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Thermodynamic investigation of the orthophosphoric acid—N,N-dimethylformamide system
Journal of Molecular Liquids 121 (2005) 53 – 57 www.elsevier.com/locate/molliq
Thermodynamic investigation of the orthophosphoric acid—N,N-dimethylformamide system L.P. Safonova*, Y.A. Fadeeva, L.E. Shmukler, A.N. Kinchin Institute of Solution Chemistry of RAS, 1 Akademicheskaya st., 153045 Ivanovo, Russia Ivanovo State University of Chemistry and Technology, 7 Engels av., 153000 Ivanovo, Russia Available online 27 September 2004
Abstract The solution and mixing enthalpies of phosphoric acid (H3PO4)–N,N-dimethylformamide (DMF) system over the whole concentration range were measured at a temperature of 25 8C. Conclusions about complex-formation in the system under investigation were drawn. The standard solution enthalpy of phosphoric acid in DMF was calculated. D 2004 Elsevier B.V. All rights reserved. Keywords: Phosphoric acid; N,N-dimethylformamide; Solution enthalpy; Dissociation constant
1. Introduction Phosphoric acid solutions in aprotic solvents are of great interest in the studies on proton transfer and the nature of acid–base interactions. Moreover, these systems have a broad potential as solutions for the treatment of cellulose materials and the development of polymeric electrolytes. The importance of phosphate systems caused extensive studies on the thermodynamic properties of nonaqueous phosphoric acid solutions. At present, no works have been done on the thermodynamic equilibrium properties of phosphoric acid solutions in organic solvents. As is generally known, the thermodynamic properties of liquid mixtures are sensitive to various association equilibria. The binary systems, in which one or both components form hydrogen bonds, are of special interest in calorimetry. The heat of mixing of two components is the measure of their molecular interactions. The sign and magnitude of the mixing enthalpy of two liquids depends upon the relative strengths of the interactions between
* Corresponding author. Institute of Solution Chemistry of RAS, 1 Akademicheskaya st., 153045 Ivanovo, Russia. E-mail address: [email protected] (L.P. Safonova). 0167-7322/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.molliq.2004.08.026
similar molecules which are present in pure liquids (homotactic interactions) and the interactions between different molecules (heterotactic interactions) which result from the mixing process [1]. For this reason, the mixing enthalpy may be considered as resulting from two different effects: a chemical effect due to breaking hydrogen bonds and a physical effect due to the interactions between the species in solution, with the chemical effect being usually dominant. The purpose of the present work was to investigate the H3PO4–DMF system by means of calorimetric technique and to discuss the character of interactions in the system in question.
2. Materials and methods A total of 100 wt.% phosphoric acid was prepared from 85 wt.% phosphoric acid (Russia, best quality). An excess of P2O5 reagent was dissolved in 85 wt.% acid at 145 8C. The concentration of the resulting solution was determined by potentiometric titration with KOH and by the density of concentrated phosphoric acid solution measurements [2] and was estimated to be above 100 wt.% of H3PO4. Then, the solution obtained was diluted with distilled water to form 100 wt.% phosphoric acid. All the solutions were held
54
L.P. Safonova et al. / Journal of Molecular Liquids 121 (2005) 53–57
Table 1 Mixing enthalpy of phosphoric acid with DMF x(H3PO4)
DmixH, kJ/mol
x(H3PO4)
DmixH, kJ/mol
0.000500 0.00120 0.00140 0.00160 0.00240 0.00280 0.00390 0.00410 0.00440 0.00520 0.00600 0.00630 0.00680 0.00680 0.00730 0.00750 0.00840 0.00850 0.00860 0.00980 0.0100 0.0110 0.0120 0.0130 0.0210 0.0280 0.0380
0.01200 0.02640 0.04200 0.04260 0.06310 0.08780 0.1132 0.1494 0.1418 0.1625 0.1995 0.2379 0.2318 0.2183 0.248 0.2864 0.2892 0.3226 0.3018 0.3477 0.3872 0.4281 0.4824 0.4942 0.8242 1.131 1.521
0.0470 0.0940 0.1040 0.155 0.163 0.171 0.303 0.306 0.309 0.466 0.473 0.476 0.500 0.515 0.601 0.841 0.868 0.928 0.932 0.940 0.955 0.968 0.973 0.975 0.983 0.993 0.997
1.894 3.913 4.326 6.407 6.743 7.086 12.07 12.16 12.25 16.59 16.66 16.72 16.96 16.94 17.20 8.889 7.444 3.978 3.667 3.222 2.667 1.484 1.250 1.184 0.8173 0.3692 0.1634
overnight at 100 8C to ensure equilibria distribution of the phosphate species. N,N-dimethylformamide (Russia, pure) was dried with CaO and molecular sieves and distilled. The content of water in DMF did not exceed 0.02 wt.%. The solutions of phosphoric acid in DMF were prepared gravimetrically. The mixing and solution enthalpies were measured with a hermetic isoperibol-type calorimeter [3]. A massive
copper block inside a Dewar vessel was used as a thermostatic jacket. A resistance thermometer and heater are situated inside the block to control the temperature. The temperature in the thermostating jacket was kept constant to within F0.001 K. The experimental procedure has been reported earlier [4]. The accuracy of measurements of the heat effects was of F1%.
