Article pubs.acs.org/jced
Phase Equilibria in the Urea−Biuret−Water System Alexey L. Voskov,† Tatyana S. Babkina,† Alexander V. Kuznetsov,‡ and Irina A. Uspenskaya*,† †
Chemistry Department, Lomonosov Moscow State University, 119991 Moscow, Russia Department of Materials Science, Lomonosov Moscow State University, 119991 Moscow, Russia
‡
ABSTRACT: A thermodynamic assessment of the urea−biuret−water ternary system and its binary subsystems has been made. The Margules model has been applied for the description of excess Gibbs energies of binary solutions, and the properties of ternary solutions have been assessed by using the Muggiani method. Thermodynamic properties of (NH2CO)2NH·(NH2)2CO (I) and (NH2CO)2NH·0.7H2O (II) have been estimated from the condition of equilibrium between the solution and stochiometric phases. The liquidus surface and isothermal sections of the phase diagram of the urea−biuret−water system at the temperature interval T = (268 to 373) K have been calculated. The comparison of calculated and experimental data is discussed.
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INTRODUCTION Urea is one of the most important and demanded nitrogen fertilizers. It manufactured by means of the Bazarov reaction, that is, interaction between carbon dioxide and ammonia at high pressures and temperatures. One of the possible byproducts is biuret, and its formation depends on the conditions of the process. This substance has a negative effect on plant growth, and the upper limit of its fraction in the final product should not be larger than 3 wt %. A knowledge of the liquidus in the urea−biuret−water ternary system is of practical interest, but there are no systematic studies of phase equilibria in this system. The water−urea system is the most investigated of the three binary subsystems, and the solubility of (NH2)2CO was measured by Speyers,1 Pinck and Kelly,2 Janecke,3 Shnidman and Sunier,4 Chadwell and Politi,5 Kakinuma,6 Frejacques,7 Miller and Dittmar,8 and Babkina and Kuznetsov9 using different methods. Phase diagrams of biuret−water and biuret−urea systems were published in the articles of Rollet et al.10,11 and Babkina and Kuznetsov.9 Isothermal sections of the ternary phase diagram are shown in the monography of Kucheriavij and Lebedev.12 In the work of Barone et al.13 the enthalpy of dilution of urea and biuret aqueous solutions as well as the enthalpy of mixing biuret and urea water solutions by the flow microcalorimetry method at T = 298 K was investigated. Infinitely diluted water solutions of components were used as their standard states. It was shown that obtained data can be adequately described by using one term in the excess Gibbs energy of solution; that is, the solutions are “regular”. The aim of this work is the thermodynamic assessment of the (NH2)2CO−(NH2CO)2NH−H2O ternary system based on the existing experimental data and calculation of isothermal sections of the ternary phase diagram. The convex hull methods have been implemented in two packages PhDi and TernAPI; the latter one was used in the present study for the calculation of phase diagrams.14,15 © 2012 American Chemical Society
THERMODYNAMIC MODELS OF PHASES IN BINARY AND TERNARY SYSTEMS
There are liquid solutions and stoichiometric solid phases in the biuret−urea−water ternary system. All components are insoluble in the solid state. Only two compounds, (NH2CO)2NH·(NH2)2CO (I) and (NH2CO)2NH·0.7H2O (II), are present in the binary subsystems, and no information about ternary solid phases have been reported. Model of Liquid. The liquid phase was described using the Margules−Muggiani formalism. The Gibbs energy of an A−B binary solution was approximated by the Margules equation: Δmix G(T , x) = −TS id(x) + Δmix Gex (x) = RT ((1 − x)ln(1 − x) + x ln x) + x(1 − x)[(1 − x)ABA + xAAB]
