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The vapour pressures of saturated aqueous solutions of magnesium, calcium, nickel and zinc acetates and molar enthalpies of solution of magnesium, calcium, zinc and lead acetates
J. Chem. Thermodynamics 2001, 33, 113–120 doi:10.1006/jcht.2000.0731 Available online at http://www.idealibrary.com on
The vapour pressures of saturated aqueous solutions of magnesium, calcium, nickel and zinc acetates and molar enthalpies of solution of magnesium, calcium, zinc and lead acetates Alexander Apelblata and Eli Korin Department of Chemical Engineering, Ben Gurion University of the Negev, Beer Sheva, Israel
Vapour pressures of water over saturated solutions of magnesium, calcium, nickel and zinc acetates were determined as a function of temperature. The vapour pressures served to evaluate the water activities, osmotic coefficients and molar enthalpies of vaporization. Molar enthalpies of solution of magnesium acetate tetrahydrate, 1sol Hm (T = 294.71 K; m = 0.01 mol · kg−1 ) = −(15.65 ± 0.97) kJ · mol−1 ; calcium acetate, 1sol Hm (T = 297.18 K; m = 0.01 mol · kg−1 ) = −(28.15 ± 0.28) kJ · mol−1 ; zinc acetate dihydrate, 1sol Hm (T = 297.36 K; m = 0.01 mol · kg−1 ) = −(22.49 ± 0.90) kJ · mol−1 and lead acetate trihydrate, 1sol Hm (T = 297.36 K; m = 0.0086 mol · kg−1 ) = c 2001 Academic Press (22.46 ± 0.94) kJ · mol−1 , were determined calorimetrically. KEYWORDS: vapour pressures; saturated solutions; water activities; osmotic coefficients; molar enthalpies of vaporization and solution
1. Introduction Magnesium, calcium, nickel, zinc, and lead acetates are used in many various industrial processes,(1) but our knowledge about thermodynamical properties of these acetates in aqueous solutions is limited. Vapour pressures of saturated solutions as a function of temperature are completely unknown in the literature. O’Brien(2) quotes one value for magnesium acetate at room temperature and one value for calcium acetate monohydrate at T = 297.65 K, but this is probably the vapour pressure over the solid Ca(CH3 CO2 )2 · H2 O. Few known thermal properties of aqueous solution of metal acetates have rather historical interest.(3, 4) Berthelot(5) (1873), Marignac(6) (1878) and Thomsen(7) (1883) reported heat capacities and enthalpies of dilution but temperatures are not specified or results are attributed to a large temperature interval. Only one modern determination of molar enthalpy of dilution is given by Plake(8) (1932) for calcium acetate. a To whom correspondence should be addressed (E-mail: [email protected]).
0021–9614/01/010113 + 08 $35.00/0
c 2001 Academic Press
114
A. Apelblat and E. Korin
Continuing our previous determinations of properties of aqueous solutions of metal acetates (solubilities of Mg, Ca, Ba, Co, Ni, Cu, Zn, Mn, Cd, Hg, and Pb acetates in water(9, 10) ), in this work systematic measurements of vapour pressures of water over saturated solutions of magnesium, calcium, nickel and zinc acetates are presented as a function of temperature. These vapour pressures were used to evaluate the water activities, osmotic coefficients and molar enthalpies of vaporization at saturation. Calorimetric determinations of molar enthalpies of solution of magnesium, calcium, zinc and lead acetates are also reported.
2. Experimental Magnesium acetate tetrahydrate, Mg(CH3 CO2 )2 · 4H2 O; nickel acetate tetrahydrate, Ni(CH3 CO2 )2 · 4H2 O; zinc acetate dihydrate, Zn(CH3 CO2 )2 · 2H2 O all mass fraction > 0.99 and calcium acetate Ca(CH3 CO2 )2 mass fraction 0.935 to 0.945 were supplied by Merck and lead acetate trihydrate, Pb(CH3 CO2 )2 · 3H2 O (mass fraction > 0.99) by Fluka. These metal acetates were used without futher purification. The vapour pressures over saturated solutions of magnesium, calcium, nickel and zinc acetates were determined using the Rotronic Hygroskop DT1 which is equipped with a measuring station WA-14TH. Saturated solutions with an excess of solid phase were placed in the measuring station in disposable polystyrene sample cups. The change of temperature was obtained by an external-mantle of the station which was heated or cooled by running water from an external thermostat. After the thermal equilibrium was attained, the system needed about 1 h to reach the (vapour + liquid) equilibrium. Thermal stability of the measuring system is estimated to be ±0.05 K and the sensitivity of the used hygrometer is about ±0.003 kPa. The applied procedure(10–16) was frequently checked by determining vapour pressures of saturated solutions of sodium chloride. The enthalpies of solution of magnesium acetate tetrahydrate, calcium acetate, zinc acetate dihydrate and lead acetate trihydrate were measured with a Parr 1455 Solution Calorimeter. The mass of water in the reaction vessel of the calorimeter was 100 g. The energy equivalent e = (525.7 ± 9.8) J · K−1 , was established using the dissolution of potassium chloride in water.(17, 18) The results of the calorimetric measurements are not adjusted for temperature and dilution effects because heat capacities are unreliable and enthalpies of dilution are unknown. The enthalpy of solution of metal acetate is reported for the mean molarity and temperature of all calorimetric measurements performed with this acetate (see table 1).
