Article pubs.acs.org/jced
Phase Diagram of HCOOK−(NH2)2CO−H2O System Alexander V. Dzuban,† Alexey L. Voskov,‡ and Irina A. Uspenskaya*,‡ †
Department of Materials Science and ‡Chemistry Department, Lomonosov Moscow State University, 119991 Moscow, Russia ABSTRACT: The temperature and enthalpy of fusion and of the solid-state phase transition in HCOOK were determined by a differential scanning calorimetry (DSC) method. The thermodynamic assessment of the potassium formate−urea−water ternary system and of two binary subsystems was made. The Redlich−Kister model was applied for the description of binary liquids. The Gibbs energy of ternary liquid was assessed by the Muggianu and Bonnier-Toop methods; both methods gave similar results. The thermodynamic properties of potassium formate hydrate were estimated from the liquidus data. The liquidus surface, isothermal and polythermal sections of the phase diagram were calculated. It was shown that the results of calculation correlated with DSC measurements of ternary mixtures.
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INTRODUCTION Aircraft surfaces have to be deiced for flight safety reasons. Urea ((NH2)2CO) and potassium formate (HCOOK) are the most widely used freezing point depressants in airfield pavement deicers. They are applied in large quantities at a number of airports, taxiways, and roadways. The advantages of these substances are their lower toxicities and the ability to biodegrade; so the risk of groundwater contamination is decreased. Urea is also a common fertilizer which enhances plant growth. Potassium formate is more environmentally benign (the organic part acts as carbon source for growth of fungi and bacteria in soil and will therefore decompose) and is also used as a fertilizer too. Therefore, the treatment with solutions in the ternary system HCOOK−(NH2)2CO−H2O can be used both for melting and removing thin ice and as liquid fertilizers providing nitrogen and potassium; that is, those solutions are a double-action reagents. The ternary phase diagram is necessary for optimization of the composition of these solutions. The urea−water binary subsystem is the most investigated in this ternary system. Its review, critical assessment and thermodynamic modeling were performed by Voskov et al.1 The liquid−solid equilibria in the potassium formate−water system were reported by Souchay,2 Groschuff,3 Sidgwick and Gentle,4 Melinder,5 and Smotrov and Cherkasov6 (the most recent and complete investigation). Beyer and Steiger7 measured vapor pressures of HCOOK−H2O mixtures. There is only one study of the liquidus in potassium formate-urea system by Vitali et al.8 To the best of our knowledge, there are no experimental or theoretical investigations of the ternary system. The aim of this work is the thermodynamic assessment of the HCOOK−(NH2)2CO−H2O ternary system based on the existing experimental data about the binary subsystems. Phase diagrams were calculated by the convex hull method using the TernAPI software.9,10 Polythermal sections were also calculated © 2013 American Chemical Society
and visualized. The system was also studied experimentally by DSC to determine the temperature and heats of phase transitions in HCOOK and to verify the results of calculations.
2. THERMODYNAMIC MODELS The investigated ternary system has one liquid phase and one binary stoichiometric compound HCOOK·1.5H2O (I). No ternary compounds, solid solutions or miscibility gaps in liquid have been reported. The model for the liquid phase was written with respect to pure liquid components, urea, potassium formate, and water. This allowed us to avoid such cumbersome expressions as the Pitzer−Simonson equation or electrolyte modified local composition. As was shown by Olaya,11 the inclusion of the Debye−Hückel term has a small affect on the solubility of electrolyte, but it should be taken into account for the correct description of the mean-ionic activity or osmotic coefficient. Model of Liquid. The liquid phase was described using the Redlich−Kister12 formalism. The Gibbs energy of binary liquids can be written as Δmix G(T , x) = − TS id(x) + Δmix Gex (x) = RT[(1 − x) ln(1 − x) + x ln x] n
+ x(1 − x) ∑ ai(1 − 2x)i , i=0
ai = ai0 + ai1T + ai2T −2 + ai3T ln T + ...
(1)
where ai is an adjustable parameter. The assessments carried out in the present study required not more than four Redlich− Kister parameters aij to obtain a satisfactory description of Received: March 17, 2013 Accepted: July 30, 2013 Published: August 23, 2013 2440
dx.doi.org/10.1021/je400255c | J. Chem. Eng. Data 2013, 58, 2440−2448
Journal of Chemical & Engineering Data
Article
phase equilibria. In this case the Gibbs energy of liquid is as follows:
Δtr G = Δtr H(1 − T /Ttr)
The values of Redlich−Kister parameters (aij) were estimated from experimental liquidus data using the phase equilibrium condition. The estimation was carried out by a nonlinear leastsquares method. The minimized target function was
Δmix G(T , x) = RT[(1 − x) ln(1 − x) + x ln x] + x(1 − x)(a00 + (a10 + a11T )(1 − 2x) + a 21T (1 − 2x)2 )
(2)
⎡
The Gibbs energy of melting of a pure component was estimated as
σ=
⎣
⎤ ⎛ T exp − T calc ⎞2 + ⎜⎜ i exp i ⎟⎟ (ωi(T ))2 ⎥ ⎥ Ti ⎝ ⎠ ⎦
= Δm H(Tm) + Δm Cp(T − Tm) ⎛ Δ H(Tm) T ⎞ − T⎜ m + Δm Cp ln ⎟ Tm Tm ⎠ ⎝
(xiexp,Tiexp)
(3)
In this equation we assume that ΔmCp = constant due to a narrow temperature interval of investigation and scarcity of available data. The thermodynamic parameters for all components of the binary systems that are required for the eq 3 are listed in Table 1. These are the temperature and
Δmix Gex =
Table 1. Thermodynamic Properties of Potassium Formate, Urea, and Water Required for eq 3a potassium formate urea water
ΔmH(Tm)/J·mol−1
Tm/K
11638 ± 200
441.85 ± 0.5
14644 ± 500 6010 ± 4
405.85 ± 0.5 273.16 ± 0.01
(5)
(xicalc,Ticalc)
where and are experimental and calculated coordinates of liquidus ith point, and ω(x) and ω(T) i i are the corresponding statistical weights. In all systems, eutectic and peritectic points were assigned greater weights ω(x,T) = 10 i compared to ω(x,T) = 1 for other points. i The binary parameters were applied for the predictions of ternary solutions properties. The ideal part of the Gibbs energy was represented as a configuration term. The excess Gibbs energy was obtained with the use of either the symmetrical Muggianu (eq 6 and 7) or asymmetrical Bonnier-Toop (eq 8) expression for the excess Gibbs energy:16−18
⎛ = (Δm H(Tm) − TmΔm Cp) + T ⎜Δm Cp(1 + ln Tm) ⎝ Δm H(Tm) ⎞ ⎟ − Δm CpT ln T Tm ⎠
∑ ⎢⎢(xiexp − xicalc)2 (ωi(x))2 i
Δ m G = Δ m H (T ) − T Δ m S (T )
−
(4)
ΔmCp/J·mol−1K−1
33.95 ± 8 38.21 ± 0.05
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)
(6)
n
Δmix Gex =
a Notation: ΔmH(Tm), enthalpy of melting at melting temperature; Tm, melting temperature; ΔmCp, change of heat capacity during melting.
∏ xixj ∑ ak(i ,j)(xi − xj)k i
