- Email: [email protected]
Thermodynamic properties of caesium–magnesium monophosphate
Available online at www.sciencedirect.com
J. Chem. Thermodynamics 40 (2008) 653–660 www.elsevier.com/locate/jct
Thermodynamic properties of caesium–magnesium monophosphate E.A. Asabina a, A.R. Zaripov b, V.I. Pet’kov a,*, A.V. Markin a, K.V. Kir’yanov a, N.N. Smirnova a, S.I. Rovny b a
Nizhni Novgorod State University, pr. Gagarina 23, Nizhni Novgorod 603950, Russia b Mayak PA, Ozersk, Chelyabinskaya Region 456780, Russia
Received 6 August 2007; received in revised form 2 November 2007; accepted 3 November 2007 Available online 20 February 2008
Abstract The heat capacity measurements of the crystalline phosphate CsMgPO4 of a tridymite structure were performed between T = (7 and 650) K. The thermodynamic functions C p;m =R, DT0 H m =RT , DT0 S m =R, and Um =R were calculated and the fractal dimension Dfr evaluated. From the solution reaction calorimetry, the standard enthalpy of CsMgPO4 formation at T = 298.15 K was found. Thermochemical parameters of formation Df Gm and lg K f;m were determined by combining the data obtained by these techniques. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Phosphate; Stuffed tridymite structure; Caesium; Heat capacity; Thermodynamic functions; Solution reaction calorimetry
1. Introduction The caesium–magnesium monophosphate belongs to the family of mixed phosphates with a general formula AIBIIPO4 (AI = monovalent metal; BII = divalent metal with a tetrahedral coordination) frequently adopting a bSiO2 tridymite structure [1]. The compounds of this family have been studied because of their ferroelectric properties [2–4]. CsMgPO4 has also been studied as a prospective candidate for the immobilization of the radiocaesium from nuclear wastes and a solid host for a 137Cs c-radiation source to be used in medical applications [5]. Despite the fact that phosphates of this type could have promising applications, their thermodynamic properties have practically not been studied up to now. Only data on the heat capacity of the crystalline phosphates CsZnPO4 and TlBePO4 over the ranges from T = (6 to 300) K [6] and T = (973 to 1323) K [4], respectively, and their phase transition temperatures occurring in condensed state [4,7,8] are available.
*
Corresponding author. Tel.: +7 83124656206; fax: +7 83124345056. E-mail address: [email protected] (V.I. Pet’kov).
0021-9614/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2007.11.001
The goal of the present work is to measure calorimetrically the heat capacity of the crystalline phosphate CsMgPO4 over the range T = (7 to 650) K at standard pressure (p = 0.1 MPa) and to determine the standard entropy of formation at T = 298.15 K. Using a nitric acid solution, calorimetric measurements and the thermodynamic cycle are proposed to calculate the enthalpy of reaction for the CsMgPO4 synthesis at T = 298.15 K and to obtain the thermochemical parameters of formation of CsMgPO4 at temperature T = 298.15 K and standard pressure. From the heat capacity measurements, the fractal dimension is determined for the crystalline phosphate in the range from (20 to 45) K. 2. Experimental The sample of phosphate CsMgPO4 was synthesized using the following procedure from the reagents provided by REACHEM [9]. Stoichiometric amounts of starting materials, high purity CsCl (mass fraction = 0.9999) and MgO (mass fraction purity = 0.9995), were previously dissolved in dilute HCl solution. Then an aqueous solution of high purity NH4H2PO4 (mass fraction 0.9995) taken in accordance with the stoichiometry of the phosphate was
654
E.A. Asabina et al. / J. Chem. Thermodynamics 40 (2008) 653–660
dropped into this mixture under stirring at room temperature. The reaction mixture was dried at T = 353 K, thermally treated in unconfined air access at T = (873 and 973) K with a 24 h plateau at each step. The thermal treatment stages were alternated with careful grinding. The obtained sample was a colourless polycrystalline powder. Confirmation of the desired compound, caesium– magnesium monophosphate, was obtained on a XRD-6000 diffractometer (Cu Ka) in the 2h range of (10° to 60°). A single phase was observed having the monoclinic structure (space group P21/a, a = 965.1(4) pm, b = 552.8(3) pm, c = 893.2(4) pm, b = 90.27(2)°) in agreement with the results [5]. The homogeneity and chemical composition of the sample were checked by electron microprobe analysis on a CamScan MV-2300 device with a Link INCA ENERGY 200C energy-dispersion detector operated at 20.0 kV. The results of electron microscopy showed the homogeneity of the sample. Microprobe analysis indicated the following average mass fractions Cs, 52.84%; Mg, 9.54%; P, 12.24%; O, 25.38% (table 1) and confirmed the stoichiometry of the sample to be close to the theoretical composition CsMgPO4 (Cs, 52.70%; Mg, 9.64%; P, 12.28%; O, 25.38%). There were no substantial impurities (within 0.5%) of other elements in the sample. The chemical composition of the sample was also confirmed by chemical analysis. A known mass of the sample was dissolved in the HNO3 aqueous solution. The caesium mass content, determined by atomic absorption method on a Perkin–Elmer device, was found to be 52.75%. The magnesium mass content, determined titrimetrically with EDTA following the procedure [10], was found to be 9.66% The phosphorus mass content, found to be 12.31%, was determined colorimetrically on a SF-46 spectrophotometer according to the method employing solutions of ammonia vanadate and ammonia molybdate [10]. Thus results of analyses proves that the stoichiometry CsMgPO4 is close to ideal. The heat capacity of the sample of CsMgPO4 over the range from T = (7 to 352) K was measured with a BCT-3 low-temperature adiabatic vacuum calorimeter with an automatic system to maintain adiabatic conditions during measurements. Its design and operational procedure were similar to those in reference [11]. The (iron + rhodium)
TABLE 1 Electron microprobe results (mass fraction w) on the calorimetric sample of caesium–magnesium monophosphate Sample sites of scanning
Cs
Mg
1 2 3 4 5
52.80 52.94 52.88 52.73 52.86
9.60 9.47 9.51 9.55 9.56
P
O
12.21 12.31 12.19 12.23 12.25
25.39 25.28 25.42 25.49 25.33
w/%
Actual composition is w(Cs) = 52.84%; w(Mg) = 9.54%; w(P) = 12.24%; w(O) = 25.38%.
resistance thermometer (R0 = 100 X) was calibrated on the basis of ITS-90. The reliability of the calorimetric operation was tested by measuring the heat capacities of highly purified copper (OSCh11-4), standard synthetic corundum [12], and K-1 benzoic acid [12] prepared at the metrological institutions of the State Standard Committee of the Russian Federation. It was established that the apparatus and the measurement procedure allowed us to obtain the C p;m values of the substances in the crystalline state with an uncertainty of not more than 2% from T = (7 to 10) K, 0.5% between T = (10 and 40) K, and within 0.2% in the range from T = (40 to 352) K. An automated dynamic calorimeter (ADCTTB) operating by the principle of triple thermal bridge was used to measure the heat capacity over the temperature range from (330 to 650) K. The apparatus design and operational procedure were reported elsewhere [13,14]. The accuracy of the calorimetric data was checked by measuring the heat capacities of standard synthetic corundum and highly purified copper at the temperatures and enthalpies of melting the standard samples [12] of indium, tin, and lead, also prepared at the metrological institutions of the State Standard Committee of the Russian Federation. The uncertainty in the measurements of C p;m over the temperature interval noted above was about 1.5%, for the transition temperatures 0.3 K and for the transition enthalpies 0.8%. However, the heat capacity of the sample over the temperature range from (330 to 352) K was also measured in the low-temperature adiabatic vacuum calorimeter with an uncertainty 0.2% and the conditions of measurements on the dynamic calorimeter were selected in the way that the C p;m values obtained by using these calorimeters coincided. It was assumed that at T > 352 K the uncertainty of the measurements of C p;m was (0.5–1.5)%. The crystalline sample of CsMgPO4 (mass, 1.1323 g) was placed in a 1.5 cm3 thin-wall cylindrical titanium vessel of the low-temperature adiabatic vacuum calorimeter. The measurements of C p;m were made between T = (7 and 352) K. The 172 experimental C p;m values were obtained for the three series reflecting the sequence of the heat capacity measurements (table 2). The calorimetric vessel contained 0.3537 g of CsMgPO4 and the heat capacity of the sample between T = (330 and 650) K (table 2) was measured by continuous heating at a mean rate of 2 K min1. The heat capacity of the sample itself was between (60 and 70)% of the total heat capacity of (the calorimetric vessel + the sample) over the temperature interval between (7 and 650) K. Averaging of the experimental C p;m points was carried out by means of power and semilogarithmic polynomials. The root-mean-square deviation of the experimental values from the corresponding smoothed curve C p;m ¼ f ðT Þ did not exceed 0.14% in the range from T = (7 to 40) K, 0.08% between T = (40 and 90) K, 0.04% from T = (90 to 330) K, and 0.15% at temperatures from T = (330 to 650) K. An automated isothermal differential Calvet-type microcalorimeter (DAC-1-1-A) was employed to measure the