3. Discussion The experimental data show the significant exothermic effect of mixing of phosphoric acid with N,N-dimethylformamide (Table 1). Earlier, it was found that the mixing enthalpy of N,N-dimethylformamide with a nonelectrolyte can be either positive or negative depending on the nonelectrolyte nature, but that the absolute value of the heat effect did not exceed 5 kJ/mol [1,5–7]. The absolute values of mixing enthalpies for the system under investigation are several times as much as that for the mixtures of DMF with nonelectrolytes (Fig. 1). The great values of mixing enthalpies of H3PO4 with DMF show that the interactions between H3PO4 and DMF molecules are more stronger than those of pure phosphoric acid and N,Ndimethylformamide. Shmakov et al. [8] have investigated the process of mixing of phosphoric acid with different organic solvents. The value of mixing enthalpy of H3PO with DMF (1:1) was determined: DmixH=15 kJ/mol. Tsvetkov et al. [9] have shown that the high negative values of mixing enthalpies of inorganic acids with organic solvents are connected with the process of complexformation. The earlier investigations of dynamic viscosity of the H3PO4–DMF system as a function of the concentration [10] have shown the presence of a significant maximum of the examined function. The appearance of this maximum seems
Fig. 1. Concentration dependence of mixing enthalpy of DMF with nonelectrolytes at 25 8C.
L.P. Safonova et al. / Journal of Molecular Liquids 121 (2005) 53–57
to be connected with the formation of complexes of H3PO4/ DMF=2:1 type. The IR-Fourier-spectroscopic investigation confirmed the conclusion on the complex-formation in the system [11]. This fact explains the shift of the extremum in the concentration dependence of mixing enthalpy of phosphoric acid with DMF to higher acid concentrations (Fig. 2). The experimental data on mixing enthalpies of H3PO4 with DMF are satisfactorily described by the Redlich– Kister equation (Eq. (1)) over the investigated concentration range: H E ¼ x2 ð1 x2 Þ
n1 X
n1 ð1 2x2 Þi
ð1Þ
i¼0
where: x 2—mole fraction of phosphoric acid; n i —fitting coefficients: n 0=67.84F0.10, n 1=20.68F0.70, n 2=22.02F 0.40, and n 3=16.71F1.20. To understand the state of H3PO4 in DMF, the dissolution enthalpy measurements were carried out. The experimental data on solution enthalpy of phosphoric acid in DMF are presented in Table 2. The data show that the effect of dissolution of H3PO4 in DMF is highly exothermic in the range of the acid mole fraction up to x=0.1. Within the range of the H3PO4 mole fraction higher than 0.1 the heat effect decreases slowly (Fig. 3). Such a shape of the DsolH m function is typical for weak electrolytes. This conclusion is confirmed by the results of conductometric investigations of the H3PO4–DMF system [10]. The standard solution enthalpy can be determined by extrapolation of concentration dependence of the experimental solution enthalpy data to infinitely diluted solution. The type of extrapolation equation depends on the chemical equilibria being in solutions and on the choice of the theoretical model for its description.