(1)
The corresponding expressions for the chemical potentials of components A and B are: μAl = μA° ,l + RT ln(1 − x) + x 2[AAB + 2(ABA − AAB) (1 − x)]
(2)
μBl = μB° ,l + RT ln x + (1 − x)2 [ABA + 2(AAB − ABA )x] (3)
where μ°i is the Gibbs energy of pure liquid i; that is, the symmetric system was chosen to represent the thermodynamic functions of melts. The Gibbs energies of melting were estimated using eq 4: ,l
Received: July 25, 2012 Accepted: August 30, 2012 Published: September 26, 2012 3225
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Cpbiuret,l(Tm)
Δ m G ( T ) = Δ m H (T ) − T Δ m S (T )
Cpbiuret,s(Tm)
= Δm H(Tm) + Δm Cp(T − Tm) ⎛ Δ H(Tm) T ⎞ − T⎜ m + Δm Cp ln ⎟ Tm Tm ⎠ ⎝
− Δm CpT ln T
ΔmH(Tm)
Tm
ΔmCp
component
J·mol−1
K
J·mol−1·K−1
urea biuret water
14644 ± 500 26100 ± 500 6010 ± 4
405.85 ± 0.5 473.8 ± 0.4 273.16 ± 0.01
33.95 ± 8a 55.98 ± 13a 38.21 ± 0.05
(8)
3
Δmix G = RT ∑ xi ln xi + Δmix Gex
(9)
i=1
Table 1. Thermodynamic Properties of Components (Urea, Biuret, and Water) That Are Required for eq 4
Δmix Gex =
4x 2x3 ex [Δmix G23 ]x2′ (2x 2 + x1)(2x3 + x1) 4x1x3 ex + [Δmix G13 ]x1′ (2x1 + x 2)(2x3 + x 2) 4x1x 2 ex + [Δmix G12 ]x1″ (2x1 + x3)(2x 2 + x3)
(10)
where numbers 1, 2, and 3 correspond to the urea, biuret, and water; x2′ = x2 + x1/2, x1′ = x1 + x2/2, x1″ = x1 + x3/2. The values of ΔmixGex ij in square brackets were calculated by eq 1 with the corresponding set of parameters AAB and ABA for each subsystem. No ternary parameters were used for the liquid phase. Stoichiometric Phases. Both stoichiometric phases, (NH2CO)2NH·(NH2)2CO and (NH2CO)2NH·0.7H2O, melt incongruently at (389.8 and 384.1) K, respectively.9 There are no experimentally obtained values of thermodynamic properties of phases I and II except for the heat of solution of biuret hydrate.23 Therefore, the Gibbs energies of these binary compounds at various temperatures were estimated by using the tangent line method24 (see Figure 1). Consider a binary solid compound in equilibrium with liquid. According to the tangent line method, the Gibbs energy of the reaction
Estimated in this work.
In this work the values Tm and ΔmH(Tm) for urea and biuret recommended in ref 9 were used. They were obtained as the mean of the most reliable literature data. The values of Tm, ΔmH(Tm), and ΔmCp for water were taken from ref 16. The experimental heat capacity of solid urea17−19 in the temperature interval (240 to 400) K was described by the truncated equation of Berman and Brown20 (Cp = a + bT−0.5, where b < 0): Cpurea,s(T ) = (253.65 ± 4) − (2763.3 ± 67)T −0.5 J· mol−1·K−1 (5)
(1 − x s)A(liquid) + x s B(liquid) = A1 − xBx (solid)
The heat capacity of liquid urea near the melting point was taken from ref 18 as the average of seven experimental points. = (150.43 ± 7) J·mol ·K
Cpurea,s(Tm)
The model parameters AAB and ABA in eq 1 were evaluated using MATLAB software, based on the experimental liquidus data available in the literature. The Muggiani method22 was used to obtain the Gibbs energy of the ternary liquid from the Gibbs energies of binary liquids:
In this equation it was assumed that the ΔmCp = const. This assumption is reasonable due to a relatively narrow temperature range under investigation. Three constant parameters for each component are required in this case: the temperature of fusion, Tm, enthalpy of fusion at Tm, ΔmH(Tm), and change of heat capacity during melting, ΔmCp. Their values for biuret, urea, and water are listed in Table 1.