E.A. Asabina et al. / J. Chem. Thermodynamics 40 (2008) 653–660 TABLE 2 Experimental molar heat capacities C p;m =R of CsMgPO4 (M = 252.1818 g mol1; R = 8.314472 J K1 mol1) T/K 7.22 7.30 7.96 8.00 8.70 9.40 10.09 10.42 11.01 11.69 12.40 13.07 13.90 14.63 15.35 16.06
C p;m =R 0.115 0.118 0.147 0.149 0.191 0.238 0.289 0.321 0.3752 0.4378 0.5051 0.5653 0.6485 0.7252 0.8065 0.8912
C p;m =R
T/K
Series 1 16.84 0.9886 17.45 1.067 18.81 1.250 19.49 1.341 20.16 1.436 21.16 1.580 22.91 1.840 25.31 2.187 27.75 2.510 30.21 2.824 32.69 3.118 35.16 3.400 37.64 3.670 40.12 3.926 42.60 4.172 45.08 4.407
7.049 7.224 7.391 7.548 7.704 7.858 8.009 8.157 8.304 11.02 11.14 11.27 11.40 11.55 11.68 11.82 11.95 12.08 12.21 12.34 12.45 12.58 12.69 12.82 12.97 13.10 13.22 13.38 13.59 13.82 14.06 14.81 15.54
Series 109.68 112.63 115.80 118.91 121.88 124.84 127.80 130.76 133.72 238.55 241.43 244.43 247.38 249.90 253.01 255.80 258.57 261.33 264.07 266.89 269.63 272.18 274.85 277.49 280.12 282.50 285.44 287.80 289.70 292.80 294.90 297.00 298.84
2
82.70 85.90 88.99 91.95 94.91 97.87 100.82 103.77 106.72 163.60 166.37 169.34 172.31 175.74 178.73 182.05 185.19 188.17 191.40 194.30 197.16 200.16 202.86 205.98 208.94 211.90 214.59 217.64 221.10 224.11 226.99 232.75 235.69
12.54 12.66 12.78 12.93 13.06 13.18 13.34 13.55 13.76
Series 226.53 232.40 235.70 237.89 240.77 243.77 246.72 249.24 252.35
3
199.50 202.40 205.51 208.48 211.44 214.13 217.18 220.64 223.65
T/K
C p;m =R
47.57 52.52 54.99 57.47 59.95 61.64 63.99 67.48 71.15 74.82 78.48 82.15 85.82 89.49
4.637 5.050 5.247 5.440 5.625 5.747 5.909 6.141 6.375 6.597 6.811 7.018 7.221 7.417
8.452 8.601 8.755 8.907 9.053 9.199 9.345 9.489 9.632 15.02 14.54 14.23 14.03 13.91 13.82 13.80 13.81 13.84 13.88 13.93 13.97 14.03 14.10 14.17 14.23 14.29 14.36 14.41 14.47 14.55 14.61 14.66 14.71
136.69 139.65 142.62 145.59 148.56 151.53 154.50 157.60 160.43 300.67 303.29 305.91 308.00 310.09 312.40 314.71 316.36 318.00 321.10 324.20 325.30 326.40 329.66 332.91 333.99 335.08 338.20 341.80 343.40 345.83 348.25 350.05 351.85
9.775 9.916 10.06 10.20 10.34 10.48 10.61 10.75 10.88 14.76 14.83 14.90 14.96 15.01 15.08 15.14 15.18 15.22 15.30 15.39 15.42 15.45 15.53 15.60 15.62 15.65 15.71 15.78 15.82 15.87 15.93 15.96 16.00
13.99 14.74 15.53 15.17 14.64 14.29 14.06 13.93 13.84
255.27 257.91 260.67 263.41 266.23 268.97 271.52 274.19 276.83
13.80 13.81 13.83 13.87 13.91 13.96 14.01 14.08 14.15
655
Table 2 (continued) T/K
C p;m =R
T/K
330.5 334.4 338.3 342.2 346.1 350.0 353.9 357.8 361.7 365.5 369.2 372.9 376.6 380.2 383.7 387.2 390.7 394.2 397.7 401.3 404.8 408.5 412.1 415.8 419.6 423.3 427.0 430.6 434.3
15.5 15.6 15.7 15.8 15.9 16.0 16.0 16.1 16.2 16.3 16.4 16.4 16.5 16.6 16.6 16.7 16.8 16.9 16.9 17.0 17.0 17.1 17.2 17.2 17.3 17.4 17.5 17.5 17.6
437.9 441.6 445.2 448.8 452.5 456.1 459.8 463.4 467.1 470.7 474.4 478.1 481.8 485.4 489.1 492.7 496.4 500.0 503.7 507.3 511.0 514.6 518.3 521.8 525.4 529.0 532.6 536.1 539.8
a
C p;m =R Series 4a 17.6 17.7 17.8 17.8 17.9 17.9 18.0 18.1 18.1 18.2 18.2 18.3 18.3 18.4 18.5 18.5 18.6 18.6 18.7 18.7 18.8 18.8 18.9 18.9 19.0 19.0 19.1 19.1 19.2
T/K
C p;m =R
543.3 546.9 550.5 554.1 557.7 561.4 565.0 568.7 572.4 576.1 579.8 583.4 587.1 590.7 594.3 597.9 603.4 607.0 610.6 614.2 617.7 621.4 625.0 628.6 632.3 636.0 639.7 643.3 648.9
19.2 19.3 19.3 19.4 19.4 19.5 19.5 19.6 19.6 19.7 19.7 19.8 19.8 19.9 19.9 20.0 20.0 20.1 20.1 20.2 20.2 20.2 20.3 20.3 20.4 20.4 20.5 20.5 20.6
This Series presents every second experimental value of heat capacity.
enthalpies of solution at T = 298.15 K. Its design and operation have already been described [15]. For calibration, a known current was passed through the cell-assembly heater over a specified time. The reliability of the calorimeter operation was tested in experiments on the solution of high-purity KCl in bi-distilled water. The value for the standard enthalpy of solution obtained by us Dsol H m ð298:15Þ ¼ ð17:6 0:4Þ kJ mol1 (average of 10 experiments) was in agreement with the published value Dsol H m ð298:15Þ ¼ ð17:58 0:34Þ kJ mol1 [16]. The enthalpies (Dr H m ) of the reactions studied at T = 298.15 K are averages of (5 to 7) replicates. In conformity with IUPAC recommendations [17], the uncertainty in DrH is given as a standard deviation of the average. The net uncertainty in the 1=2 enthalpy of formation was evaluated as r ¼ ðRi r2i Þ , where ri represents the uncertainty in a single measurement. 3. Results and discussion 3.1. Heat capacity and phase transition The experimental values of the molar heat capacity of CsMgPO4 between T = (7 and 650) K and the smoothed curve C p;m ¼ f ðT Þ are shown in figure 1. It is seen that a solid-to-solid phase transition appears over the temperature
656
E.A. Asabina et al. / J. Chem. Thermodynamics 40 (2008) 653–660
C p;m ¼ 120:04 þ 6:45435T 1:034267 101 T 2 þ 9:28663
E
104 T 3 4:59517 106 T 4 þ 1:18379 108 T 5
cr I
C op,m /(J⋅ mol-1⋅ K -1 )
150
1:24119 1011 T 6 :
C D B 100 cr II
15
15
10
10
5
50
0
A
0
5
0
200
10
400
20
600
T/K FIGURE 1. Plot of heat capacity against temperature dependence for crystalline CsMgPO4.
interval from (209 to 270) K. The analogous phase transition was found in [8] for the tridymite structure-type phosphate CsZnPO4. In [6], the transition of the Zncontaining sample was detected as the broad anomaly on the heat capacity curve with a maximum around T = 220 K. It was suggested [6] that this transition should proceed with an extremely heterogeneous nucleation process. It was accompanied by a step increase in lattice parameters, its volume and absorption of a quantity of heat, and so, it was characterized as a first-order phase transition. The phase transition of CsMgPO4 was reproduced on repeated cooling and heating (table 2). The temperature corresponding to the maximum value of the apparent heat capacity in the transition range from (209 to 270) K at first heating of the sample (C p;m ¼ 129:2 J mol1 K1 ), is regarded as the transition temperature for CsMgPO4, T trs ¼ ð235:69 0:03Þ K. The enthalpy of the solid-to-solid phase transition Dtrs H m ¼ ð0:2713 0:0025Þ kJ mol1 , was obtained graphically for the area BCDB (figure 1). The values of entropy of the first-order phase transition, calculated by integrating the C p;m =T ¼ f ðT Þ dependence and by formula Dtrs S m ¼ Dtrs H m =T trs , coincided within the uncertainty of experiment and amounted to (1.15 ± 0.01) J mol1 K1. The temperature dependence of the heat capacity does not exhibit any peculiarity. Below T = 209 K (crystal II, section AB on curve) and above 270 K (crystal I, section DE on curve), it gradually increases as the temperature rises. For example, over the temperature range (50 to 100) K the heat capacity of CsMgPO4 is described by the equation: C p;m ¼ 22:97 þ 2:349T 4:098 102 T 2 þ 6:436 104 T 3 7:081 106 T 4 þ 4:427 108 T 5 1:141 1010 T 6 ; and over the range (100 to 200) K by the equation:
In the above given equations, the C p;m is in J mol1 K1 and T is in Kelvin. In view of a development of models describing the temperature dependence of heat capacity, it was of interest to evaluate the fractal dimension Dfr for the crystalline phosphate CsMgPO4. In the fractal theory of heat capacity [18– 20] of solids, Dfr is the exponent at T in the C v;m ¼ f ðT Þ function. The significance of Dfr value for solids gives information on the topology of their structure. The relation ‘‘heat capacity versus T” is proportional to T1 in the lower temperature range for chain-structured bodies, T2 for solids with layer structure and it is proportional to T3 in the case of spatial structure. We have assumed that C p;m ¼ C v;m at T < 45 K. From the ln C p;m versus ln T plot, it is found that at temperatures between (20 and 45) K the Dfr = 3, Hmax = 126.5 K for CsMgPO4, within an uncertainty of 1.6%. This means that crystalline CsMgPO4 has a spatial (three-dimensional) structure. At lower temperatures, in order to calculate the thermodynamic functions (table 3) the heat capacity of CsMgPO4 was described by Debye function, C p;m T 3 : C p;m ¼ nDðHD =T Þ; where D denotes the Debye heat capacity function, n = 3 and HD = 92.16 K are specially selected parameters. With those values, the given equation describes the experimental values of C p;m over the range from (7 to 11) K within an uncertainty of about 1.8%. While calculating the thermodynamic functions, it was assumed that, at T < 7 K, this equation reproduces the C p;m values almost with the same accuracy. 3.2. Thermodynamic functions The thermodynamic functions of crystalline CsMgPO4 were calculated from the C p;m ðT Þ curve over the range from (0 to 650) K. The enthalpies DT0 H m and entropies DT0 S m were calculated by using the following equations: Z T trs Z T C p;m ðT Þ dT þ Dtrs H m þ C p;m ðT Þ dT ; DT0 H m ¼ DT0 S m
¼
Z
T trs
0 T trs
C p;m ðT Þ d ln T
0
þ
Dtrs S m
þ
Z
T T trs
C p;m ðT Þ d ln T :
The functions Um ðT Þ were found from the corresponding values of DT0 H m and DT0 S m and by the equation: Um ¼ DT0 S m DT0 H m =T : The smoothed heat capacities C p;m =R and derived thermodynamic functions of the investigated phosphate are given in table 3. It is suggested that the uncertainty of
E.A. Asabina et al. / J. Chem. Thermodynamics 40 (2008) 653–660 TABLE 3 Thermodynamic functions of CsMgPO4 (M = 252.1818 g mol1); R = 8.314472 J K1 mol1; C p;m , standard molar heat capacity; DT0 H m , standard molar enthalpy; DT0 S m , standard molar entropy; and Um ¼ DT0 S m DT0 H m =T ðp ¼ 0:1 MPaÞ T/K
C p;m =R
DT0 H m =RT
DT0 S m =R
5 10 15 20 25 30 35 40 45 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 235.69
0.0383 0.2850 0.7661 1.415 2.145 2.796 3.383 3.916 4.401 4.845 5.630 6.303 6.898 7.445 7.967 8.468 8.962 9.451 9.933 10.40 10.86 11.30 11.73 12.16 12.57 12.98 13.38 13.78 14.00
Crystal II 0.00962 0.07337 0.2133 0.4312 0.7009 0.9971 1.297 1.591 1.877 2.152 2.668 3.140 3.574 3.974 4.347 4.699 5.034 5.355 5.665 5.965 6.257 6.541 6.817 7.087 7.351 7.609 7.863 8.111 8.251
0.0128 0.09867 0.2912 0.5980 0.9924 1.443 1.919 2.406 2.896 3.383 4.338 5.257 6.139 6.983 7.795 8.578 9.336 10.07 10.79 11.49 12.18 12.85 13.51 14.15 14.79 15.41 16.02 16.63 16.97
235.69 240 250 260 270 280 290 298.15 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500
16.06 13.24 13.49 13.74 13.99 14.23 14.47 14.69 14.74 15.01 15.28 15.54 15.75 15.96 16.2 16.4 16.6 16.8 17.0 17.1 17.3 17.5 17.7 17.8 18.0 18.2 18.3 18.5 18.6
Crystal I 8.389 8.475 8.671 8.861 9.046 9.227 9.404 9.545 9.577 9.748 9.917 10.08 10.25 10.41 10.6 10.7 10.9 11.0 11.2 11.3 11.4 11.6 11.7 11.9 12.0 12.1 12.2 12.4 12.5
17.11 17.34 17.89 18.42 18.95 19.11 19.46 19.96 20.37 20.46 20.95 21.43 21.90 22.37 22.8 23.3 23.7 24.2 24.6 25.0 25.4 25.9 26.3 26.7 27.1 27.5 27.9 28.2 28.6
Um =R 0.00320 0.02523 0.07807 0.1670 0.2914 0.4462 0.6223 0.8148 1.019 1.231 1.670 2.117 2.565 3.009 3.447 3.878 4.302 4.717 5.126 5.527 5.921 6.309 6.691 7.067 7.437 7.802 8.162 8.517 8.717
8.717 8.869 9.219 9.563 9.901 9.762 9.880 10.27 10.76 10.53 10.85 11.16 11.47 11.78 12.1 12.4 12.7 13.0 13.2 13.5 13.8 14.1 14.4 14.6 14.9 15.1 15.4 15.7 15.9
657
Table 3 (continued) T/K
C p;m =R
DT0 H m =RT
DT0 S m =R
Um =R
510 520 530 540 550 560 570 580 590 600 610 620 630 640 650
18.8 18.9 19.1 19.2 19.3 19.5 19.6 19.7 19.9 20.0 20.1 20.2 20.3 20.5 20.6
12.6 12.7 12.9 13.0 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 14.0 14.1
29.0 29.4 29.7 30.1 30.5 30.8 31.2 31.5 31.8 32.2 32.5 32.8 33.2 33.5 33.8
16.2 16.4 16.7 16.9 17.2 17.4 17.6 17.9 18.1 18.3 18.6 18.8 19.0 19.2 19.5
the function values lie within 2% at T < 10 K, between (0.5 and 0.7)% at temperatures from (10 to 40) K, 0.3% from (40 to 330) K, and between (0.5 and 1.6)% from (330 to 650) K. 3.3. Thermochemical parameters of formation As a part of the thermodynamic description of the CsMgPO4, we estimated the standard thermochemical parameters of its formation at T = 298.15 K. K Using the standard entropy D298:15 S m ðCsMgPO4 ; 0 1 1 crÞ ¼ 169:3 J K mol and reference data [22] on the absolute entropy of the constituent simple substances (table 4), we calculated the standard molar entropy of formation Df S m ðCsMgPO4 ; cr;298:15KÞ ¼ ð400:0 0:7Þ J K1 mol1 . To derive the standard enthalpy of formation of the phosphate investigated, we used the thermodynamic cycle by considering the enthalpy of reaction of CsMgPO4 with nitric acid. Table 5 lists the mean values with twice standard deviations of the mean of the independent determinations taken of the molar enthalpies of reaction of the stoichiometric amounts of the reactants and products required for the determination of the Dr H 7 . According to our experimental data, reactions numbers 1 to 6 in table 5 refer to true solutions. So we can, without analyzing the nature of the products, sum up the reaction numbers 1 to 6 with the corresponding signs to obtain the
TABLE 4 Absolute entropies of the simple substances necessary to calculate the standard entropy of formation of CsMgPO4 at T = 298.15 K Substance
Physical statea
D298:15 S m =ðJ K1 mol1 Þ 0
Cs Mg P O2
cr cr cr g
85.23 ± 0.40 32.67 ± 0.10 41.09 ± 0.25 205.152 ± 0.005
a
cr, crystalline; g, gaseous.
658
E.A. Asabina et al. / J. Chem. Thermodynamics 40 (2008) 653–660
TABLE 5 Experimental scheme for the calculation of enthalpy of reaction of CsMgPO4 synthesis Dr H m ð298:15Þ obtained from Hess cycle: Dr H 7 ¼ Dr H 1 þ Dr H 2 þ Dr H 3 Dr H 4 Dr H 5 þ Dr H 6 DrH(298.15)/(kJ mol1)
Reaction 1. 2. 3. 4. 5. 6. 7.
17.0 ± 1.0 CsNO3(cr) + 143.6[HNO3 5.55.2 H2O](sln 1) = CsNO3 143.6HNO3 797.3H2O(sln 2) Mg(NO3)2 6H2O(cr) + sln 2 = CsNO3 Mg(NO3)2 143.6HNO3 803.3H2O (sln 3) 31.4 ± 0.6 15.18 ± 0.16 NH4H2PO4(cr) + sln 3 = CsNO3 Mg(NO3)2 H3PO4 NH4NO3 142.6HNO3 803.3H2O(sln 4) CsMgPO4(cr) + 145.6[HNO3 5.55.2H2O](sln 1)=CsNO3 Mg(NO3)2 H3PO4 14 2.6HNO3 808.4H2O(sln 5) 106 ± 3 NH4NO3(cr) + sln 5 = CsNO3 Mg(NO3)2 H3 PO4 NH4NO3 142.6HNO3 808.4H2O(sln 6) 16.7 ± 0.3 5.1(0.89 ± 0.29) 5.1H2O(l) + sln 4 = sln 6 CsNO3(cr) + Mg(NO3)2 6H2O(cr) + NH4H2PO4(cr) + 5.1H2O(l) = CsMgPO4(cr) + NH4NO3(cr) + 2[HNO3 5.55.2H2O] 148 ± 4 (sln 1)
reaction scheme of CsMgPO4 synthesis (reaction 7 = reaction 1 + reaction 2 + reaction 3 reaction 4 reaction 5 + reaction 6) and to calculate the enthalpy of this reaction. All the enthalpies of determined reactions are collected in tables 6 to 11. The standard molar enthalpy of formation of CsMgPO4 was obtained from the equation:
TABLE 6 Calorimetric results for the reaction of CsNO3 with HNO3 5.55.2H2Oa,b Experiment
m(CsNO3)
1 2 3 4 5 6
DrH
Q
g
J
Jg
kJ mol1
0.031085 0.030810 0.031000 0.030880 0.030905 0.030980
2.7105 2.5818 2.7211 2.6017 2.6585 2.6034
88.64 85.26 89.23 85.71 87.47 85.48
17.3 16.6 17.4 16.7 17.0 16.7
TABLE 7 Calorimetric results for the reaction of Mg(NO3)2 6H2O with CsNO3 143.6HNO3 797.3H2O
1 2 3 4 5 6
m(Mg(NO3)2 6H2O)
Q
Experiment
1 2 3 4 5 6 7 a
of
NH4H2PO4
with
m(NH4H2PO4)
Q
DrH
Dr H m a
g
J
J g1
kJ mol1
0.018305 0.018255 0.018510 0.018505 0.018015 0.018250 0.018215
2.3593 2.3775 2.4315 2.3577 2.3422 2.3344 2.3861
131.34 132.70 133.79 129.84 132.51 130.37 133.46
15.11 15.26 15.39 14.93 15.24 15.00 15.35
The molar mass of NH4H2PO4 was taken to be 115.0255 g mol1.
Dr H m c
1
a The symbols in table denote the following: m(CsNO3) is the mass of CsNO3 in the experiments; Q is the quantity of energy released from calorimetric system during the process investigated; DrH is the enthalpy of reaction per unit mass of the sample which includes a combined correction of 0.0449 J for the enthalpies of the sample forced out into the HNO3 solution, of the reaction of paraffin with the solution, of stirring of the reaction mixture and of solvent vaporization; Dr H m is the molar enthalpy of reaction investigated. b In each experiment 3.00 cm3 of HNO3 solution was used. The mean temperature of each experiment was 298.15 K. c The molar mass of CsNO3 was taken to be 194.9103 g mol1.
Experiment
TABLE 8 Calorimetric results for the reaction CsNO3 Mg(NO3)2 143.6HNO3 803.3H2O
DrH
Dr H m a
g
J
Jg
kJ mol1
0.041260 0.040680 0.040875 0.040885 0.040795 0.041010
5.0570 4.8618 4.8807 4.9497 5.0166 5.0511
123.7 120.6 120.5 122.2 124.1 124.3
31.7 30.9 30.9 31.3 31.8 31.9
1
a The molar mass of Mg(NO3)2 6H2O was taken to be 256.4060 g mol1.