Fig. 2. Concentration dependence of mix enthalpy of H3PO4–DMF system at 25 8C.
55
Table 2 The solution enthalpy of phosphoric acid in N,N-dimethylformamide x(H3PO4)
DsolH, kJ/mol
x(H3PO4)
DsolH, kJ/mol
0.000504 0.000707 0.00118 0.00144 0.00162 0.00243 0.00286 0.00400 0.00399 0.00446 0.00508 0.00530 0.00608 0.00671 0.00683 0.00689 0.00689 0.00735 0.00849 0.00862 0.00988 0.0100 0.0108 0.0114
25.29 24.36 23.08 27.31 26.31 25.99 30.74 28.34 30.66 31.81 31.86 30.70 32.84 33.66 33.95 33.17 31.71 33.77 34.06 35.01 35.20 35.46 35.92 36.37
0.0117 0.0129 0.0129 0.0136 0.0215 0.0216 0.0288 0.0381 0.0470 0.0940 0.0941 0.104 0.155 0.163 0.172 0.303 0.306 0.308 0.309 0.466 0.473 0.476 0.500 0.515
36.56 36.70 37.31 36.48 38.41 38.17 39.23 39.88 40.26 41.47 41.59 41.54 41.42 41.37 41.32 39.77 39.73 39.69 39.69 35.61 35.23 35.12 33.88 32.91
In our earlier work [12], we have used, for calculation of standard solution enthalpy, the extrapolation equation based on the second approximation of the Debye–Hqckel theory, in which the first stage of the phosphoric acid dissociation was taken into account: n 1 v Ds H ¼ Ds H 0 þ a jzþ z jAH I 1=2 1 þ BaI 1=2 2 o 1 r BaI 1=2 ð2Þ þ bI þ ð1 aÞDass H 0 3 However, the later investigations of molar conductivity of phosphoric acid in DMF at low acid concentrations
Fig. 3. Concentration dependence of solution enthalpy of H3PO4 in DMF at 25 8C.
56
L.P. Safonova et al. / Journal of Molecular Liquids 121 (2005) 53–57
and the method of comparative calculation have shown that the magnitude range of the dissociation constant of the acid was K=106H108. At such poor dissociation of the acid in DMF, the use of the mentioned model is not proper. The authors of Refs. [13,14] have found that, in 100 wt.% phosphoric acid, the most part of molecules form dimers. The IR-Fourier-spectroscopic investigation has shown the presence of phosphoric acid dimers in DMF even at low acid concentration [11]. Therefore, for the description of the concentration dependence of phosphoric acid solution enthalpy in DMF, we used the equation taking into account the molecular dimerization of the acid: a Dsol H ¼ Dsol H 0 þ adm þ Ddimer H 0 2
ters were calculated at the condition of function minimum (Eq. (5)): X Dsol H calc Dsol H exp 2 d10 ð5Þ f ð Kdimer ;Ddimer H Þ ¼ nð n 3Þ Fig. 4 shows the magnitudes of function f(K dimer, DdimerH) depending on the variation in K dimer and DdimerH 0 values. The above-determined value of solution enthalpy of phosphoric acid in DMF is DsolH 0=16.6 kJ/mol. This value is the standard solution enthalpy of H3PO4 in DMF when phosphoric acid is in molecular form. The parameters of phosphoric acid dimerization were evaluated: K dimer=31 kg/mol, DdimerH 0=60 kJ/mol.
ð3Þ
where: m—molality of phosphoric acid, [mol/kg]; a— dimerization degree of phosphoric acid, connected with the dimerization process equilibrium constant by equation (activity coefficients of H3PO4 and (H3PO4)2 were assumed to be equal 1): ½ H3 PO4 Þ2 a Kdimer ¼ ¼ ð4Þ 2 ½H3 PO4 2ð1 aÞ2 dm Eqs. (3) and (4) include three adjustable parameters: standard solution enthalpy (DsolH 0), phosphoric acid dimerization constant (K dimer) and standard enthalpy of phosphoric acid dimerization (DdimerH 0). These parame-
4. Conclusions The earlier conclusion about the formation of (H3PO4)2/ DMF complexes in this system has been confirmed by the concentration dependence of the mixing enthalpy of the components. For the description of the concentration dependence of the solution enthalpy of phosphoric acid in DMF, one can use the theoretical model considering the phosphoric acid dimers formation. The standard solution enthalpy of H3PO4 in DMF when phosphoric acid is in molecular form is equal to DsolH 0= 16.6 kJ/mol.