−1
Cpbiuret,s(Tm)
⎛ C urea,l ⎞ p = Cpbiuret,s(Tm)⎜⎜ urea,s − 1⎟⎟ ⎝ Cp ⎠ (4)
−1
Cpurea,s(Tm)
= Δm Cpurea
⎛ Δ H(Tm) ⎞ + T ⎜Δm Cp(1 + ln Tm) − m ⎟ Tm ⎝ ⎠
Cpliq(Tm)
Cpurea,l(Tm)
⇔ Δm Cpbiuret
= (Δm H(Tm) − Δm CpTm)
a
=
(11)
which corresponds to formation of a binary solid compound from pure liquid components and can be expressed as
(6)
Δf G(T ) = Δmix G(T )|x = x l + (x s − x l)
Equation 7 from ref 21 for the calculation of the heat capacity of solid biuret over the temperature interval from (240 to 450) K has been used:
= μ1liq (x l , T ) + x s
Cp(T ) = (27.04 ± 1) + (0.3483 ± 0.0030)T J·mol−1·K−1
∂Δmix G(T ) ∂x
∂Δmix G(T ) ∂x
x = xl
x=xl
(12)
∂Δmix G(T ) = RT (ln x − ln(1 − x)) + (1 − 2x) ∂x
(7)
The difference between the heat capacity of liquid and solid biuret was estimated assuming equality of the relative heat capacity change during melting for biuret and urea:
((1 − x)ABA + AAB) + x(1 − x) (AAB − ABA ) 3226
(13)
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of data points and the values of the target function are listed in Table 2. Table 2. Some Statistic Characteristics of Thermodynamic Models of Melts in the Binary System with Urea, Biuret, and Water (N is the Number of Points, σ is a Value of Target Function) system
N
σ
urea−biuret water−biuret water−urea
17 4 80
1.3·10−3 9.6·10−5 3.0·10−2
2. Values of ΔfH298 and ΔfS298 for the binary stoichiometric compounds were obtained by the minimization of the target function: ⎛ T calc − T exp ⎞2 ⎛ T calc − T exp ⎞2 per per eut eut 2 2 ⎟ ωper ⎟⎟ ωeut + ⎜⎜ σ = ⎜⎜ exp exp ⎟ Teut T ⎝ ⎠ per ⎝ ⎠
Figure 1. Tangent line connecting Gibbs energies of coexisting liquid and solid phases in the water−biuret system at T = 380 K. The curve is the Gibbs energy of liquid; the solid line is a tangent line, and symbols and dashed lines indicate values of variables (the molar fraction of biuret and Gibbs energy) of coexisting liquid (l) and stoichiometric (s) phases. l
+
i
where x and x are the compositions of the liquid and solid phases, respectively. The values of ΔfG(T) calculated at various temperatures can be fitted to obtain ΔfH298 and ΔfS298 assuming that the enthalpy and entropy of reaction 11 are independent of temperature. (14)
To calculate Gibbs energy formation from pure solid components the Gibbs energy of melting of pure substances are necessary: Δf G°(T ) = Δf G(T ) + (1 − x s)Δm GA (T ) + x sΔm G B(T )
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(17)
where superscripts calc and exp correspond to calculated is calculated and experimental values, respectively, ΔfGcalc i from eqs 12 and 13, and ΔfGfit i values are obtained from the eq 14. Teut and Tper are the eutectic and peritectic temperatures. In the case of the urea−biuret system, ωeut = 1 and ωper = 2.5, and in the system water−biuret, ωper = 0. In all cases, ωGi = 1. Thermodynamic functions defined this way are essentially fictitious values because they are obtained by solving mathematically incorrect inverse task of thermodynamics (an inverse task is a reconstruction of thermodynamic properties from equilibria only, this task has non single decision unlike a direct task, where the equilibrium condition is calculated on the basis of known thermodynamic properties of coexisting phases). In ref 25 it was shown that it is possible to reproduce conditions of phase equilibria by means of these values with high accuracy, but the probability of “guessing” real value of thermodynamic property is low. To find the confidence intervals of the model parameters, the Jacobian
s
Δf G(T ) = Δf H298 − T Δf S298
⎛ Δ G fit − Δ G calc ⎞2 f i f i ⎟⎟ (ωiG)2 calc Δf Gi ⎝ ⎠
∑ ⎜⎜
(15)
