Experimental apparatus

The solubility of urea was measured using an equilibrium cell similar to that reported in the literature ^{10,11,12,13,14}. The solubility of urea was determined in a temperature range from 278.2 to 333.2K at atmospheric pressure (92654.3Pa), in pure ethanol and mixtures of water and ethanol with ethanol mole fractions of 0.0901, 0.2096 and 0.3757, in a previously prepared solution using analytical balance (Gehaka, AY-220± 0.0001g). A jacketed borosilicate glass cell with capacity of

40.0mL and with sampling points at the side was used in this work. Urea was added in excess to the solution, which was stirred for two hours using a magnetic stirrer (Marconi, MA-089).

Subsequently, the system was left decanting for two hours, keeping the temperature control of the cell through a thermostatic bath (Marconi, MA-184). A thermocouple (Full-Gauge, TIC-17RGTi ± 0.1K), which was calibrated using an Incoterm standard thermometer (± 0.1K), was used to measure the temperature inside the cell. The experimental apparatus can be seen in Figure 1.

Figure 1 The experimental apparatus: (A) Equilibrium cell; (B) Magnetic stirrer; (C) Latex hose; (D) Thermocouple; (E) Thermostatic bath. 

For each temperature, four samples were drawn using a glass syringe (10mL, Artiglass) to check the reproducibility of the procedure. The samples were quantified by gravimetric analysis, remaining 48h in a stove (Medicate, MD-1.3) at 338.2K.

After the drying period, the samples containing crystallized urea was placed in a desiccator with silica for 30min, then the molar fraction of dry urea was quantified to determinate the value of solubility. Four solubility values ( ^_xexp ) were determined for each temperature. Afterwards, the average of those four measurements was computed. Equation 1 was used to calculate the mole fraction solubility ¹⁰:

where ^{_{m1, m2}} and ^_m3 represent the mass of the solute (urea), solvent (water, ethanol) and ethanol only, respectively. M ₁, M ₂ and M ₃ are the respective molecular weights.

Experimental data

Table 1 contains solubility data experimentally obtained for the urea in a mixture of ethanol and water with ethanol mole fraction of 0.0901; 0.2096 and 0.3757 and in pure ethanol. This table also reports standard deviations (δ) of the value of solubility for each temperature and shows data available in the Lee and Lahti’s ¹³ work for urea in ethanol and water mixtures in compositions of 0.1242 and 0.3095 (mole fraction) and in pure ethanol. These results were used for comparison and validation of the data found on this paper.

Table 1 Experimental solubility of urea in ethanol-water mixtures and in pure ethanol at different temperatures along with the solubility of urea in Lee and Lahti ¹³. 

It is noticeable that the solubility of urea in a mixture of ethanol and water increases with increasing temperature and decreases with increasing ethanol concentration to the mixture. The fact that the solubility decreases with decreasing temperature at low pressures is attributed to the reduction in density ¹⁹. Figure 2 shows the decrease in solubility of urea with increasing mole fraction of ethanol in the solution.

We can also observe that the standard deviation was low in all cases (about 4.7%). Figure 3 shows solubility data for urea in mixture of ethanol and water obtained in this study, along with the data of Lee and Lahti ¹³. Comparing the data obtained in this study with the data provided by literature, the results were consistent.

Figure 2 Solubility of urea (in mole fraction) in all temperaturas 

Figure 3 Solubility of urea: (○), 20.2% ethanol; (●), 26.64% ethanol (Lee and Lahti); (◊), 40.4% ethanol; (♦),53.36% ethanol (Lee and Lahti); (□), 60.6% ethanol; (+), 100% ethanol; (▲), 100% ethanol (Lee and Lahti). 

Adjustments of solubility

Literature ^{(13, 20, 21, 22)} reports several equations or models to correlate solubility data. In this paper, we can cite the useful correlations proposed by Lee and Lahti ¹³, Yaws et al.²⁰, Buchowski et al.²². The solubility of urea in mixture of solvents was correlated by Eqs. (2), (3) and (4).

where ^_xc1 represents the solubility calculated using the Lee and Lahti equation; A and B represent the parameters of the equation and T represents the temperature measured in Kelvin.

where ^_xc2 represents the solubility calculated using the Yaws equation; A’, B’ and C’ represent the parameters of the equation and T represents the temperature measured in Kelvin.

where x _c3 is the solubility of urea calculated using the Buschowski equation; λ and h are the model parameters, T and ^_Tm are the experimental and the standard melting point of urea in Kelvin, respectively.

The correlations of experimental data and data calculated using the thermodynamic models obtained from the relative deviation (RD) expressed by Equation 5 are listed in Table 2. The parameters of models obtained from linear and nonlinear regressions and their values are listed in Tables 3−4. The relative average deviation (RAD) and the corresponding root mean square deviation (RMSD) along with the R² as expressed by eqs 5, 6, 7 are shown in Tables 3−5.

Table 2 shows the experimental and calculated results of solubility for urea in ethanol+water and in pure ethanol using the Equations 2 - 4. It is important to comment that to calculate the values in Table 2 it was follow the same experimental temperatures showed in Table 1.

According to the above-mentioned correlations of experimental data obtained at different temperatures in various mixtures of ethanol and water and in pure ethanol together with the calculated data (Tables 2−5), it was indicated that the solubility of urea calculated from the studied models showed good agreement. Taking the solubility data in the selected solvents fitted by the Yaws et al. model as an illustration, the relative average deviations are 0.01%, 0.06%, 0.16%, and 0.62%, respectively; which indicate that the modified Yaws et al. equation is suitable for correlating the solubility data of urea in the mixtures of ethanol and water and in pure ethanol. The same conclusion can be drawn after analyzing the solubility data and the parameters that fitted by the Lee and Lahti equation and the Buchowski λh equation.

However, we can see that the RAD values of Lee and Lahti equation, the Yaws et al. equation and the Buchowski−Ksiazaczak λh equation are 4.84%, 0.86%, and 0.97%.

This result indicates that the Yaws et al. model proved to be more accurate and suitable for the description of dissolution of urea in the studied solvents at various temperatures.

Figure 4 shows the solubility of urea in a mixture of ethanol and water and in pure ethanol correlated with Equation (3). Analyzing Figure 4, it can be noted that the equation proposed by Yaws et al. (Equation 3) correlates the solubility of urea data well.

Table 2 Experimental and calculated (Eq. 2 - 4) solubility of urea in pure ethanol and ethanol+water mixtures. 

Table 3 Parameters of the Lee and Lahti model for Urea in pure ethanol and ethanol+water mixtures 

Table 4 Parameters of the Yaws model for Urea in pure ethanol and ethanol+water mixtures. 

Figure 4 Mole fraction solubility of urea: (○), 20.2% ethanol; (□), 40.4% ethanol; (◊), 60.6% ethanol; (▲), 100% ethanol; (-) correlated data with Equation (3) 

Table 5 Parameters of the Bucchowski λh model for Urea in pure ethanol and ethanol+water mixtures.