3. Results and discussion The vapour pressures over saturated aqueous solutions of magnesium acetate, calcium acetate, nickel acetate and zinc acetate as a function of temperature are presented in table 2. There is no corresponding data for comparison in the literature. The temperature dependence of the vapour pressure for saturated solutions is given by the Clausius– Clapeyron equation(19) g
d ln p/d(1/T ) = −1cr Hm (T )/R,
(1)
Vapour pressures and enthalpies of solution of metal acetates TABLE 1. Calorimetric molar enthalpies of solution 1sol Hm (T ) of magnesium, calcium, zinc and lead acetates; m denotes mass of substance, m f the molality of the product solution and 1sol H the experimental enthalpy of solution w g
mf mol · kg−1
−1sol H J
hT i K
−1sol Hm (T ) J · mol−1
Mg(CH3 CO2 )2 · 4H2 O 0.2143
0.009988
16.455
294.73
16463
0.2144
0.009993
14.717
295.05
14717
0.2145
0.009997
14.825
294.53
14818
0.2145
0.009997
14.352
295.83
14345
0.2145
0.009997
16.455
291.67
16447
0.2145
0.009997
16.296
295.07
16288
0.2146
0.010002
15.901
293.33
15887
0.2149
0.010016
14.733
295.02
14738
0.2150
0.010021
15.351
295.21
15308
0.2150
0.010021
14.353
296.26
14312
0.2150
0.010021
16.666
293.59
16619
0.2151
0.010025
17.086
295.18
17030
0.2155
0.010044
16.560
295.71
16475
0.1580
0.009989
28.177
296.85
28208
0.1585
0.010021
27.913
297.44
27855
0.1585
0.010021
28.652
297.42
28592
0.1586
0.010027
28.229
297.50
28153
0.1589
0.010046
27.970
297.15
27841
0.1592
0.010065
28.441
296.72
28257
0.2064
0.009400
21.027
296.17
22361
0.2202
0.010029
22.467
297.05
22374
0.2203
0.010033
21.867
297.56
21786
0.2204
0.010038
23.079
297.80
22983
0.2204
0.010038
21.343
297.05
21255
0.2209
0.010061
23.657
297.24
23506
0.2212
0.010074
23.815
297.52
23631
0.2212
0.010074
22.659
297.34
22484
0.2214
0.010083
23.550
297.43
23347
0.2239
0.010197
21.551
297.32
21126
Ca(CH3 CO2 )2
Zn(CH3 CO2 )2 · 2H2 O
115
116
A. Apelblat and E. Korin TABLE 1—continued w g
mf mol · kg−1
0.3795
0.008556
−1sol H J
hT i K
−1sol Hm (T ) J · mol−1
Pb(CH3 CO2 )2 · 3H2 O −21.763
295.24
−21753
0.3797
0.008560
−21.711
293.69
−21690
0.3808
0.008593
−22.815
295.54
−22727
0.3809
0.008595
−23.447
294.68
−23350
0.3811
0.008600
−23.550
294.20
−23441
0.3820
0.008620
−22.975
295.10
−22814
0.3822
0.008624
−23.289
294.50
−23115
0.3835
0.008654
−21.027
295.10
−20798
g
where 1cr Hm (T ) is the molar enthalpy change associated with the evaporation of water and simultaneously crystallizing the salt. Assuming that over the considered range of g temperature, 1cr Hm (T ) depends linearly on temperature, the integral form of equation (1) for the studied systems is: ln[ p{Mg(CH3 CO2 )2 , T, m}/kPa] = 197.064 − 13481.6 · (T /K)−1 − 26.5012 · ln(T /K), (2) −1 ln[ p{Ca(CH3 CO2 )2 , T, m}/kPa] = 56.396 − 7174.6(T /K) − 5.5045 · ln(T /K),(3) ln[ p{Ni(CH3 CO2 )2 , T, m}/kPa] = 206.142 − 13463.0(T /K)−1 − 28.0628 · ln(T /K), (4) −1 ln[ p{Zn(CH3 CO2 )2 , T, m}/kPa] = 19.769 − 5650.2(T /K) , (5) where m = m sat . The parameters of these equations were evaluated by an unweighted multivariate least-squares method. In table 3 are reported at 5 K intervals the values of vapour pressures p, solubilities of the acetates(9) m, activities of water a1 = p/ p ∗ , osmotic coefficients φ = −(3 · M1 m)−1 · ln a1 , (M1 is the molar mass of H2 O), and the molar g enthalpies of vaporization 1cr Hm (T ). The vapour pressures p ∗ of pure water at given T , were calculated from the Saul and Wagner equation.