TABLE 9 Calorimetric results for the reaction of CsMgPO4 with HNO3 5.55.2H2O Experiment
1 2 3 4 5 6 7 a
m(CsMgPO4)
Q
DrH
Dr H m a
g
J
J g1
kJ mol1
0.039995 0.040210 0.040140 0.040105 0.040155 0.040115 0.040160
17.1321 17.0151 16.7583 17.0282 16.7380 17.1088 16.6433
427.2 422.0 416.4 423.5 415.7 425.4 413.3
108 106 105 107 105 107 104
The molar mass of CsMgPO4 was taken to be 252.1818 g mol1.
TABLE 10 Calorimetric results for the reaction of CsNO3 Mg(NO3)2 H3PO4 142.6HNO3 808.4H2O Experiment
1 2 3 4 5 a
NH4NO3
with
m(NH4NO3)
Q
DrH
Dr H m a
g
J
J g1
kJ mol1
0.012795 0.012785 0.012835 0.012960 0.012820
2.6661 2.6163 2.6057 2.6223 2.6528
211.9 208.2 206.5 205.8 210.4
17.0 16.7 16.5 16.5 16.8
The molar mass of NH4NO3 was taken to be 80.0432 g mol1.
Dr H 7 ¼ Df H m ðCsMgPO4 ; cr;298:15Þþ Df H m ðNH4 NO3 ; cr;298:15Þ þ 2Df H m ðHNO3 5:55 2H2 O; sol;298:15Þ Df H m ðCsNO3 ; cr;298:15Þ Df H m ðMgðNO3 Þ2 6H2 O; cr;298:15Þ Df H m ðNH4 H2 PO4 ; cr;298:15Þ 5:1Df H m ðH2 O; l;298:15Þ
E.A. Asabina et al. / J. Chem. Thermodynamics 40 (2008) 653–660 TABLE 11 Calorimetric results for the reaction of H2O Mg(NO3)2 H3PO4 NH4NO3 142.6HNO3 803.3H2O Experiment
1 2 3 4 5 a
m(H2O)
Q
CsNO3
with
DrH 1
Dr H m a 1
659
TABLE 13 Standard thermodynamic functions of the reaction of CsMgPO4 solidstate synthesis; ðDnC p;m Þ ¼ 20:8 J mol1 K1 Dr S m
Dr H m
T
1
Dr Gm 1
g
J
Jg
kJ mol
K
kJ mol
J mol
0.017465 0.019180 0.023665 0.019960 0.021820
0.9323 0.9500 1.2254 1.0451 1.0884
50.8 47.2 49.9 50.1 47.8
0.92 0.85 0.90 0.90 0.86
298.15 350 400 430 500 550 600
278.9 277.9 276.8 276.2 274.7 273.7 272.7
580.1 576.8 574.0 572.5 569.3 567.4 565.6
The molar mass of H2O was taken to be 18.0152 g mol1.
K1
kJ mol1 106.0 76.0 47.2 30.0 9.9 38.4 66.7
and literature data [21,22] collected in table 12. Its value: Df H m ðCsMgPO4 ; cr;298:15Þ ¼ Dr H 7 Df H m ðNH4 NO3 ; cr;298:15Þ 2Df H m ðHNO3 ; sol5:55 2H2 O;298:15Þ 6Df H m ðH2 O; l;298:15Þþ Df H m ðCsNO3 ; cr;298:15Þþ Df H m ðMgðNO3 Þ2 6H2 O; cr;298:15Þþ Df H m ðNH4 H2 PO4 ; cr;298:15Þ ¼ ð1931 5Þ kJ mol1 :
Combination of the enthalpy of formation of CsMgPO4 with its entropy of formation allowed us to calculate the standard molar Gibbs function of formation, Df Gm ðCsMgPO4 ; cr;298:15 KÞ ¼ ð1812 5Þ kJ mol1 . The logarithmic value of the formation reaction constant for CsMgPO4 was calculated from the value Df Gm by the following equation: lg K f;m ¼ Df Gm =½2:303R 298:15ðKÞ ¼ 317. The values of the thermodynamic parameters of formation obtained correspond to the process CsðcrÞ þ MgðcrÞ þ Pðcr; whiteÞ þ 2O2 ðgÞ ¼ CsMgPO4 ðcrÞ: Taking into account the usage of tridymite-like compounds in medical and other applications, we analyzed the conditions of CsMgPO4 formation by the reaction of solid-state synthesis:
TABLE 12 Enthalpies of formation substances necessary to calculate the standard enthalpies of formation of CsMgPO4 at T = 298.15 K Substance
Physical statea
Df H m =kJ mol1
CsNO3 Mg(NO3)2 6H2O NH4H2PO4 H2O NH4NO3 HNO3 b
cr cr cr l cr sol
505.720 ± 0.585 2614.665 ± 1.338 1445.572 ± 2.552 285.830 ± 0.040 365.430 ± 0.418 203.4 ± 0.5
CsClðcrÞ þ MgCl2 ðcrÞ þ NH4 H2 PO4 ðcrÞ ¼ CsMgPO4 ðcrÞ þ NH3 ðgÞ þ 3HClðgÞ: The standard enthalpy and entropy of the reaction at T = 298.15 K were calculated from the standard enthalpy of formation of CsMgPO4 together with its absolute entropy and literature data [21,22]. The standard thermodynamic functions of the synthesis reaction at higher temperatures (table 13) were found from the equations: Dr H m ðT Þ ¼ Dr H m ð298:15Þ þ DnC p;m ðT 298:15Þ; Dr S m ðT Þ ¼ Dr S m ð298:15Þ þ DnC p;m lnðT =298:15Þ; by assuming that the algebraic sum of heat capacities of reagents DnC p;m is constant over the temperature interval from 298.15 K to T. It is seen that the reaction of synthesis at T = 298.15 K is characterized by a positive Gibbs function value. The theoretical temperature of CsMgPO4 synthesis was found as the temperature at which Dr Gm changes sign from positive to negative. The derived temperature was not high: T 483 K. This is the reason why ceramic technology is one of the commonly used methods for such phosphates synthesis. 4. Conclusion The general aim of this investigation was to report the results of the complex thermodynamic study of the CsMgPO4 compound belonging to the vast family of solids with a tridymite structure. The heat capacity of this phosphate was measured over the temperature range from (7 to 650) K, the thermodynamic functions C p;m =R; DT0 H m =RT , DT0 S m =R, and Um =R calculated and the fractal dimension Dfr evaluated. Thermochemical parameters of formation Df H m , Df S m , Df Gm and lg K f;m were determined by combining the data obtained by using solution reaction calorimetry and heat capacity measurements. The theoretical temperature of CsMgPO4 solid-state synthesis was evaluated. Acknowledgements
a
cr, crystalline; sol, solution, l, liquid. The value of Df H m corresponds to HNO3 in the solution of composition HNO3 5.55.2H2O. b
This research was supported by the Russian Foundation for Basic Research (Project Nos. 08-03-00082, 08-03-
660
E.A. Asabina et al. / J. Chem. Thermodynamics 40 (2008) 653–660
00485) and National Project ‘‘Education” of innovational educational program of NNSU. References [1] [2] [3] [4] [5]
[6] [7] [8] [9] [10]
R. Masse, A. Durif, J. Solid State Chem. 73 (1988) 468–472. D. Blum, J.C. Peuzin, J.Y. Henry, Ferroelectrics 61 (1984) 265–279. B. Elouadi, L. Elamnari, J. Ravez, Ferroelectrics 56 (1984) 17–20. G. Wallez, S. Jaulmes, A. Elfakir, M. Quarton, J. Phys. III France 4 (1994) 1197–1204. A.R. Zaripov, O.M. Slunchev, V.A. Orlova, D.D. Galouzin, P.V. Sizov, S.I. Rovny, V.I. Pet’kov, Radiat. Saf. Probl. 2 (2006) 18–28 (in Russian). I. Yamashita, T. Tojo, H. Kawaji, T. Atake, Phys. Rev. B 65 (2002) 212104. D. Blum, A. Durif, M.T. Averbuch-Pouchot, Ferroelectrics 69 (1986) 283–292. A. Sawada, T. Azumi, Y. Kuroiwa, Ferroelectrics 237 (2000) 245– 252. Chemical reagents and high-pure chemicals. Catalog, Khimia, Moscow, 1990 (in Russian). F. Umbland, A. Janssen, D. Thierig, G. Wu¨nsch (Eds.), Theorie und praktisch anwendung von komplexbildnern, Akademisch verlagsgesellschaft, Frankfurt Am Main, 1971.
[11] R.M. Varuschenko, A.I. Druzhinina, E.L. Sorkin, J. Chem. Thermodyn. 29 (1997) 623–637. [12] O.M. Sergeev (Ed.), Metrological Principles of Thermophysical Measurements, Standard Publisher, Moscow, 1972 (in Russian). [13] M. Yagfarov, Sh. Zh. Fiz. Khim. 43 (1969) 1620–1625 (in Russian). [14] A.G. Kabo, V.V. Diky, Thermochim. Acta 347 (2000) 79–84. [15] E. Calvet, H. Prat (Eds.), Microcalorimetrie: Applications Physicochimiques et Biologicules, Masson, Paris, 1956. [16] V.P. Glushko (Ed.), Thermal Constants of Substances, Issue 10, VINITI, Moscow, 1981 (in Russian). [17] F.D. Rossini, in: F.D. Rossini (Ed.), Experimental Thermochemistry, vol. 1, Interscience, New York, 1956 (Chapter 14). [18] T.S. Yakubov, Docl. Akad. Nauk SSSR 310 (1990) 145–149 (in Russian). [19] A.D. Izotov, O.V. Shebershneva, K.S. Gavrichev, in: Proceedings of the all Russian Conference on Thermal Analysis and Calorimetry, Kazan, 1996, 200–202 (in Russian). [20] V.B. Lazarev, A.D. Izotov, K.S. Gavrichev, O.V. Shebersheneva, Thermochim. Acta 269–270 (1995) 109–116. [21] J.D. Cox, D.D. Wagman, V.A. Medvedev (Eds.), CODATA Key Values for Thermodynamics, Hemisphere, New York, 1989. [22] V.P. Glushko (Ed.), Thermal Constants of Substances, Issues 1–9, Nauka, Moscow, 1965 (in Russian).