Fig. 4. Mean square deviation of calculated and experimental values of acid solution enthalpy in DMF taking into consideration the dimerization of phosphoric acid.
L.P. Safonova et al. / Journal of Molecular Liquids 121 (2005) 53–57
Acknowledgements This work was supported by Ministry of Education of the Russian Federation (grant 1 19-G-E-03) and by grant for scientific researches of young scientists at the leading research and educational groups of academies and scientific organizations of Education Department of Russia (PD02-1.3-305).
References [1] J.B. Ott, J.T. Sipowska, J. Chem. Eng. Data 41 (1996) 987 – 1004. [2] N.N. Postnikov, The thermic phosphoric acid, Chemistry and Technology, Khimia, Moscow, 1970, p. 304. [3] A.M. Kolker, A.N. Kinchin, L.P. Safonova, Thermochim. Acta 169 (1990) 347 – 352. [4] A.N. Kinchin, A.M. Kolker, G.A. Krestov, Russ. J. Phys. Chem. 60 (1986) 782 – 783.
57
[5] R.S. Ramadevi, P. Venkatesu, M.V. Prabhakara Rao, M. Krishna Rama, Fluid Phase Equilib. 114 (1996) 189 – 197. [6] P. Venkatesu, R.S. Ramadevi, M.V. Prabhakara Rao, D.H.L. Prasad, J. Chem. Eng. Data. 45 (2000) 515 – 517. [7] P. Venkatesu, M.V. Prabhakara Rao, D.H.L. Prasad, Y.V.L. Kumar Ravi, Thermochim. Acta 342 (1999) 73 – 78. [8] V.A. Shmakov, N.V. Ivanov, Russ. J. Gen. Chem. 61 (1991) 1545 – 1551. [9] V.G. Tsvetkov, L.J. Tsvetkova, E.A. Shabarova, Russ. J. Gen. Chem. 56 (1986) 1962 – 1967. [10] J.A. Fadeeva, L.E. Shmukler, L.P. Safonova, J. Mol. Liq. 103–104 (2003) 339 – 347. [11] J.A. Fadeeva, L.I. Demina, G.Yu. Gorbunova, L.E. Shmukler, L.P. Safonova, A.Yu. Tsivadze, Russ. J. Coord. Chem. 29 (2003) 515 – 518. [12] J.A. Fadeeva, L.E. Shmukler, L.P. Safonova, A.N. Kinchin, Thermochim. Acta 405 (2003) 117 – 122. [13] R.H. Tromp, S.H. Spieser, G.W. Neilson, J. Chem. Phys. 110 (1999) 2145 – 2150. [14] D.L. Wertz, G.A. Cook, J. Solid Chem. 14 (1985) 41 – 47.