(20) At T = 298.15 K, the molar enthalpies of vaporization (table 3) are similar for all metal acetates (the lowest is for nickel acetate) and, in the studied range of T , decrease strongly with temperature for magnesium acetate and nickel acetate but are nearly independent of temperature for calcium acetate and zinc acetate. Thus, predictions about the temperature dependence of enthalpies of vaporization for other metal acetates is rather uncertain. The results of calorimetric measurements with magnesium acetate tetrahydrate, calcium acetate, zinc acetate dihydrate and lead acetate trihydrate are presented in table 3, where 1sol H denotes the enthalpy change during dissolution of mass m at temperature hT i, which is the average of the initial and final temperatures of the calorimetric experiment. In the absence of reliable heat capacities and enthalpies of dilution the molar enthalpies of
Vapour pressures and enthalpies of solution of metal acetates TABLE 2. Vapour pressures p of saturated aqueous solutions of magnesium, calcium, nickel and zinc acetates at temperatures T T /K
p/kPa
T /K
p/kPa
T /K
p/kPa
Mg(CH3 CO2 )2 (aq) 283.20
0.845
296.45
2.121
310.70
4.894
283.80
0.888
297.45
2.285
311.75
5.124
284.70
0.946
298.40
2.409
312.65
5.353
285.30
1.000
299.25
2.527
313.55
5.593
286.55
1.069
300.25
2.670
313.95
5.932
287.45
1.142
301.20
2.820
314.90
6.196
288.30
1.213
301.65
2.990
315.90
6.445
289.10
1.288
302.75
3.133
316.95
6.735
289.85
1.359
303.75
3.304
318.00
7.072
290.95
1.455
304.65
3.454
319.05
7.363
291.60
1.518
305.60
3.606
319.45
7.889
292.50
1.623
306.20
3.891
320.40
8.193
293.20
1.716
307.30
4.052
321.45
8.468
294.45
1.818
308.20
4.234
322.55
8.875
295.25
1.925
308.90
4.356
295.90
2.031
309.50
4.698
278.25
0.722
292.95
1.963
303.95
3.769
279.35
0.747
293.85
2.107
304.85
3.929
280.65
0.816
294.85
2.179
305.55
4.224
282.35
0.938
295.85
2.188
306.55
4.417
282.45
0.878
295.85
2.257
307.45
4.628
283.35
0.951
296.75
2.375
308.15
4.884
284.15
1.024
296.85
2.345
309.15
5.137
284.95
1.126
297.55
2.565
310.15
5.388
285.95
1.156
297.65
2.473
311.15
5.669
286.75
1.234
298.45
2.671
312.05
5.937
287.55
1.342
298.55
2.625
312.95
6.295
288.45
1.478
299.35
2.797
314.05
6.659
289.65
1.511
300.25
2.942
314.65
6.954
290.45
1.620
301.25
3.180
315.55
7.257
291.25
1.732
302.15
3.302
316.65
7.651
292.15
1.824
302.85
3.610
317.45
7.955
Ca(CH3 CO2 )2 (aq)
117
118
A. Apelblat and E. Korin TABLE 2—continued T /K
p/kPa
T /K
T /K
p/kPa
278.25
0.823
290.65
279.05
0.879
291.55
1.912
303.35
4.011
2.021
304.15
280.15
0.959
4.167
292.45
2.141
305.15
4.387
281.25 282.05
1.000
293.15
2.212
306.05
4.610
1.070
294.15
2.353
307.05
4.865
282.85
1.139
295.05
2.468
307.75
4.926
283.65
1.210
295.95
2.638
308.85
5.322
284.65
1.280
296.95
2.796
309.45
5.567
285.45
1.362
297.85
2.945
310.55
5.840
286.25
1.444
298.95
3.137
311.65
6.198
287.05
1.528
299.85
3.312
312.45
6.129
288.05
1.616
300.65
3.464
313.15
6.533
288.85
1.712
301.55
3.631
314.25
6.941
289.85
1.818
302.45
3.817
315.25
7.325
277.65
0.741
290.45
1.835
303.75
4.082
281.75
1.026
294.85
2.462
308.45
5.246
286.45
1.375
299.45
3.218
313.15
6.710
p/kPa
Ni(CH3 CO2 )2 (aq)
Zn(CH3 CO2 )2 (aq)