JCT 07-245
J. Chem. Thermodynamics 40 (2008) 653–660 www.elsevier.com/locate/jct
Thermodynamic properties of caesium–magnesium monophosphate E.A. Asabina a, A.R. Zaripov b, V.I. Pet’kov a,*, A.V. Markin a, K.V. Kir’yanov a, N.N. Smirnova a, S.I. Rovny b a
Nizhni Novgorod State University, pr. Gagarina 23, Nizhni Novgorod 603950, Russia b Mayak PA, Ozersk, Chelyabinskaya Region 456780, Russia
Received 6 August 2007; received in revised form 2 November 2007; accepted 3 November 2007 Available online 20 February 2008
Abstract The heat capacity measurements of the crystalline phosphate CsMgPO4 of a tridymite structure were performed between T = (7 and 650) K. The thermodynamic functions C p;m =R, DT0 H m =RT , DT0 S m =R, and Um =R were calculated and the fractal dimension Dfr evaluated. From the solution reaction calorimetry, the standard enthalpy of CsMgPO4 formation at T = 298.15 K was found. Thermochemical parameters of formation Df Gm and lg K f;m were determined by combining the data obtained by these techniques. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Phosphate; Stuffed tridymite structure; Caesium; Heat capacity; Thermodynamic functions; Solution reaction calorimetry
1. Introduction The caesium–magnesium monophosphate belongs to the family of mixed phosphates with a general formula AIBIIPO4 (AI = monovalent metal; BII = divalent metal with a tetrahedral coordination) frequently adopting a bSiO2 tridymite structure [1]. The compounds of this family have been studied because of their ferroelectric properties [2–4]. CsMgPO4 has also been studied as a prospective candidate for the immobilization of the radiocaesium from nuclear wastes and a solid host for a 137Cs c-radiation source to be used in medical applications [5]. Despite the fact that phosphates of this type could have promising applications, their thermodynamic properties have practically not been studied up to now. Only data on the heat capacity of the crystalline phosphates CsZnPO4 and TlBePO4 over the ranges from T = (6 to 300) K [6] and T = (973 to 1323) K [4], respectively, and their phase transition temperatures occurring in condensed state [4,7,8] are available.
*
Corresponding author. Tel.: +7 83124656206; fax: +7 83124345056. E-mail address: [email protected] (V.I. Pet’kov).
0021-9614/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2007.11.001
The goal of the present work is to measure calorimetrically the heat capacity of the crystalline phosphate CsMgPO4 over the range T = (7 to 650) K at standard pressure (p = 0.1 MPa) and to determine the standard entropy of formation at T = 298.15 K. Using a nitric acid solution, calorimetric measurements and the thermodynamic cycle are proposed to calculate the enthalpy of reaction for the CsMgPO4 synthesis at T = 298.15 K and to obtain the thermochemical parameters of formation of CsMgPO4 at temperature T = 298.15 K and standard pressure. From the heat capacity measurements, the fractal dimension is determined for the crystalline phosphate in the range from (20 to 45) K. 2. Experimental The sample of phosphate CsMgPO4 was synthesized using the following procedure from the reagents provided by REACHEM [9]. Stoichiometric amounts of starting materials, high purity CsCl (mass fraction = 0.9999) and MgO (mass fraction purity = 0.9995), were previously dissolved in dilute HCl solution. Then an aqueous solution of high purity NH4H2PO4 (mass fraction 0.9995) taken in accordance with the stoichiometry of the phosphate was
654
E.A. Asabina et al. / J. Chem. Thermodynamics 40 (2008) 653–660
dropped into this mixture under stirring at room temperature. The reaction mixture was dried at T = 353 K, thermally treated in unconfined air access at T = (873 and 973) K with a 24 h plateau at each step. The thermal treatment stages were alternated with careful grinding. The obtained sample was a colourless polycrystalline powder. Confirmation of the desired compound, caesium– magnesium monophosphate, was obtained on a XRD-6000 diffractometer (Cu Ka) in the 2h range of (10° to 60°). A single phase was observed having the monoclinic structure (space group P21/a, a = 965.1(4) pm, b = 552.8(3) pm, c = 893.2(4) pm, b = 90.27(2)°) in agreement with the results [5]. The homogeneity and chemical composition of the sample were checked by electron microprobe analysis on a CamScan MV-2300 device with a Link INCA ENERGY 200C energy-dispersion detector operated at 20.0 kV. The results of electron microscopy showed the homogeneity of the sample. Microprobe analysis indicated the following average mass fractions Cs, 52.84%; Mg, 9.54%; P, 12.24%; O, 25.38% (table 1) and confirmed the stoichiometry of the sample to be close to the theoretical composition CsMgPO4 (Cs, 52.70%; Mg, 9.64%; P, 12.28%; O, 25.38%). There were no substantial impurities (within 0.5%) of other elements in the sample. The chemical composition of the sample was also confirmed by chemical analysis. A known mass of the sample was dissolved in the HNO3 aqueous solution. The caesium mass content, determined by atomic absorption method on a Perkin–Elmer device, was found to be 52.75%. The magnesium mass content, determined titrimetrically with EDTA following the procedure [10], was found to be 9.66% The phosphorus mass content, found to be 12.31%, was determined colorimetrically on a SF-46 spectrophotometer according to the method employing solutions of ammonia vanadate and ammonia molybdate [10]. Thus results of analyses proves that the stoichiometry CsMgPO4 is close to ideal. The heat capacity of the sample of CsMgPO4 over the range from T = (7 to 352) K was measured with a BCT-3 low-temperature adiabatic vacuum calorimeter with an automatic system to maintain adiabatic conditions during measurements. Its design and operational procedure were similar to those in reference [11]. The (iron + rhodium)
TABLE 1 Electron microprobe results (mass fraction w) on the calorimetric sample of caesium–magnesium monophosphate Sample sites of scanning
Cs
Mg
1 2 3 4 5
52.80 52.94 52.88 52.73 52.86
9.60 9.47 9.51 9.55 9.56
P
O
12.21 12.31 12.19 12.23 12.25
25.39 25.28 25.42 25.49 25.33
w/%
Actual composition is w(Cs) = 52.84%; w(Mg) = 9.54%; w(P) = 12.24%; w(O) = 25.38%.
resistance thermometer (R0 = 100 X) was calibrated on the basis of ITS-90. The reliability of the calorimetric operation was tested by measuring the heat capacities of highly purified copper (OSCh11-4), standard synthetic corundum [12], and K-1 benzoic acid [12] prepared at the metrological institutions of the State Standard Committee of the Russian Federation. It was established that the apparatus and the measurement procedure allowed us to obtain the C p;m values of the substances in the crystalline state with an uncertainty of not more than 2% from T = (7 to 10) K, 0.5% between T = (10 and 40) K, and within 0.2% in the range from T = (40 to 352) K. An automated dynamic calorimeter (ADCTTB) operating by the principle of triple thermal bridge was used to measure the heat capacity over the temperature range from (330 to 650) K. The apparatus design and operational procedure were reported elsewhere [13,14]. The accuracy of the calorimetric data was checked by measuring the heat capacities of standard synthetic corundum and highly purified copper at the temperatures and enthalpies of melting the standard samples [12] of indium, tin, and lead, also prepared at the metrological institutions of the State Standard Committee of the Russian Federation. The uncertainty in the measurements of C p;m over the temperature interval noted above was about 1.5%, for the transition temperatures 0.3 K and for the transition enthalpies 0.8%. However, the heat capacity of the sample over the temperature range from (330 to 352) K was also measured in the low-temperature adiabatic vacuum calorimeter with an uncertainty 0.2% and the conditions of measurements on the dynamic calorimeter were selected in the way that the C p;m values obtained by using these calorimeters coincided. It was assumed that at T > 352 K the uncertainty of the measurements of C p;m was (0.5–1.5)%. The crystalline sample of CsMgPO4 (mass, 1.1323 g) was placed in a 1.5 cm3 thin-wall cylindrical titanium vessel of the low-temperature adiabatic vacuum calorimeter. The measurements of C p;m were made between T = (7 and 352) K. The 172 experimental C p;m values were obtained for the three series reflecting the sequence of the heat capacity measurements (table 2). The calorimetric vessel contained 0.3537 g of CsMgPO4 and the heat capacity of the sample between T = (330 and 650) K (table 2) was measured by continuous heating at a mean rate of 2 K min1. The heat capacity of the sample itself was between (60 and 70)% of the total heat capacity of (the calorimetric vessel + the sample) over the temperature interval between (7 and 650) K. Averaging of the experimental C p;m points was carried out by means of power and semilogarithmic polynomials. The root-mean-square deviation of the experimental values from the corresponding smoothed curve C p;m ¼ f ðT Þ did not exceed 0.14% in the range from T = (7 to 40) K, 0.08% between T = (40 and 90) K, 0.04% from T = (90 to 330) K, and 0.15% at temperatures from T = (330 to 650) K. An automated isothermal differential Calvet-type microcalorimeter (DAC-1-1-A) was employed to measure the