OPTIMIZATION OF MODEL PARAMETERS The parameters of the Margules model for the liquid phase and the ΔfH298 and ΔfS298 values for each binary compound were obtained by a nonlinear least-squares method, using experimental data on phase equilibria. The optimization was carried out in two steps: 1. The model parameters for the liquid phase were obtained from the liquidus in the binary systems by minimization of the following (target function): ⎡ ⎛ T exp − T calc ⎞2 exp calc 2 (x) 2 ⎢ σ = ∑ (xi − xi ) (ωi ) + ⎜⎜ i exp i ⎟⎟ ⎢ Ti ⎝ ⎠ i ⎣ ⎤ (T ) 2 ⎥ (ωi ) ⎥ ⎦ (16) exp exp calc calc where (xi ,Ti ) and (xi ,Ti ) are experimental and calculated coordinates of the ith liquidus point, and ω(T) are the corresponding respectively, and ω(x) i i statistical weights. In the water−biuret and urea−biuret binary systems, ω(x) = 1 and ω(T) = 0. For the water− i i (x) urea system, ωi = 1 and ω(T) = 0 for ordinary liquidus i (T) points but for the eutectic, ω(x) = 20. The number i = ωi
⎛ ∂F ⎞ Jij = ⎜⎜ i ⎟⎟ ⎝ ∂θj ⎠θ = θ m
(18)
0, m
was calculated. Here, 1 ≤ i ≤ n, 1 ≤ j ≤ m, n is the total number of experimental points, m is the number of parameters to be estimated (i.e., nonlinear regression coefficients) Fi(θ1, ..., θp) is the i-th component of the vector function F (it is a difference between predicted and experimental values), θj denotes model parameters, and θ0,m stands for optimized model parameters. Target functions (eq 16 and 17) can be represented as: σ=
∑ Fi2
(19)
i T
−1
We calculated the covariance matrix C = (J J) , which diagonal elements Cjj were used to calculate the confidence intervals of model parameters as 3227
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Δf G(0.5[(NH 2CO)2 NH ·(NH 2)2 CO])
(20)
= −(23.509 ± 10) ·103 + (53.416 ± 30)T J·mol−1·K−1
where t0.05,v is the Student test value for v = n − m degrees of freedom and a 95 % probability and s2R is the residual variance.
(21)
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Δf G°(0.5[(NH 2CO)2 NH ·(NH 2)2 CO])
RESULTS AND DISCUSSION Binary Systems. The first study of the phase diagram of the urea−biuret was reported by Rollet et al.10 The components were mixed in various ratios over the whole composition range and studied by the thermal analysis method. During the experiments, an interesting phenomenon was observed: first melting curves at random had a plateau at (379.1 or 384.1) K, and heating conditions did not affect its position contrary unlike to the second round of melting. Slow cooling of melts resulted in a plateau at 384.1 K, while rapid cooling produced a plateau at 379.1 K. The authors attributed these observations to the removal of ammonia at temperatures above 400 K, which would result in increasing the biuret content in the system. However, we believe that the true reason for this phenomenon is the formation of a stable or metastable eutectic depending on the cooling and heating conditions. If to kinetic restrictions the stoichiometric phase with equimolar ratio of components is not formed, the metastable eutectic is observed at 379.1 K. If there is enough time to form the compound, the stable eutectic point is detected at 384.1 K. As can be seen from Figure 2, our
= −(5.852 ± 10) ·103 + (14.214 ± 30)T J·mol−1·K−1 (22)
Phase equilibria were calculated assuming negligible mutual solubility of solid components and so-called regular interparticle interactions in the liquid phase. Parameters of eq 1 for the urea−biuret subsystem are listed in Table 3. The results of Table 3. Parameters ABA and AAB of the Liquid Model Given by eq 1 for the Binary Subsystems of the Urea(1)− Biuret(2)−Water(3) Ternary System subsystem
ABA/J·mol−1
AAB/J·mol−1
(1)−(2) (2)−(3) (3)−(1)
−(372 ± 169) (466 ± 198) (648 ± 63)
−(372 ± 169) (466 ± 198) −(390 ± 196)
Rollet et al.10 at temperatures higher than 420 K were not used for the determination of these parameters due to possible decomposition of biuret during the experiments. The thermal stability of biuret and the influence of the heating rate on the melting point of (NH2CO)2NH were discussed in detail earlier.9 Invariant points of the urea−biuret phase diagram are given in Table 4. As can be seen from Figure 2, a good Table 4. Calculated Coordinates of Invariant Points in the Urea(1)−Biuret(2)−Water(3) Ternary Systema