Thermodynamic investigation of the orthophosphoric acid—N,N-dimethylformamide system L.P. Safonova*, Y.A. Fadeeva, L.E. Shmukler, A.N. Kinchin Institute of Solution Chemistry of RAS, 1 Akademicheskaya st., 153045 Ivanovo, Russia Ivanovo State University of Chemistry and Technology, 7 Engels av., 153000 Ivanovo, Russia Available online 27 September 2004
Abstract The solution and mixing enthalpies of phosphoric acid (H3PO4)–N,N-dimethylformamide (DMF) system over the whole concentration range were measured at a temperature of 25 8C. Conclusions about complex-formation in the system under investigation were drawn. The standard solution enthalpy of phosphoric acid in DMF was calculated. D 2004 Elsevier B.V. All rights reserved. Keywords: Phosphoric acid; N,N-dimethylformamide; Solution enthalpy; Dissociation constant
1. Introduction Phosphoric acid solutions in aprotic solvents are of great interest in the studies on proton transfer and the nature of acid–base interactions. Moreover, these systems have a broad potential as solutions for the treatment of cellulose materials and the development of polymeric electrolytes. The importance of phosphate systems caused extensive studies on the thermodynamic properties of nonaqueous phosphoric acid solutions. At present, no works have been done on the thermodynamic equilibrium properties of phosphoric acid solutions in organic solvents. As is generally known, the thermodynamic properties of liquid mixtures are sensitive to various association equilibria. The binary systems, in which one or both components form hydrogen bonds, are of special interest in calorimetry. The heat of mixing of two components is the measure of their molecular interactions. The sign and magnitude of the mixing enthalpy of two liquids depends upon the relative strengths of the interactions between
* Corresponding author. Institute of Solution Chemistry of RAS, 1 Akademicheskaya st., 153045 Ivanovo, Russia. E-mail address: [email protected] (L.P. Safonova). 0167-7322/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.molliq.2004.08.026
similar molecules which are present in pure liquids (homotactic interactions) and the interactions between different molecules (heterotactic interactions) which result from the mixing process [1]. For this reason, the mixing enthalpy may be considered as resulting from two different effects: a chemical effect due to breaking hydrogen bonds and a physical effect due to the interactions between the species in solution, with the chemical effect being usually dominant. The purpose of the present work was to investigate the H3PO4–DMF system by means of calorimetric technique and to discuss the character of interactions in the system in question.
2. Materials and methods A total of 100 wt.% phosphoric acid was prepared from 85 wt.% phosphoric acid (Russia, best quality). An excess of P2O5 reagent was dissolved in 85 wt.% acid at 145 8C. The concentration of the resulting solution was determined by potentiometric titration with KOH and by the density of concentrated phosphoric acid solution measurements [2] and was estimated to be above 100 wt.% of H3PO4. Then, the solution obtained was diluted with distilled water to form 100 wt.% phosphoric acid. All the solutions were held
54
L.P. Safonova et al. / Journal of Molecular Liquids 121 (2005) 53–57
Table 1 Mixing enthalpy of phosphoric acid with DMF x(H3PO4)
DmixH, kJ/mol
x(H3PO4)
DmixH, kJ/mol
0.000500 0.00120 0.00140 0.00160 0.00240 0.00280 0.00390 0.00410 0.00440 0.00520 0.00600 0.00630 0.00680 0.00680 0.00730 0.00750 0.00840 0.00850 0.00860 0.00980 0.0100 0.0110 0.0120 0.0130 0.0210 0.0280 0.0380
0.01200 0.02640 0.04200 0.04260 0.06310 0.08780 0.1132 0.1494 0.1418 0.1625 0.1995 0.2379 0.2318 0.2183 0.248 0.2864 0.2892 0.3226 0.3018 0.3477 0.3872 0.4281 0.4824 0.4942 0.8242 1.131 1.521
0.0470 0.0940 0.1040 0.155 0.163 0.171 0.303 0.306 0.309 0.466 0.473 0.476 0.500 0.515 0.601 0.841 0.868 0.928 0.932 0.940 0.955 0.968 0.973 0.975 0.983 0.993 0.997
1.894 3.913 4.326 6.407 6.743 7.086 12.07 12.16 12.25 16.59 16.66 16.72 16.96 16.94 17.20 8.889 7.444 3.978 3.667 3.222 2.667 1.484 1.250 1.184 0.8173 0.3692 0.1634
overnight at 100 8C to ensure equilibria distribution of the phosphate species. N,N-dimethylformamide (Russia, pure) was dried with CaO and molecular sieves and distilled. The content of water in DMF did not exceed 0.02 wt.%. The solutions of phosphoric acid in DMF were prepared gravimetrically. The mixing and solution enthalpies were measured with a hermetic isoperibol-type calorimeter [3]. A massive
copper block inside a Dewar vessel was used as a thermostatic jacket. A resistance thermometer and heater are situated inside the block to control the temperature. The temperature in the thermostating jacket was kept constant to within F0.001 K. The experimental procedure has been reported earlier [4]. The accuracy of measurements of the heat effects was of F1%.