solution 1sol Hm (T, m) are only given for an average value of molality m and temperature T (based on all calorimetric experiments for the considered metal acetate). The molar enthalpies of solution as determined in this study are: 1sol Hm {Mg(CH3 CO2 )2 · 4H2 O; T = 294.71 K; m = 0.01 mol · kg−1 } = −(15.65 ± 0.97) kJ · mol−1 , (6) 1sol Hm {Ca(CH3 CO2 )2 ; T = 297.18 K; m = 0.01 mol · kg−1 } = −(28.15 ± 0.28) kJ · mol−1 , (7) 1sol Hm {Zn(CH3 CO2 )2 · 2H2 O; T = 297.36 K ; m = 0.01 mol · kg−1 } = −(22.49 ± 0.90) kJ · mol−1 , (8) 1sol Hm {Pb(CH3 CO2 )2 · 3H2 O; T = 297.36 K; m = 0.0086 mol · kg−1 } = (22.46 ± 0.94) kJ · mol−1 . (9) It is probable that, the deviation from stoichiometric composition of the investigated acetate hydrates, and not the neglected heat capacities, are responsable for a relatively large scattering of results. This is clearly indicated if the uncertainties of the results for anhydrous calcium acetate are compared with those of the other acetates.
Vapour pressures and enthalpies of solution of metal acetates TABLE 3. Solubilities(9) m, vapour pressures p, water activities a1 , osmotic coefficients φ, and molar enthalpies g of vaporization 1cr Hm (T ) as a function of temperature T , (R = 8.3136 J · K−1 · mol−1 ) g
φ
1cr Hm (T ) R·K
Mg(CH3 CO2 )2 (aq) 0.840 0.684 1.207 0.708 1.700 0.727 2.348 0.741 3.185 0.750 4.249 0.755 5.577 0.756 7.209 0.752 9.187 0.744
1.811 1.584 1.406 1.270 1.169 1.099 1.055 1.033 1.029
5978 5845 5713 5580 5448 5315 5183 5050 4918
2.302 2.268 2.235 2.204 2.174 2.146 2.119 2.093 2.080
Ca(CH3 CO2 )2 (aq) 0.685 0.785 0.797 0.797 1.380 0.809 1.920 0.821 2.637 0.832 3.578 0.843 4.801 0.853 6.372 0.863 8.371 0.873
1.946 1.848 1.752 1.657 1.565 1.474 1.386 1.300 1.209
5644 5616 5588 5561 5533 5506 5478 5451 5423
278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15
0.5890 0.6356 0.6841 0.7345 0.7866 0.8406 0.8964 0.9538
Ni(CH3 CO2 )2 (aq) 0.817 0.937 1.165 0.949 1.627 0.954 2.228 0.953 2.994 0.945 3.953 0.931 5.135 0.913 6.566 0.890
2.053 1.525 1.270 1.225 1.337 1.568 1.887 2.269
5657 5517 5377 5236 5096 4956 4815 4675
283.15 288.15 293.15 298.15 303.15 308.15 313.15
1.662 1.741 1.829 1.925 2.031 2.146 2.272
Zn(CH3 CO2 )2 (aq) 1.118 0.910 1.554 0.912 2.138 0.914 2.908 0.918 3.918 0.923 5.225 0.929 6.907 0.936
1.049 0.985 0.909 0.823 0.732 0.637 0.540
5383 5383 5383 5383 5383 5383 5383
T K
m mol · kg−1
283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15
3.88 4.03 4.20 4.37 4.55 4.73 4.92 5.11 5.32
278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15
p kPa
a1
119
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A. Apelblat and E. Korin
The authors appreciate the technical assistance of Mrs Mary Mamana. REFERENCES 1. The Merck Index, An Encyclopedia of Chemicals, Drugs and Biologicals: 11th edition. Budavari, S.: editor. Merck Co., Inc.: Rahway, NJ. 1989. 2. O’Brien, F. E. M. J. Sci. Instruments 1948, 25, 73–76. 3. Beggerow, G. Heat of Mixing and Solution, Landdolt-B¨ornstein, New Ser. IV/2. Hellwege, K. H.: editor. Springer-Verlag: Berlin. 1976. 4. Smith-Magowan, D.; Goldberg, R. N. A Bibliography of Sources of Experimental Data Leading to Thermal Properties of Binary Aqueous Electrolyte Solutions. U.S. Nat. Bureau of Standards. Special Publ. 537. Washington, D.C. March 1979. 5. Berthelot, M. Ann. Chim. Phys. 1875, 4, 90–95. 6. Marignac, M. C. Ann. Chim. Phys. 1878, 8, 410–430. 7. Thomsen, J. Thermochemische Untersuchungen, Vol. III. Barth Verlag: J. A. Leipzig. 