Figure 2. Phase diagram of the (NH2)2CO−(NH2CO)2NH binary system. Solid lines indicate the calculated diagram, dashed lines the metastable eutectic equilibria, and symbols the experimental data: ○, Rollet et al.;10 ▽, Babkina and Kuznetsov.9
special point
T/K
x2
x3
(1)−(2) eutectic (1)−(2) peritectic (1)−(2) eutectic (no compounds)b (2)−(3) eutectic (2)−(3) peritectic (1)−(3) eutectic (1)−(2)−(3) eutectic (1)−(2)−(3) eutectic (no compounds)b (1)−(2)−(3) peritecticc
384.0 390.3 379.6
0.2095 0.2937 0.2469
0.0000 0.0000 0.0000
273.1 384.4 260.6 260.6 259.1
0.0009 0.2300 0.0000 0.0004 0.0170
0.9991 0.7700 0.8763 0.8760 0.8616
363.4
0.1723
0.4268
a
Standard uncertainties u are: u(T) = 0.1 K and u(x) = 0.0001. These uncertainties are not deviations of calculated values from the experiment. bMetastable equilibria without binary compounds. c Coexistence of liquid phase, solid biuret, and binary compounds I and II.
agreement was obtained between the calculated lines and the experimental points. This is to be expected, since most of the experimental data were used for the assessment of model parameters. The phase diagram of the water−biuret system was studied in ref 11 at normal and elevated pressures. The equilibrium phase boundaries were obtained by thermal analysis (analysis of heating and cooling curves) and by determination of the solubility limits, using visual observation of the disappearance of the solid phases. A good agreement between the results obtained by different methods was reported by Rollet and Cohen-Adad.11 The solubility of biuret in water at 273 K is
calculations substantiated this hypothesis (see Figure 2). The solid lines in Figure 2 correspond to the stable phase diagram while the dashed show metastable phase equilibria, symbols illustrate experimental data. Thermodynamic functions of the stoichiometric phase (NH2CO)2NH·(NH2)2CO were estimated as described in previous sections. The composition of this phase reported in the work of Babkina and Kuznetsov9 was accepted in the present study. The temperature dependence of the Gibbs energy of formation from liquid (eq 21) or from solid components (eq 22) can be expressed as 3228
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negligible and increases rapidly with increasing temperature, reaching 1.2 wt %, 7.0 wt %, and 20.0 wt % at (298, 323, and 348) K, respectively. At the normal boiling point of the saturated solution (378.2 K), the content of biuret is equal to 53.5 wt %. At atmospheric pressure crystalline monohydrate of biuret is in the equilibrium with the liquid phase. Some refinements of the phase diagram and the composition of the crystal hydrate were reported earlier.9 The correct formula of the hydrate was determined to be C2N3O2H5·(0.70 ± 0.05)H2O. A good description of the phase boundaries in the binary water−biuret system was obtained with a single parameter AAB = ABA in eq 1 (see the second line in Table 3). The estimated temperature dependence of the Gibbs energy of formation from liquid components (eq 23) and from liquid water and solid biuret (eq 24) may be expressed as ⎛ 1 ⎞ Δf G⎜ [(NH 2CO)2 NH· 0.7H 2O]⎟ ⎝ 1.7 ⎠
Figure 3. Phase diagram of the H2O−(NH2CO)2NH binary system. Solid lines indicate the calculated diagram, symbols the experimental data: ○, Rollet and Cohen-Adad;11 ▽, Babkina and Kuznetsov.9
= −(24.273 ± 2) ·103 + (55.515 ± 5)T J·mol−1·K−1 (23)
⎛ 1 ⎞ Δf G◦⎜ [(NH 2CO)2 NH· 0.7H 2O]⎟ ⎝ 1.7 ⎠ = −(13.682 ± 2) ·103 + (34.932 ± 5)T J·mol−1·K−1 (24)
Experimental values of the heat released during dissolution of solid biuret and hydrate of biuret in water were published in ref 23. The recalculation of the measured heat effects to the enthalpy of the reaction (NH 2CO)2 NH(s) + 0.7H 2O(l) = (NH 2CO)2 NH ·0.7H 2O(s)