3. Discussion The experimental data show the significant exothermic effect of mixing of phosphoric acid with N,N-dimethylformamide (Table 1). Earlier, it was found that the mixing enthalpy of N,N-dimethylformamide with a nonelectrolyte can be either positive or negative depending on the nonelectrolyte nature, but that the absolute value of the heat effect did not exceed 5 kJ/mol [1,5–7]. The absolute values of mixing enthalpies for the system under investigation are several times as much as that for the mixtures of DMF with nonelectrolytes (Fig. 1). The great values of mixing enthalpies of H3PO4 with DMF show that the interactions between H3PO4 and DMF molecules are more stronger than those of pure phosphoric acid and N,Ndimethylformamide. Shmakov et al. [8] have investigated the process of mixing of phosphoric acid with different organic solvents. The value of mixing enthalpy of H3PO with DMF (1:1) was determined: DmixH=15 kJ/mol. Tsvetkov et al. [9] have shown that the high negative values of mixing enthalpies of inorganic acids with organic solvents are connected with the process of complexformation. The earlier investigations of dynamic viscosity of the H3PO4–DMF system as a function of the concentration [10] have shown the presence of a significant maximum of the examined function. The appearance of this maximum seems
Fig. 1. Concentration dependence of mixing enthalpy of DMF with nonelectrolytes at 25 8C.
L.P. Safonova et al. / Journal of Molecular Liquids 121 (2005) 53–57
to be connected with the formation of complexes of H3PO4/ DMF=2:1 type. The IR-Fourier-spectroscopic investigation confirmed the conclusion on the complex-formation in the system [11]. This fact explains the shift of the extremum in the concentration dependence of mixing enthalpy of phosphoric acid with DMF to higher acid concentrations (Fig. 2). The experimental data on mixing enthalpies of H3PO4 with DMF are satisfactorily described by the Redlich– Kister equation (Eq. (1)) over the investigated concentration range: H E ¼ x2 ð1 x2 Þ
n1 X
n1 ð1 2x2 Þi
ð1Þ
i¼0
where: x 2—mole fraction of phosphoric acid; n i —fitting coefficients: n 0=67.84F0.10, n 1=20.68F0.70, n 2=22.02F 0.40, and n 3=16.71F1.20. To understand the state of H3PO4 in DMF, the dissolution enthalpy measurements were carried out. The experimental data on solution enthalpy of phosphoric acid in DMF are presented in Table 2. The data show that the effect of dissolution of H3PO4 in DMF is highly exothermic in the range of the acid mole fraction up to x=0.1. Within the range of the H3PO4 mole fraction higher than 0.1 the heat effect decreases slowly (Fig. 3). Such a shape of the DsolH m function is typical for weak electrolytes. This conclusion is confirmed by the results of conductometric investigations of the H3PO4–DMF system [10]. The standard solution enthalpy can be determined by extrapolation of concentration dependence of the experimental solution enthalpy data to infinitely diluted solution. The type of extrapolation equation depends on the chemical equilibria being in solutions and on the choice of the theoretical model for its description.
Fig. 2. Concentration dependence of mix enthalpy of H3PO4–DMF system at 25 8C.
55
Table 2 The solution enthalpy of phosphoric acid in N,N-dimethylformamide x(H3PO4)
DsolH, kJ/mol
x(H3PO4)
DsolH, kJ/mol
0.000504 0.000707 0.00118 0.00144 0.00162 0.00243 0.00286 0.00400 0.00399 0.00446 0.00508 0.00530 0.00608 0.00671 0.00683 0.00689 0.00689 0.00735 0.00849 0.00862 0.00988 0.0100 0.0108 0.0114
25.29 24.36 23.08 27.31 26.31 25.99 30.74 28.34 30.66 31.81 31.86 30.70 32.84 33.66 33.95 33.17 31.71 33.77 34.06 35.01 35.20 35.46 35.92 36.37
0.0117 0.0129 0.0129 0.0136 0.0215 0.0216 0.0288 0.0381 0.0470 0.0940 0.0941 0.104 0.155 0.163 0.172 0.303 0.306 0.308 0.309 0.466 0.473 0.476 0.500 0.515
36.56 36.70 37.31 36.48 38.41 38.17 39.23 39.88 40.26 41.47 41.59 41.54 41.42 41.37 41.32 39.77 39.73 39.69 39.69 35.61 35.23 35.12 33.88 32.91
In our earlier work [12], we have used, for calculation of standard solution enthalpy, the extrapolation equation based on the second approximation of the Debye–Hqckel theory, in which the first stage of the phosphoric acid dissociation was taken into account: n 1 v Ds H ¼ Ds H 0 þ a jzþ z jAH I 1=2 1 þ BaI 1=2 2 o 1 r BaI 1=2 ð2Þ þ bI þ ð1 aÞDass H 0 3 However, the later investigations of molar conductivity of phosphoric acid in DMF at low acid concentrations
Fig. 3. Concentration dependence of solution enthalpy of H3PO4 in DMF at 25 8C.