1883. 8. Plake, E. Z. Physik. Chem. (Leipzig) 1932, A162, 257–280. 9. Apelblat, A.; Manzurola, E. J. Chem. Thermodynamics 1999, 31, 1347–1357. 10. Apelblat, A.; Manzurola, E. J. Chem. Thermodynamics (in press) [WE-221]. 11. Apelblat, A.; Manzurola, E. J. Chem. Thermodynamics 1997, 29, 1527–1533. 12. Apelblat, A.; Korin, E. J. Chem. Thermodynamics 1998, 30, 59–71. 13. Apelblat, A.; Korin, E. J. Chem. Thermodynamics 1998, 30, 459–471. 14. Apelblat, A. J. Chem. Thermodynamics 1998, 25, 1191–1198. 15. Apelblat, A.; Korin, E. J. Chem. Thermodynamics 1998, 30, 1263–1269. 16. Apelblat, A.; Manzurola, E. J. Chem. Thermodynamics 1999, 31, 85–91. 17. Montgomery, R. L.; Melaugh, R. A.; Lau, C. C.; Meier, G. H.; Chan, H. H.; Rossini, F. D. J. Chem. Thermodynamics 1977, 9, 915–936. 18. Kilday, M. V. J. Res. Nat. Bur. Stand. (U.S.) 1980, 85, 467–481. 19. Modell, M.; Reid, R. C. Thermodynamics and its Applications. Prentice-Hall: Englewood Cliffs, NJ. 1974, 338–339. 20. Saul, S.; Wagner, W. J. Phys. Chem. Ref. Data 1987, 16, 893–901. (Received 21 February 2000; in final form 9 July 2000)
O-824
The vapour pressures of saturated aqueous solutions of magnesium, calcium, nickel and zinc acetates and molar enthalpies of solution of magnesium, calcium, zinc and lead acetates Alexander Apelblata and Eli Korin Department of Chemical Engineering, Ben Gurion University of the Negev, Beer Sheva, Israel
Vapour pressures of water over saturated solutions of magnesium, calcium, nickel and zinc acetates were determined as a function of temperature. The vapour pressures served to evaluate the water activities, osmotic coefficients and molar enthalpies of vaporization. Molar enthalpies of solution of magnesium acetate tetrahydrate, 1sol Hm (T = 294.71 K; m = 0.01 mol · kg−1 ) = −(15.65 ± 0.97) kJ · mol−1 ; calcium acetate, 1sol Hm (T = 297.18 K; m = 0.01 mol · kg−1 ) = −(28.15 ± 0.28) kJ · mol−1 ; zinc acetate dihydrate, 1sol Hm (T = 297.36 K; m = 0.01 mol · kg−1 ) = −(22.49 ± 0.90) kJ · mol−1 and lead acetate trihydrate, 1sol Hm (T = 297.36 K; m = 0.0086 mol · kg−1 ) = c 2001 Academic Press (22.46 ± 0.94) kJ · mol−1 , were determined calorimetrically. KEYWORDS: vapour pressures; saturated solutions; water activities; osmotic coefficients; molar enthalpies of vaporization and solution
1. Introduction Magnesium, calcium, nickel, zinc, and lead acetates are used in many various industrial processes,(1) but our knowledge about thermodynamical properties of these acetates in aqueous solutions is limited. Vapour pressures of saturated solutions as a function of temperature are completely unknown in the literature. O’Brien(2) quotes one value for magnesium acetate at room temperature and one value for calcium acetate monohydrate at T = 297.65 K, but this is probably the vapour pressure over the solid Ca(CH3 CO2 )2 · H2 O. Few known thermal properties of aqueous solution of metal acetates have rather historical interest.(3, 4) Berthelot(5) (1873), Marignac(6) (1878) and Thomsen(7) (1883) reported heat capacities and enthalpies of dilution but temperatures are not specified or results are attributed to a large temperature interval. Only one modern determination of molar enthalpy of dilution is given by Plake(8) (1932) for calcium acetate. a To whom correspondence should be addressed (E-mail: [email protected]).
