a crystalline sample of oxalic acid dihydrate
where A and B are the solubility parameters. The values of A (monoclinic prism shape) is shown in Figure 4. The first peak
and B obtained from the exponential regression of the solubility at 378.35 K represents a phase transformation from dihydrate
data are 4 × 10-7 and 0.0368 K-1, respectively. The correlation to anhydrous crystals (rhombic bipyramid shape).1 The onset
coefficient (R-squared) is 0.9927. The values of the relative of the second peak of Figure 4 at 465.26 K is considered as the
standard deviation (σ) and the absolute average deviations (∆) melting temperature of anhydrous oxalic acid. The amount of
between the data calculated using eq 1 and the measured enthalpy of fusion estimated using the measured DSC data is
solubility data are 0.1005 and 5.41 × 10-3, respectively. 58.158 kJ mol-1 with an accuracy of (0.04 kJ mol-1. Figure 4
Enthalpy of Dissolution. The enthalpy of dissolution (∆dissH) shows, however, that partial decomposition takes place before
for the oxalic acid-water system can be determined from the 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
Teq/K kN/(#/m2‚min) n R-squared standard error
294.75 0.0084 3.2419 0.93854 0.11212
303.75 0.0115 3.5048 0.94501 0.10605
313.25 0.0180 3.4199 0.80829 0.19802
320.75 0.0628 2.8292 0.75966 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
Figure 5. Cooling rate against the measured width of metastable zone to the maximum allowable supercooling (∆Tmax) by eq 5.
for oxalic acid-water solutions at the different equilibrium tempera-
tures: ([) Teq ) 294.75 K, (9) Teq ) 303.75 K, (2) Teq) 313.25 K,
(×) Teq ) 320.25 K. Bn ) kN∆Cn (4)

Enthalpy of Mixing. The enthalpy of mixing (∆mixH) is an d ) kN(∆Tmax)n (5)

important thermodynamic quantity, which reflects the degree
of the interaction of the solvent and solute molecules. It has a where kN and n are the nucleation rate constant and the
significant meaning in describing many crystallization aspects nucleation order, respectively. The nucleation rate constant (kn)
such as relative growth rate of the different phases (i.e., is strongly temperature dependent and depends on many other
morphology), growth kinetics, and nucleation kinetics. The parameters such as fluid dynamics, the presence of additives,
degree of solvent solute interaction has an impact on the solid- and type of solvent. The nucleation rate order (n) reflects the
liquid interfacial energy, which is an important physical property role of supersaturation and the mechanism of nucleation. The
affecting growth and nucleation processes as discussed by experimental measurements of the metastable zone width can
Walton,7 Davey,8 Ohara and Reid,9 and Mersmann.10 The be satisfactorily fitted to eq 5 as can be viewed by the solid
enthalpy of mixing (∆mixH) for nonideal systems is related to lines in Figure 5. The values of the nucleation rate constant
the enthalpy of dissolution (∆dissH) and enthalpy of fusion and the nucleation order are evaluated by the logarithmic
(∆fusH) by the following thermodynamic relation: straight-line regression analysis of the data points presented in
Figure 5. The results of the regression analysis at the different
∆dissH ) ∆mixH + ∆fusH (3) equilibrium temperatures studied are listed in Table 2. There is
an obvious increase in the value of the nucleation rate constant
The temperature range of the values in eq 3 must be the same with an increase in the equilibrium temperature, whereas the
as the temperature range over which the enthalpy of dissolution order of nucleation is slightly influenced by the equilibrium
(∆dissH) is determined by implementing the experimental temperature.
solubility data within the range from 284.19 to 352.02 K. Using It is sometimes very useful for the practical crystallizer design,
the ∆fusH and ∆dissH values measured in this work, the enthalpy control, or operation to have a correlation by which the
of mixing (∆mixH) of the oxalic acid-water system can be metastable zone width (∆Tmax) can be calculated as a function
calculated to be -27.358 kJ mol-1. Such large enthalpy of of the cooling rate (d) and equilibrium temperature (Teq). It was
mixing indicates strong solute-solvent interactions. found that the best formula, which fits the experimental data
Metastable Zone Width. The width of the metastable zone shown in Figure 4, has the form:
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 ∆Tmax ) kdgTheq
solution with a constant cooling rate (d) until homogeneous
nucleation takes place at the upper limit of the metastable zone. where k, g, and h are constants with their values, obtained by
In the experiments, all measures have be taken such that only the multiple linear regression analysis of the logarithmic form
homogeneous nucleation is considered, and heterogeneous of eq 6, are 7.2206 × 1015 K1-g-h ming, 0.266 and -6.17,
nucleation will not take place. The solution was filtered to ensure respectively. Figure 6 shows the degree by which eq 6 can be
that no nondissolved foreign solid particles exist. The jacketed used to determine the metastable zone width compared to the
vessel and the corresponding equipment were washed carefully real experimental measurements. The relative standard deviation
with filtered deionized water, and the experiments were carried and the average absolute deviation between the calculated from
out in the absence of seed crystals. eq 6 and the measured experimentally are 0.0758 and 0.1155,
The difference between the saturation or equilibrium tem- respectively.
perature (Teq) and the nucleation temperature (Tn) is taken as Effect of H2SO4 on the Metastable Zone. The metastable
the metastable zone width (∆Tmax) or the maximum allowable boundaries, i.e., nucleation and saturation temperatures are
supercooling. Plots of the measured metastable zone width significantly influenced by the addition of small amounts of
against the cooling rate at different saturation temperatures are additives. In this work, the effect of the presence of traces of
presented in Figure 5. The presented results show that the sulfuric acid in a saturated oxalic acid solution with its
metastable zone increases remarkably with an increase in the equilibrium temperature chosen to be 313.65 K was investigated.
cooling rate at all the equilibrium temperatures studied. Also, The variation of the equilibrium and nucleation temperatures
the width of the metastable zone increases with a decrease in due to the addition of sulfuric acid is shown in Figure 7.
1930 Crystal Growth & Design, Vol. 6, No. 8, 2006 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 crystal-
lization 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
Figure 6. The calculated values of the width of the metastable zone width of the metastable zone due to the addition of small
by eq 6 versus the measured values.
amounts of sulfuric acid is of importance in controlling the
metastability.
Acknowledgment. The authors gratefully acknowledge the
financial support from the Deutsche Forschungsgemeinschaft
(DFG).

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exponential increase in solubility with temperature means that CG060112N