56
L.P. Safonova et al. / Journal of Molecular Liquids 121 (2005) 53–57
and the method of comparative calculation have shown that the magnitude range of the dissociation constant of the acid was K=106H108. At such poor dissociation of the acid in DMF, the use of the mentioned model is not proper. The authors of Refs. [13,14] have found that, in 100 wt.% phosphoric acid, the most part of molecules form dimers. The IR-Fourier-spectroscopic investigation has shown the presence of phosphoric acid dimers in DMF even at low acid concentration [11]. Therefore, for the description of the concentration dependence of phosphoric acid solution enthalpy in DMF, we used the equation taking into account the molecular dimerization of the acid: a Dsol H ¼ Dsol H 0 þ adm þ Ddimer H 0 2
ters were calculated at the condition of function minimum (Eq. (5)): X Dsol H calc Dsol H exp 2 d10 ð5Þ f ð Kdimer ;Ddimer H Þ ¼ nð n 3Þ Fig. 4 shows the magnitudes of function f(K dimer, DdimerH) depending on the variation in K dimer and DdimerH 0 values. The above-determined value of solution enthalpy of phosphoric acid in DMF is DsolH 0=16.6 kJ/mol. This value is the standard solution enthalpy of H3PO4 in DMF when phosphoric acid is in molecular form. The parameters of phosphoric acid dimerization were evaluated: K dimer=31 kg/mol, DdimerH 0=60 kJ/mol.
ð3Þ
where: m—molality of phosphoric acid, [mol/kg]; a— dimerization degree of phosphoric acid, connected with the dimerization process equilibrium constant by equation (activity coefficients of H3PO4 and (H3PO4)2 were assumed to be equal 1): ½ H3 PO4 Þ2 a Kdimer ¼ ¼ ð4Þ 2 ½H3 PO4 2ð1 aÞ2 dm Eqs. (3) and (4) include three adjustable parameters: standard solution enthalpy (DsolH 0), phosphoric acid dimerization constant (K dimer) and standard enthalpy of phosphoric acid dimerization (DdimerH 0). These parame-
4. Conclusions The earlier conclusion about the formation of (H3PO4)2/ DMF complexes in this system has been confirmed by the concentration dependence of the mixing enthalpy of the components. For the description of the concentration dependence of the solution enthalpy of phosphoric acid in DMF, one can use the theoretical model considering the phosphoric acid dimers formation. The standard solution enthalpy of H3PO4 in DMF when phosphoric acid is in molecular form is equal to DsolH 0= 16.6 kJ/mol.
Fig. 4. Mean square deviation of calculated and experimental values of acid solution enthalpy in DMF taking into consideration the dimerization of phosphoric acid.
L.P. Safonova et al. / Journal of Molecular Liquids 121 (2005) 53–57
Acknowledgements This work was supported by Ministry of Education of the Russian Federation (grant 1 19-G-E-03) and by grant for scientific researches of young scientists at the leading research and educational groups of academies and scientific organizations of Education Department of Russia (PD02-1.3-305).
References [1] J.B. Ott, J.T. Sipowska, J. Chem. Eng. Data 41 (1996) 987 – 1004. [2] N.N. Postnikov, The thermic phosphoric acid, Chemistry and Technology, Khimia, Moscow, 1970, p. 304. [3] A.M. Kolker, A.N. Kinchin, L.P. Safonova, Thermochim. Acta 169 (1990) 347 – 352. [4] A.N. Kinchin, A.M. Kolker, G.A. Krestov, Russ. J. Phys. Chem. 60 (1986) 782 – 783.
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