E.A. Asabina et al. / J. Chem. Thermodynamics 40 (2008) 653–660 TABLE 2 Experimental molar heat capacities C p;m =R of CsMgPO4 (M = 252.1818 g mol1; R = 8.314472 J K1 mol1) T/K 7.22 7.30 7.96 8.00 8.70 9.40 10.09 10.42 11.01 11.69 12.40 13.07 13.90 14.63 15.35 16.06
C p;m =R 0.115 0.118 0.147 0.149 0.191 0.238 0.289 0.321 0.3752 0.4378 0.5051 0.5653 0.6485 0.7252 0.8065 0.8912
C p;m =R
T/K
Series 1 16.84 0.9886 17.45 1.067 18.81 1.250 19.49 1.341 20.16 1.436 21.16 1.580 22.91 1.840 25.31 2.187 27.75 2.510 30.21 2.824 32.69 3.118 35.16 3.400 37.64 3.670 40.12 3.926 42.60 4.172 45.08 4.407
7.049 7.224 7.391 7.548 7.704 7.858 8.009 8.157 8.304 11.02 11.14 11.27 11.40 11.55 11.68 11.82 11.95 12.08 12.21 12.34 12.45 12.58 12.69 12.82 12.97 13.10 13.22 13.38 13.59 13.82 14.06 14.81 15.54
Series 109.68 112.63 115.80 118.91 121.88 124.84 127.80 130.76 133.72 238.55 241.43 244.43 247.38 249.90 253.01 255.80 258.57 261.33 264.07 266.89 269.63 272.18 274.85 277.49 280.12 282.50 285.44 287.80 289.70 292.80 294.90 297.00 298.84
2
82.70 85.90 88.99 91.95 94.91 97.87 100.82 103.77 106.72 163.60 166.37 169.34 172.31 175.74 178.73 182.05 185.19 188.17 191.40 194.30 197.16 200.16 202.86 205.98 208.94 211.90 214.59 217.64 221.10 224.11 226.99 232.75 235.69
12.54 12.66 12.78 12.93 13.06 13.18 13.34 13.55 13.76
Series 226.53 232.40 235.70 237.89 240.77 243.77 246.72 249.24 252.35
3
199.50 202.40 205.51 208.48 211.44 214.13 217.18 220.64 223.65
T/K
C p;m =R
47.57 52.52 54.99 57.47 59.95 61.64 63.99 67.48 71.15 74.82 78.48 82.15 85.82 89.49
4.637 5.050 5.247 5.440 5.625 5.747 5.909 6.141 6.375 6.597 6.811 7.018 7.221 7.417
8.452 8.601 8.755 8.907 9.053 9.199 9.345 9.489 9.632 15.02 14.54 14.23 14.03 13.91 13.82 13.80 13.81 13.84 13.88 13.93 13.97 14.03 14.10 14.17 14.23 14.29 14.36 14.41 14.47 14.55 14.61 14.66 14.71
136.69 139.65 142.62 145.59 148.56 151.53 154.50 157.60 160.43 300.67 303.29 305.91 308.00 310.09 312.40 314.71 316.36 318.00 321.10 324.20 325.30 326.40 329.66 332.91 333.99 335.08 338.20 341.80 343.40 345.83 348.25 350.05 351.85
9.775 9.916 10.06 10.20 10.34 10.48 10.61 10.75 10.88 14.76 14.83 14.90 14.96 15.01 15.08 15.14 15.18 15.22 15.30 15.39 15.42 15.45 15.53 15.60 15.62 15.65 15.71 15.78 15.82 15.87 15.93 15.96 16.00
13.99 14.74 15.53 15.17 14.64 14.29 14.06 13.93 13.84
255.27 257.91 260.67 263.41 266.23 268.97 271.52 274.19 276.83
13.80 13.81 13.83 13.87 13.91 13.96 14.01 14.08 14.15
655
Table 2 (continued) T/K
C p;m =R
T/K
330.5 334.4 338.3 342.2 346.1 350.0 353.9 357.8 361.7 365.5 369.2 372.9 376.6 380.2 383.7 387.2 390.7 394.2 397.7 401.3 404.8 408.5 412.1 415.8 419.6 423.3 427.0 430.6 434.3
15.5 15.6 15.7 15.8 15.9 16.0 16.0 16.1 16.2 16.3 16.4 16.4 16.5 16.6 16.6 16.7 16.8 16.9 16.9 17.0 17.0 17.1 17.2 17.2 17.3 17.4 17.5 17.5 17.6
437.9 441.6 445.2 448.8 452.5 456.1 459.8 463.4 467.1 470.7 474.4 478.1 481.8 485.4 489.1 492.7 496.4 500.0 503.7 507.3 511.0 514.6 518.3 521.8 525.4 529.0 532.6 536.1 539.8
a
C p;m =R Series 4a 17.6 17.7 17.8 17.8 17.9 17.9 18.0 18.1 18.1 18.2 18.2 18.3 18.3 18.4 18.5 18.5 18.6 18.6 18.7 18.7 18.8 18.8 18.9 18.9 19.0 19.0 19.1 19.1 19.2
T/K
C p;m =R
543.3 546.9 550.5 554.1 557.7 561.4 565.0 568.7 572.4 576.1 579.8 583.4 587.1 590.7 594.3 597.9 603.4 607.0 610.6 614.2 617.7 621.4 625.0 628.6 632.3 636.0 639.7 643.3 648.9
19.2 19.3 19.3 19.4 19.4 19.5 19.5 19.6 19.6 19.7 19.7 19.8 19.8 19.9 19.9 20.0 20.0 20.1 20.1 20.2 20.2 20.2 20.3 20.3 20.4 20.4 20.5 20.5 20.6
This Series presents every second experimental value of heat capacity.
enthalpies of solution at T = 298.15 K. Its design and operation have already been described [15]. For calibration, a known current was passed through the cell-assembly heater over a specified time. The reliability of the calorimeter operation was tested in experiments on the solution of high-purity KCl in bi-distilled water. The value for the standard enthalpy of solution obtained by us Dsol H m ð298:15Þ ¼ ð17:6 0:4Þ kJ mol1 (average of 10 experiments) was in agreement with the published value Dsol H m ð298:15Þ ¼ ð17:58 0:34Þ kJ mol1 [16]. The enthalpies (Dr H m ) of the reactions studied at T = 298.15 K are averages of (5 to 7) replicates. In conformity with IUPAC recommendations [17], the uncertainty in DrH is given as a standard deviation of the average. The net uncertainty in the 1=2 enthalpy of formation was evaluated as r ¼ ðRi r2i Þ , where ri represents the uncertainty in a single measurement. 3. Results and discussion 3.1. Heat capacity and phase transition The experimental values of the molar heat capacity of CsMgPO4 between T = (7 and 650) K and the smoothed curve C p;m ¼ f ðT Þ are shown in figure 1. It is seen that a solid-to-solid phase transition appears over the temperature
656
E.A. Asabina et al. / J. Chem. Thermodynamics 40 (2008) 653–660
C p;m ¼ 120:04 þ 6:45435T 1:034267 101 T 2 þ 9:28663
E
104 T 3 4:59517 106 T 4 þ 1:18379 108 T 5
cr I
C op,m /(J⋅ mol-1⋅ K -1 )
150
1:24119 1011 T 6 :
C D B 100 cr II
15
15
10
10
5
50
0
A
0
5
0
200
10
400
20
600
T/K FIGURE 1. Plot of heat capacity against temperature dependence for crystalline CsMgPO4.
interval from (209 to 270) K. The analogous phase transition was found in [8] for the tridymite structure-type phosphate CsZnPO4. In [6], the transition of the Zncontaining sample was detected as the broad anomaly on the heat capacity curve with a maximum around T = 220 K. It was suggested [6] that this transition should proceed with an extremely heterogeneous nucleation process. It was accompanied by a step increase in lattice parameters, its volume and absorption of a quantity of heat, and so, it was characterized as a first-order phase transition. The phase transition of CsMgPO4 was reproduced on repeated cooling and heating (table 2). The temperature corresponding to the maximum value of the apparent heat capacity in the transition range from (209 to 270) K at first heating of the sample (C p;m ¼ 129:2 J mol1 K1 ), is regarded as the transition temperature for CsMgPO4, T trs ¼ ð235:69 0:03Þ K. The enthalpy of the solid-to-solid phase transition Dtrs H m ¼ ð0:2713 0:0025Þ kJ mol1 , was obtained graphically for the area BCDB (figure 1). The values of entropy of the first-order phase transition, calculated by integrating the C p;m =T ¼ f ðT Þ dependence and by formula Dtrs S m ¼ Dtrs H m =T trs , coincided within the uncertainty of experiment and amounted to (1.15 ± 0.01) J mol1 K1. The temperature dependence of the heat capacity does not exhibit any peculiarity. Below T = 209 K (crystal II, section AB on curve) and above 270 K (crystal I, section DE on curve), it gradually increases as the temperature rises. For example, over the temperature range (50 to 100) K the heat capacity of CsMgPO4 is described by the equation: C p;m ¼ 22:97 þ 2:349T 4:098 102 T 2 þ 6:436 104 T 3 7:081 106 T 4 þ 4:427 108 T 5 1:141 1010 T 6 ; and over the range (100 to 200) K by the equation:
In the above given equations, the C p;m is in J mol1 K1 and T is in Kelvin. In view of a development of models describing the temperature dependence of heat capacity, it was of interest to evaluate the fractal dimension Dfr for the crystalline phosphate CsMgPO4. In the fractal theory of heat capacity [18– 20] of solids, Dfr is the exponent at T in the C v;m ¼ f ðT Þ function. The significance of Dfr value for solids gives information on the topology of their structure. The relation ‘‘heat capacity versus T” is proportional to T1 in the lower temperature range for chain-structured bodies, T2 for solids with layer structure and it is proportional to T3 in the case of spatial structure. We have assumed that C p;m ¼ C v;m at T < 45 K. From the ln C p;m versus ln T plot, it is found that at temperatures between (20 and 45) K the Dfr = 3, Hmax = 126.5 K for CsMgPO4, within an uncertainty of 1.6%. This means that crystalline CsMgPO4 has a spatial (three-dimensional) structure. At lower temperatures, in order to calculate the thermodynamic functions (table 3) the heat capacity of CsMgPO4 was described by Debye function, C p;m T 3 : C p;m ¼ nDðHD =T Þ; where D denotes the Debye heat capacity function, n = 3 and HD = 92.16 K are specially selected parameters. With those values, the given equation describes the experimental values of C p;m over the range from (7 to 11) K within an uncertainty of about 1.8%. While calculating the thermodynamic functions, it was assumed that, at T < 7 K, this equation reproduces the C p;m values almost with the same accuracy. 3.2. Thermodynamic functions The thermodynamic functions of crystalline CsMgPO4 were calculated from the C p;m ðT Þ curve over the range from (0 to 650) K. The enthalpies DT0 H m and entropies DT0 S m were calculated by using the following equations: Z T trs Z T C p;m ðT Þ dT þ Dtrs H m þ C p;m ðT Þ dT ; DT0 H m ¼ DT0 S m
¼
Z
T trs
0 T trs
C p;m ðT Þ d ln T
0
þ
Dtrs S m
þ
Z
T T trs
C p;m ðT Þ d ln T :
The functions Um ðT Þ were found from the corresponding values of DT0 H m and DT0 S m and by the equation: Um ¼ DT0 S m DT0 H m =T : The smoothed heat capacities C p;m =R and derived thermodynamic functions of the investigated phosphate are given in table 3. It is suggested that the uncertainty of
E.A. Asabina et al. / J. Chem. Thermodynamics 40 (2008) 653–660 TABLE 3 Thermodynamic functions of CsMgPO4 (M = 252.1818 g mol1); R = 8.314472 J K1 mol1; C p;m , standard molar heat capacity; DT0 H m , standard molar enthalpy; DT0 S m , standard molar entropy; and Um ¼ DT0 S m DT0 H m =T ðp ¼ 0:1 MPaÞ T/K
C p;m =R
DT0 H m =RT
DT0 S m =R
5 10 15 20 25 30 35 40 45 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 235.69
0.0383 0.2850 0.7661 1.415 2.145 2.796 3.383 3.916 4.401 4.845 5.630 6.303 6.898 7.445 7.967 8.468 8.962 9.451 9.933 10.40 10.86 11.30 11.73 12.16 12.57 12.98 13.38 13.78 14.00
Crystal II 0.00962 0.07337 0.2133 0.4312 0.7009 0.9971 1.297 1.591 1.877 2.152 2.668 3.140 3.574 3.974 4.347 4.699 5.034 5.355 5.665 5.965 6.257 6.541 6.817 7.087 7.351 7.609 7.863 8.111 8.251
0.0128 0.09867 0.2912 0.5980 0.9924 1.443 1.919 2.406 2.896 3.383 4.338 5.257 6.139 6.983 7.795 8.578 9.336 10.07 10.79 11.49 12.18 12.85 13.51 14.15 14.79 15.41 16.02 16.63 16.97
235.69 240 250 260 270 280 290 298.15 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500
16.06 13.24 13.49 13.74 13.99 14.23 14.47 14.69 14.74 15.01 15.28 15.54 15.75 15.96 16.2 16.4 16.6 16.8 17.0 17.1 17.3 17.5 17.7 17.8 18.0 18.2 18.3 18.5 18.6
Crystal I 8.389 8.475 8.671 8.861 9.046 9.227 9.404 9.545 9.577 9.748 9.917 10.08 10.25 10.41 10.6 10.7 10.9 11.0 11.2 11.3 11.4 11.6 11.7 11.9 12.0 12.1 12.2 12.4 12.5
17.11 17.34 17.89 18.42 18.95 19.11 19.46 19.96 20.37 20.46 20.95 21.43 21.90 22.37 22.8 23.3 23.7 24.2 24.6 25.0 25.4 25.9 26.3 26.7 27.1 27.5 27.9 28.2 28.6
Um =R 0.00320 0.02523 0.07807 0.1670 0.2914 0.4462 0.6223 0.8148 1.019 1.231 1.670 2.117 2.565 3.009 3.447 3.878 4.302 4.717 5.126 5.527 5.921 6.309 6.691 7.067 7.437 7.802 8.162 8.517 8.717
8.717 8.869 9.219 9.563 9.901 9.762 9.880 10.27 10.76 10.53 10.85 11.16 11.47 11.78 12.1 12.4 12.7 13.0 13.2 13.5 13.8 14.1 14.4 14.6 14.9 15.1 15.4 15.7 15.9
657
Table 3 (continued) T/K
C p;m =R
DT0 H m =RT
DT0 S m =R
Um =R
510 520 530 540 550 560 570 580 590 600 610 620 630 640 650
18.8 18.9 19.1 19.2 19.3 19.5 19.6 19.7 19.9 20.0 20.1 20.2 20.3 20.5 20.6
12.6 12.7 12.9 13.0 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 14.0 14.1
29.0 29.4 29.7 30.1 30.5 30.8 31.2 31.5 31.8 32.2 32.5 32.8 33.2 33.5 33.8
16.2 16.4 16.7 16.9 17.2 17.4 17.6 17.9 18.1 18.3 18.6 18.8 19.0 19.2 19.5
the function values lie within 2% at T < 10 K, between (0.5 and 0.7)% at temperatures from (10 to 40) K, 0.3% from (40 to 330) K, and between (0.5 and 1.6)% from (330 to 650) K. 3.3. Thermochemical parameters of formation As a part of the thermodynamic description of the CsMgPO4, we estimated the standard thermochemical parameters of its formation at T = 298.15 K. K Using the standard entropy D298:15 S m ðCsMgPO4 ; 0 1 1 crÞ ¼ 169:3 J K mol and reference data [22] on the absolute entropy of the constituent simple substances (table 4), we calculated the standard molar entropy of formation Df S m ðCsMgPO4 ; cr;298:15KÞ ¼ ð400:0 0:7Þ J K1 mol1 . To derive the standard enthalpy of formation of the phosphate investigated, we used the thermodynamic cycle by considering the enthalpy of reaction of CsMgPO4 with nitric acid. Table 5 lists the mean values with twice standard deviations of the mean of the independent determinations taken of the molar enthalpies of reaction of the stoichiometric amounts of the reactants and products required for the determination of the Dr H 7 . According to our experimental data, reactions numbers 1 to 6 in table 5 refer to true solutions. So we can, without analyzing the nature of the products, sum up the reaction numbers 1 to 6 with the corresponding signs to obtain the
TABLE 4 Absolute entropies of the simple substances necessary to calculate the standard entropy of formation of CsMgPO4 at T = 298.15 K Substance
Physical statea
D298:15 S m =ðJ K1 mol1 Þ 0
Cs Mg P O2
cr cr cr g
85.23 ± 0.40 32.67 ± 0.10 41.09 ± 0.25 205.152 ± 0.005
a
cr, crystalline; g, gaseous.
658
E.A. Asabina et al. / J. Chem. Thermodynamics 40 (2008) 653–660
TABLE 5 Experimental scheme for the calculation of enthalpy of reaction of CsMgPO4 synthesis Dr H m ð298:15Þ obtained from Hess cycle: Dr H 7 ¼ Dr H 1 þ Dr H 2 þ Dr H 3 Dr H 4 Dr H 5 þ Dr H 6 DrH(298.15)/(kJ mol1)
Reaction 1. 2. 3. 4. 5. 6. 7.
17.0 ± 1.0 CsNO3(cr) + 143.6[HNO3 5.55.2 H2O](sln 1) = CsNO3 143.6HNO3 797.3H2O(sln 2) Mg(NO3)2 6H2O(cr) + sln 2 = CsNO3 Mg(NO3)2 143.6HNO3 803.3H2O (sln 3) 31.4 ± 0.6 15.18 ± 0.16 NH4H2PO4(cr) + sln 3 = CsNO3 Mg(NO3)2 H3PO4 NH4NO3 142.6HNO3 803.3H2O(sln 4) CsMgPO4(cr) + 145.6[HNO3 5.55.2H2O](sln 1)=CsNO3 Mg(NO3)2 H3PO4 14 2.6HNO3 808.4H2O(sln 5) 106 ± 3 NH4NO3(cr) + sln 5 = CsNO3 Mg(NO3)2 H3 PO4 NH4NO3 142.6HNO3 808.4H2O(sln 6) 16.7 ± 0.3 5.1(0.89 ± 0.29) 5.1H2O(l) + sln 4 = sln 6 CsNO3(cr) + Mg(NO3)2 6H2O(cr) + NH4H2PO4(cr) + 5.1H2O(l) = CsMgPO4(cr) + NH4NO3(cr) + 2[HNO3 5.55.2H2O] 148 ± 4 (sln 1)
reaction scheme of CsMgPO4 synthesis (reaction 7 = reaction 1 + reaction 2 + reaction 3 reaction 4 reaction 5 + reaction 6) and to calculate the enthalpy of this reaction. All the enthalpies of determined reactions are collected in tables 6 to 11. The standard molar enthalpy of formation of CsMgPO4 was obtained from the equation:
TABLE 6 Calorimetric results for the reaction of CsNO3 with HNO3 5.55.2H2Oa,b Experiment
m(CsNO3)
1 2 3 4 5 6
DrH
Q
g
J
Jg
kJ mol1
0.031085 0.030810 0.031000 0.030880 0.030905 0.030980
2.7105 2.5818 2.7211 2.6017 2.6585 2.6034
88.64 85.26 89.23 85.71 87.47 85.48
17.3 16.6 17.4 16.7 17.0 16.7
TABLE 7 Calorimetric results for the reaction of Mg(NO3)2 6H2O with CsNO3 143.6HNO3 797.3H2O
1 2 3 4 5 6
m(Mg(NO3)2 6H2O)
Q
Experiment
1 2 3 4 5 6 7 a
of
NH4H2PO4
with
m(NH4H2PO4)
Q
DrH
Dr H m a
g
J
J g1
kJ mol1
0.018305 0.018255 0.018510 0.018505 0.018015 0.018250 0.018215
2.3593 2.3775 2.4315 2.3577 2.3422 2.3344 2.3861
131.34 132.70 133.79 129.84 132.51 130.37 133.46
15.11 15.26 15.39 14.93 15.24 15.00 15.35
The molar mass of NH4H2PO4 was taken to be 115.0255 g mol1.
Dr H m c
1
a The symbols in table denote the following: m(CsNO3) is the mass of CsNO3 in the experiments; Q is the quantity of energy released from calorimetric system during the process investigated; DrH is the enthalpy of reaction per unit mass of the sample which includes a combined correction of 0.0449 J for the enthalpies of the sample forced out into the HNO3 solution, of the reaction of paraffin with the solution, of stirring of the reaction mixture and of solvent vaporization; Dr H m is the molar enthalpy of reaction investigated. b In each experiment 3.00 cm3 of HNO3 solution was used. The mean temperature of each experiment was 298.15 K. c The molar mass of CsNO3 was taken to be 194.9103 g mol1.
Experiment
TABLE 8 Calorimetric results for the reaction CsNO3 Mg(NO3)2 143.6HNO3 803.3H2O
DrH
Dr H m a
g
J
Jg
kJ mol1
0.041260 0.040680 0.040875 0.040885 0.040795 0.041010
5.0570 4.8618 4.8807 4.9497 5.0166 5.0511
123.7 120.6 120.5 122.2 124.1 124.3
31.7 30.9 30.9 31.3 31.8 31.9
1
a The molar mass of Mg(NO3)2 6H2O was taken to be 256.4060 g mol1.