0021–9614/01/010113 + 08 $35.00/0
c 2001 Academic Press
114
A. Apelblat and E. Korin
Continuing our previous determinations of properties of aqueous solutions of metal acetates (solubilities of Mg, Ca, Ba, Co, Ni, Cu, Zn, Mn, Cd, Hg, and Pb acetates in water(9, 10) ), in this work systematic measurements of vapour pressures of water over saturated solutions of magnesium, calcium, nickel and zinc acetates are presented as a function of temperature. These vapour pressures were used to evaluate the water activities, osmotic coefficients and molar enthalpies of vaporization at saturation. Calorimetric determinations of molar enthalpies of solution of magnesium, calcium, zinc and lead acetates are also reported.
2. Experimental Magnesium acetate tetrahydrate, Mg(CH3 CO2 )2 · 4H2 O; nickel acetate tetrahydrate, Ni(CH3 CO2 )2 · 4H2 O; zinc acetate dihydrate, Zn(CH3 CO2 )2 · 2H2 O all mass fraction > 0.99 and calcium acetate Ca(CH3 CO2 )2 mass fraction 0.935 to 0.945 were supplied by Merck and lead acetate trihydrate, Pb(CH3 CO2 )2 · 3H2 O (mass fraction > 0.99) by Fluka. These metal acetates were used without futher purification. The vapour pressures over saturated solutions of magnesium, calcium, nickel and zinc acetates were determined using the Rotronic Hygroskop DT1 which is equipped with a measuring station WA-14TH. Saturated solutions with an excess of solid phase were placed in the measuring station in disposable polystyrene sample cups. The change of temperature was obtained by an external-mantle of the station which was heated or cooled by running water from an external thermostat. After the thermal equilibrium was attained, the system needed about 1 h to reach the (vapour + liquid) equilibrium. Thermal stability of the measuring system is estimated to be ±0.05 K and the sensitivity of the used hygrometer is about ±0.003 kPa. The applied procedure(10–16) was frequently checked by determining vapour pressures of saturated solutions of sodium chloride. The enthalpies of solution of magnesium acetate tetrahydrate, calcium acetate, zinc acetate dihydrate and lead acetate trihydrate were measured with a Parr 1455 Solution Calorimeter. The mass of water in the reaction vessel of the calorimeter was 100 g. The energy equivalent e = (525.7 ± 9.8) J · K−1 , was established using the dissolution of potassium chloride in water.(17, 18) The results of the calorimetric measurements are not adjusted for temperature and dilution effects because heat capacities are unreliable and enthalpies of dilution are unknown. The enthalpy of solution of metal acetate is reported for the mean molarity and temperature of all calorimetric measurements performed with this acetate (see table 1).
3. Results and discussion The vapour pressures over saturated aqueous solutions of magnesium acetate, calcium acetate, nickel acetate and zinc acetate as a function of temperature are presented in table 2. There is no corresponding data for comparison in the literature. The temperature dependence of the vapour pressure for saturated solutions is given by the Clausius– Clapeyron equation(19) g
d ln p/d(1/T ) = −1cr Hm (T )/R,
(1)
Vapour pressures and enthalpies of solution of metal acetates TABLE 1. Calorimetric molar enthalpies of solution 1sol Hm (T ) of magnesium, calcium, zinc and lead acetates; m denotes mass of substance, m f the molality of the product solution and 1sol H the experimental enthalpy of solution w g
mf mol · kg−1
−1sol H J
hT i K
−1sol Hm (T ) J · mol−1
Mg(CH3 CO2 )2 · 4H2 O 0.2143
0.009988
16.455
294.73
16463
0.2144