(25)
demonstrates reasonable agreement between the experimental and the calculated results. Since the thermochemical data were not taken into account in the estimation of the hydrate properties, this result confirms the correctness of the proposed thermodynamic models of phases in the water−biuret system. Invariant points of the water−biuret phase diagram are given in Table 4. The phase diagram of the water−biuret system is presented in Figure 3. Invariant points of the water−biuret phase diagram are given in Table 4. The phase diagram of the urea−water system was studied repeatedly.1−9 The experimental data are in good agreement, so they were used with equal statistic weight to obtain model parameters for the liquid phase. Most authors agree that liquid in this system is close to ideal. This was disputed in the work of Shnidman and Sunier,4 but later investigations8 confirmed that solutions containing more than 60 mol % urea demonstrate ideal behavior. Our attempts to reproduce the solubility of urea with Gex = 0 resulted in a satisfactory description of the liquidus curve over a wide range of compositions but too low eutectic temperature. Because the eutectic is determined by thermal analysis with a relatively small error, we used a more complex two-parametric Margules model for the calculation of phase equilibria in the urea−water system. The values of AAB and ABA are listed in the last line of Table 3. The phase diagram is presented in Figure 4, and the invariant points are given in Table 4.
Figure 4. Phase diagram of the H2O−(NH2)2CO binary system. Solid lines indicate the calculated diagram, symbols the experimental data: ○, Speyers et al.;1 ◀, Pinck and Kelly;2 □, Janecke;3 ▽, Miller and Dittmar;8 △, Chadwell and Politi;5 ◁, Shnidman and Sunier;4 ▷, Kakinuma;6 *, Babkina and Kuznetsov.9
Ternary Urea−Biuret−Water System. The liquidus surface of the ternary system was calculated with TernAPI software.15 As an example, the result of the calculation without taking into account the binary stoichiometric phases is presented in Figure 5. In this case one ternary and three binary eutectics are realized in the urea−biuret−water system. If both binary compounds I and II are taken into consideration, three additional peritectics appear. Coordinates of all invariant points in the ternary system are given in Table 4. The calculated isothermal sections are shown in Figures 6, 7, and 8. The sections in Figure 6 illustrate the origin of phase equilibria in the temperature interval from −5 °C (268.15 K) to 80 °C (353.15 K). Both stoichiometric phases, I and II, were taken into consideration in the calculation, so these diagrams show stable phase equilibria in the urea−biuret−water system. These results can be used for the optimization of the urea and biuret mutual purification procedure. 3229
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the ternary system. It is a well-known fact that metastable phases may precipitate first during fast cooling. Due to crystallization of the binary compounds I or II, the liquid phase field is constricted, so an excess mutual solubility may be observed under rapid cooling. To the best of our knowledge, there is only one experimental study of the ternary phase diagram.26 These results as cited in ref 12 are superimposed on the calculated phase diagram shown in Figure 8. The agreement is fair, taking into account that no details of the experiment are given in ref 12. The composition of biuret hydrate equimolar in ref 12 should be noted, whereas the ratio accepted in the present work is (NH2CO)2NH:H2O = 1:0.7. Additional experimental investigations of the liquid composition in equilibrium with biuret hydrate and urea would be useful.