TABLE 9 Calorimetric results for the reaction of CsMgPO4 with HNO3 5.55.2H2O Experiment
1 2 3 4 5 6 7 a
m(CsMgPO4)
Q
DrH
Dr H m a
g
J
J g1
kJ mol1
0.039995 0.040210 0.040140 0.040105 0.040155 0.040115 0.040160
17.1321 17.0151 16.7583 17.0282 16.7380 17.1088 16.6433
427.2 422.0 416.4 423.5 415.7 425.4 413.3
108 106 105 107 105 107 104
The molar mass of CsMgPO4 was taken to be 252.1818 g mol1.
TABLE 10 Calorimetric results for the reaction of CsNO3 Mg(NO3)2 H3PO4 142.6HNO3 808.4H2O Experiment
1 2 3 4 5 a
NH4NO3
with
m(NH4NO3)
Q
DrH
Dr H m a
g
J
J g1
kJ mol1
0.012795 0.012785 0.012835 0.012960 0.012820
2.6661 2.6163 2.6057 2.6223 2.6528
211.9 208.2 206.5 205.8 210.4
17.0 16.7 16.5 16.5 16.8
The molar mass of NH4NO3 was taken to be 80.0432 g mol1.
Dr H 7 ¼ Df H m ðCsMgPO4 ; cr;298:15Þþ Df H m ðNH4 NO3 ; cr;298:15Þ þ 2Df H m ðHNO3 5:55 2H2 O; sol;298:15Þ Df H m ðCsNO3 ; cr;298:15Þ Df H m ðMgðNO3 Þ2 6H2 O; cr;298:15Þ Df H m ðNH4 H2 PO4 ; cr;298:15Þ 5:1Df H m ðH2 O; l;298:15Þ
E.A. Asabina et al. / J. Chem. Thermodynamics 40 (2008) 653–660 TABLE 11 Calorimetric results for the reaction of H2O Mg(NO3)2 H3PO4 NH4NO3 142.6HNO3 803.3H2O Experiment
1 2 3 4 5 a
m(H2O)
Q
CsNO3
with
DrH 1
Dr H m a 1
659
TABLE 13 Standard thermodynamic functions of the reaction of CsMgPO4 solidstate synthesis; ðDnC p;m Þ ¼ 20:8 J mol1 K1 Dr S m
Dr H m
T
1
Dr Gm 1
g
J
Jg
kJ mol
K
kJ mol
J mol
0.017465 0.019180 0.023665 0.019960 0.021820
0.9323 0.9500 1.2254 1.0451 1.0884
50.8 47.2 49.9 50.1 47.8
0.92 0.85 0.90 0.90 0.86
298.15 350 400 430 500 550 600
278.9 277.9 276.8 276.2 274.7 273.7 272.7
580.1 576.8 574.0 572.5 569.3 567.4 565.6
The molar mass of H2O was taken to be 18.0152 g mol1.
K1
kJ mol1 106.0 76.0 47.2 30.0 9.9 38.4 66.7
and literature data [21,22] collected in table 12. Its value: Df H m ðCsMgPO4 ; cr;298:15Þ ¼ Dr H 7 Df H m ðNH4 NO3 ; cr;298:15Þ 2Df H m ðHNO3 ; sol5:55 2H2 O;298:15Þ 6Df H m ðH2 O; l;298:15Þþ Df H m ðCsNO3 ; cr;298:15Þþ Df H m ðMgðNO3 Þ2 6H2 O; cr;298:15Þþ Df H m ðNH4 H2 PO4 ; cr;298:15Þ ¼ ð1931 5Þ kJ mol1 :
Combination of the enthalpy of formation of CsMgPO4 with its entropy of formation allowed us to calculate the standard molar Gibbs function of formation, Df Gm ðCsMgPO4 ; cr;298:15 KÞ ¼ ð1812 5Þ kJ mol1 . The logarithmic value of the formation reaction constant for CsMgPO4 was calculated from the value Df Gm by the following equation: lg K f;m ¼ Df Gm =½2:303R 298:15ðKÞ ¼ 317. The values of the thermodynamic parameters of formation obtained correspond to the process CsðcrÞ þ MgðcrÞ þ Pðcr; whiteÞ þ 2O2 ðgÞ ¼ CsMgPO4 ðcrÞ: Taking into account the usage of tridymite-like compounds in medical and other applications, we analyzed the conditions of CsMgPO4 formation by the reaction of solid-state synthesis:
TABLE 12 Enthalpies of formation substances necessary to calculate the standard enthalpies of formation of CsMgPO4 at T = 298.15 K Substance
Physical statea
Df H m =kJ mol1
CsNO3 Mg(NO3)2 6H2O NH4H2PO4 H2O NH4NO3 HNO3 b
cr cr cr l cr sol
505.720 ± 0.585 2614.665 ± 1.338 1445.572 ± 2.552 285.830 ± 0.040 365.430 ± 0.418 203.4 ± 0.5
CsClðcrÞ þ MgCl2 ðcrÞ þ NH4 H2 PO4 ðcrÞ ¼ CsMgPO4 ðcrÞ þ NH3 ðgÞ þ 3HClðgÞ: The standard enthalpy and entropy of the reaction at T = 298.15 K were calculated from the standard enthalpy of formation of CsMgPO4 together with its absolute entropy and literature data [21,22]. The standard thermodynamic functions of the synthesis reaction at higher temperatures (table 13) were found from the equations: Dr H m ðT Þ ¼ Dr H m ð298:15Þ þ DnC p;m ðT 298:15Þ; Dr S m ðT Þ ¼ Dr S m ð298:15Þ þ DnC p;m lnðT =298:15Þ; by assuming that the algebraic sum of heat capacities of reagents DnC p;m is constant over the temperature interval from 298.15 K to T. It is seen that the reaction of synthesis at T = 298.15 K is characterized by a positive Gibbs function value. The theoretical temperature of CsMgPO4 synthesis was found as the temperature at which Dr Gm changes sign from positive to negative. The derived temperature was not high: T 483 K. This is the reason why ceramic technology is one of the commonly used methods for such phosphates synthesis. 4. Conclusion The general aim of this investigation was to report the results of the complex thermodynamic study of the CsMgPO4 compound belonging to the vast family of solids with a tridymite structure. The heat capacity of this phosphate was measured over the temperature range from (7 to 650) K, the thermodynamic functions C p;m =R; DT0 H m =RT , DT0 S m =R, and Um =R calculated and the fractal dimension Dfr evaluated. Thermochemical parameters of formation Df H m , Df S m , Df Gm and lg K f;m were determined by combining the data obtained by using solution reaction calorimetry and heat capacity measurements. The theoretical temperature of CsMgPO4 solid-state synthesis was evaluated. Acknowledgements
a
cr, crystalline; sol, solution, l, liquid. The value of Df H m corresponds to HNO3 in the solution of composition HNO3 5.55.2H2O. b
This research was supported by the Russian Foundation for Basic Research (Project Nos. 08-03-00082, 08-03-
660
E.A. Asabina et al. / J. Chem. Thermodynamics 40 (2008) 653–660
00485) and National Project ‘‘Education” of innovational educational program of NNSU. References [1] [2] [3] [4] [5]
[6] [7] [8] [9] [10]
R. Masse, A. Durif, J. Solid State Chem. 73 (1988) 468–472. D. Blum, J.C. Peuzin, J.Y. Henry, Ferroelectrics 61 (1984) 265–279. B. Elouadi, L. Elamnari, J. Ravez, Ferroelectrics 56 (1984) 17–20. G. Wallez, S. Jaulmes, A. Elfakir, M. Quarton, J. Phys. III France 4 (1994) 1197–1204. A.R. Zaripov, O.M. Slunchev, V.A. Orlova, D.D. Galouzin, P.V. Sizov, S.I. Rovny, V.I. Pet’kov, Radiat. Saf. Probl. 2 (2006) 18–28 (in Russian). I. Yamashita, T. Tojo, H. Kawaji, T. Atake, Phys. Rev. B 65 (2002) 212104. D. Blum, A. Durif, M.T. Averbuch-Pouchot, Ferroelectrics 69 (1986) 283–292. A. Sawada, T. Azumi, Y. Kuroiwa, Ferroelectrics 237 (2000) 245– 252. Chemical reagents and high-pure chemicals. Catalog, Khimia, Moscow, 1990 (in Russian). F. Umbland, A. Janssen, D. Thierig, G. Wu¨nsch (Eds.), Theorie und praktisch anwendung von komplexbildnern, Akademisch verlagsgesellschaft, Frankfurt Am Main, 1971.
[11] R.M. Varuschenko, A.I. Druzhinina, E.L. Sorkin, J. Chem. Thermodyn. 29 (1997) 623–637. [12] O.M. Sergeev (Ed.), Metrological Principles of Thermophysical Measurements, Standard Publisher, Moscow, 1972 (in Russian). [13] M. Yagfarov, Sh. Zh. Fiz. Khim. 43 (1969) 1620–1625 (in Russian). [14] A.G. Kabo, V.V. Diky, Thermochim. Acta 347 (2000) 79–84. [15] E. Calvet, H. Prat (Eds.), Microcalorimetrie: Applications Physicochimiques et Biologicules, Masson, Paris, 1956. [16] V.P. Glushko (Ed.), Thermal Constants of Substances, Issue 10, VINITI, Moscow, 1981 (in Russian). [17] F.D. Rossini, in: F.D. Rossini (Ed.), Experimental Thermochemistry, vol. 1, Interscience, New York, 1956 (Chapter 14). [18] T.S. Yakubov, Docl. Akad. Nauk SSSR 310 (1990) 145–149 (in Russian). [19] A.D. Izotov, O.V. Shebershneva, K.S. Gavrichev, in: Proceedings of the all Russian Conference on Thermal Analysis and Calorimetry, Kazan, 1996, 200–202 (in Russian). [20] V.B. Lazarev, A.D. Izotov, K.S. Gavrichev, O.V. Shebersheneva, Thermochim. Acta 269–270 (1995) 109–116. [21] J.D. Cox, D.D. Wagman, V.A. Medvedev (Eds.), CODATA Key Values for Thermodynamics, Hemisphere, New York, 1989. [22] V.P. Glushko (Ed.), Thermal Constants of Substances, Issues 1–9, Nauka, Moscow, 1965 (in Russian).
JCT 07-245