0.009993
14.717
295.05
14717
0.2145
0.009997
14.825
294.53
14818
0.2145
0.009997
14.352
295.83
14345
0.2145
0.009997
16.455
291.67
16447
0.2145
0.009997
16.296
295.07
16288
0.2146
0.010002
15.901
293.33
15887
0.2149
0.010016
14.733
295.02
14738
0.2150
0.010021
15.351
295.21
15308
0.2150
0.010021
14.353
296.26
14312
0.2150
0.010021
16.666
293.59
16619
0.2151
0.010025
17.086
295.18
17030
0.2155
0.010044
16.560
295.71
16475
0.1580
0.009989
28.177
296.85
28208
0.1585
0.010021
27.913
297.44
27855
0.1585
0.010021
28.652
297.42
28592
0.1586
0.010027
28.229
297.50
28153
0.1589
0.010046
27.970
297.15
27841
0.1592
0.010065
28.441
296.72
28257
0.2064
0.009400
21.027
296.17
22361
0.2202
0.010029
22.467
297.05
22374
0.2203
0.010033
21.867
297.56
21786
0.2204
0.010038
23.079
297.80
22983
0.2204
0.010038
21.343
297.05
21255
0.2209
0.010061
23.657
297.24
23506
0.2212
0.010074
23.815
297.52
23631
0.2212
0.010074
22.659
297.34
22484
0.2214
0.010083
23.550
297.43
23347
0.2239
0.010197
21.551
297.32
21126
Ca(CH3 CO2 )2
Zn(CH3 CO2 )2 · 2H2 O
115
116
A. Apelblat and E. Korin TABLE 1—continued w g
mf mol · kg−1
0.3795
0.008556
−1sol H J
hT i K
−1sol Hm (T ) J · mol−1
Pb(CH3 CO2 )2 · 3H2 O −21.763
295.24
−21753
0.3797
0.008560
−21.711
293.69
−21690
0.3808
0.008593
−22.815
295.54
−22727
0.3809
0.008595
−23.447
294.68
−23350
0.3811
0.008600
−23.550
294.20
−23441
0.3820
0.008620
−22.975
295.10
−22814
0.3822
0.008624
−23.289
294.50
−23115
0.3835
0.008654
−21.027
295.10
−20798
g
where 1cr Hm (T ) is the molar enthalpy change associated with the evaporation of water and simultaneously crystallizing the salt. Assuming that over the considered range of g temperature, 1cr Hm (T ) depends linearly on temperature, the integral form of equation (1) for the studied systems is: ln[ p{Mg(CH3 CO2 )2 , T, m}/kPa] = 197.064 − 13481.6 · (T /K)−1 − 26.5012 · ln(T /K), (2) −1 ln[ p{Ca(CH3 CO2 )2 , T, m}/kPa] = 56.396 − 7174.6(T /K) − 5.5045 · ln(T /K),(3) ln[ p{Ni(CH3 CO2 )2 , T, m}/kPa] = 206.142 − 13463.0(T /K)−1 − 28.0628 · ln(T /K), (4) −1 ln[ p{Zn(CH3 CO2 )2 , T, m}/kPa] = 19.769 − 5650.2(T /K) , (5) where m = m sat . The parameters of these equations were evaluated by an unweighted multivariate least-squares method. In table 3 are reported at 5 K intervals the values of vapour pressures p, solubilities of the acetates(9) m, activities of water a1 = p/ p ∗ , osmotic coefficients φ = −(3 · M1 m)−1 · ln a1 , (M1 is the molar mass of H2 O), and the molar g enthalpies of vaporization 1cr Hm (T ). The vapour pressures p ∗ of pure water at given T , were calculated from the Saul and Wagner equation.(20) At T = 298.15 K, the molar enthalpies of vaporization (table 3) are similar for all metal acetates (the lowest is for nickel acetate) and, in the studied range of T , decrease strongly with temperature for magnesium acetate and nickel acetate but are nearly independent of temperature for calcium acetate and zinc acetate. Thus, predictions about the temperature dependence of enthalpies of vaporization for other metal acetates is rather uncertain. The results of calorimetric measurements with magnesium acetate tetrahydrate, calcium acetate, zinc acetate dihydrate and lead acetate trihydrate are presented in table 3, where 1sol H denotes the enthalpy change during dissolution of mass m at temperature hT i, which is the average of the initial and final temperatures of the calorimetric experiment. In the absence of reliable heat capacities and enthalpies of dilution the molar enthalpies of