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CONCLUSIONS In this work thermodynamic models of the liquid and solid phases in the urea−biuret−water system were proposed. The model parameters were optimized based on the available experimental phase diagrams. It was shown that simple regular (or subregular) solution models can be used for adequate description of the phase equilibria in the binary subsystems. Contrary to assumptions of some authors, the ideal solution
Figure 5. Liquidus surface of the ternary urea−biuret−water phase diagram calculated without taking into account the binary compounds.
The second group of sections shown in Figure 7 illustrates the variation of phase boundaries at 100 °C (373.15 K) if one or both binary compounds do not crystallize, for example, due to kinetic restrictions. These metastable equilibria are very important for the understanding of crystallization processes in
Figure 6. Calculated isothermal sections of the urea−biuret−water phase diagram: (a) 268.15 K, (b) 298.15 K, (c) 323.15 K, (d) 353.15 K. (I) (NH2CO)2NH·(NH2)2CO and (II) (NH2CO)2NH·0.7H2O. 3230
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Figure 7. Calculated isothermal sections of the urea−biuret−water phase diagram at 373.15 K: (a) without any binary compounds, (b) one compound, I, in the biuret−urea system, (c) with only biuret hydrate, II, taking into account (d) assuming that both binary compounds I and II are present.
Figure 8. Isothermal sections of the urea−biuret−water system: (a) 298.15 K, (b) 323.15 K. Dashed lines with circles correspond to the result of ref 12. Compositions are in weight percent.
model is not suitable for the simulation of the eutectic point in the water−urea system. The enthalpy and entropy of the urea−biuret binary compound and of biuret hydrate were estimated using the solubility data. An experimental confirmation of the proposed thermodynamic properties is desirable. The estimated enthalpy of biuret hydrate is in reasonable agreement with the
calorimetric data that were not used for the optimization of model parameters. The Gibbs energy of ternary liquid was extrapolated from the binary subsystems using the Muggiani formalism. The liquidus surface and isothermal sections of the urea−biuret−water stable and metastable phase diagram were calculated. According to our calculations, the solubility of biuret hydrate in water in the 3231
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(21) Kozyro, A. A.; Frenkel, M. L.; Krasulin, A. P.; Simirsky, V.; Kabo, G. Y. Thermodynamic properties of variuos phase of biuret. Russ. J. Phys. Chem. 1988, 42, 1752−1756. (22) Muggiani, J.-M.; Gambino, M.; Bros, J.-P. Enthalpies de formation des alliages liquides bismuth−etain−gallium a 723 K. Choix d’une representation analytique des grandeurs d’exces integrales et partieles de mélange. J. Chim. Phys. 1975, 72, 83−88. (23) Babkina, T. S.; Kuznetsov, A. V.; Miroshnichenko, E. A.; Paschenko, L. L. Book of Abstracts, XXV-th Int. Chugaev Conference of Coordination Chemistry, Suzdal, Russia, June 6−11, 2011. (24) Baker, L. E.; Pierce, A. C.; Luks, K. D. Gibbs energy analysis of phase equilbria. Soc. Pet. Eng. AIME J. 1982, 731−742. (25) Voronin, G. F.; Pentin, I. V. Decomposition of Solid Solutions of Cadmium, Mercury and Zinc Tellurides. Russ. J. Phys. Chem. A 2005, 79, 1572−1578. (26) Babkina, T. S.; Kuznetsov, A. V.; Miroshnichenko, E. A.; Paschenko, L. L. Thermochemical properties of biuret hydrate. Abs. XXVth Int. Chugaev Conference of Coordination Chemistry, Suzdal, Russia, June 6−11, 2011.
presence of urea is smaller than it was proposed earlier; this result should be confirmed experimentally.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Funding
The investigations were financially supported by RFBR (Grant No. 11-03-00499-a and 12-03-31069-mol-a) and the URALCHEM OJSC. Notes
The authors declare no competing financial interest.
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REFERENCES
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