Vapour pressures and enthalpies of solution of metal acetates TABLE 2. Vapour pressures p of saturated aqueous solutions of magnesium, calcium, nickel and zinc acetates at temperatures T T /K
p/kPa
T /K
p/kPa
T /K
p/kPa
Mg(CH3 CO2 )2 (aq) 283.20
0.845
296.45
2.121
310.70
4.894
283.80
0.888
297.45
2.285
311.75
5.124
284.70
0.946
298.40
2.409
312.65
5.353
285.30
1.000
299.25
2.527
313.55
5.593
286.55
1.069
300.25
2.670
313.95
5.932
287.45
1.142
301.20
2.820
314.90
6.196
288.30
1.213
301.65
2.990
315.90
6.445
289.10
1.288
302.75
3.133
316.95
6.735
289.85
1.359
303.75
3.304
318.00
7.072
290.95
1.455
304.65
3.454
319.05
7.363
291.60
1.518
305.60
3.606
319.45
7.889
292.50
1.623
306.20
3.891
320.40
8.193
293.20
1.716
307.30
4.052
321.45
8.468
294.45
1.818
308.20
4.234
322.55
8.875
295.25
1.925
308.90
4.356
295.90
2.031
309.50
4.698
278.25
0.722
292.95
1.963
303.95
3.769
279.35
0.747
293.85
2.107
304.85
3.929
280.65
0.816
294.85
2.179
305.55
4.224
282.35
0.938
295.85
2.188
306.55
4.417
282.45
0.878
295.85
2.257
307.45
4.628
283.35
0.951
296.75
2.375
308.15
4.884
284.15
1.024
296.85
2.345
309.15
5.137
284.95
1.126
297.55
2.565
310.15
5.388
285.95
1.156
297.65
2.473
311.15
5.669
286.75
1.234
298.45
2.671
312.05
5.937
287.55
1.342
298.55
2.625
312.95
6.295
288.45
1.478
299.35
2.797
314.05
6.659
289.65
1.511
300.25
2.942
314.65
6.954
290.45
1.620
301.25
3.180
315.55
7.257
291.25
1.732
302.15
3.302
316.65
7.651
292.15
1.824
302.85
3.610
317.45
7.955
Ca(CH3 CO2 )2 (aq)
117
118
A. Apelblat and E. Korin TABLE 2—continued T /K
p/kPa
T /K
T /K
p/kPa
278.25
0.823
290.65
279.05
0.879
291.55
1.912
303.35
4.011
2.021
304.15
280.15
0.959
4.167
292.45
2.141
305.15
4.387
281.25 282.05
1.000
293.15
2.212
306.05
4.610
1.070
294.15
2.353
307.05
4.865
282.85
1.139
295.05
2.468
307.75
4.926
283.65
1.210
295.95
2.638
308.85
5.322
284.65
1.280
296.95
2.796
309.45
5.567
285.45
1.362
297.85
2.945
310.55
5.840
286.25
1.444
298.95
3.137
311.65
6.198
287.05
1.528
299.85
3.312
312.45
6.129
288.05
1.616
300.65
3.464
313.15
6.533
288.85
1.712
301.55
3.631
314.25
6.941
289.85
1.818
302.45
3.817
315.25
7.325
277.65
0.741
290.45
1.835
303.75
4.082
281.75
1.026
294.85
2.462
308.45
5.246
286.45
1.375
299.45
3.218
313.15
6.710
p/kPa
Ni(CH3 CO2 )2 (aq)
Zn(CH3 CO2 )2 (aq)
solution 1sol Hm (T, m) are only given for an average value of molality m and temperature T (based on all calorimetric experiments for the considered metal acetate). The molar enthalpies of solution as determined in this study are: 1sol Hm {Mg(CH3 CO2 )2 · 4H2 O; T = 294.71 K; m = 0.01 mol · kg−1 } = −(15.65 ± 0.97) kJ · mol−1 , (6) 1sol Hm {Ca(CH3 CO2 )2 ; T = 297.18 K; m = 0.01 mol · kg−1 } = −(28.15 ± 0.28) kJ · mol−1 , (7) 1sol Hm {Zn(CH3 CO2 )2 · 2H2 O; T = 297.36 K ; m = 0.01 mol · kg−1 } = −(22.49 ± 0.90) kJ · mol−1 , (8) 1sol Hm {Pb(CH3 CO2 )2 · 3H2 O; T = 297.36 K; m = 0.0086 mol · kg−1 } = (22.46 ± 0.94) kJ · mol−1 . (9) It is probable that, the deviation from stoichiometric composition of the investigated acetate hydrates, and not the neglected heat capacities, are responsable for a relatively large scattering of results. This is clearly indicated if the uncertainties of the results for anhydrous calcium acetate are compared with those of the other acetates.
Vapour pressures and enthalpies of solution of metal acetates TABLE 3. Solubilities(9) m, vapour pressures p, water activities a1 , osmotic coefficients φ, and molar enthalpies g of vaporization 1cr Hm (T ) as a function of temperature T , (R = 8.3136 J · K−1 · mol−1 ) g
φ
1cr Hm (T ) R·K
Mg(CH3 CO2 )2 (aq) 0.840 0.684 1.207 0.708 1.700 0.727 2.348 0.741 3.185 0.750 4.249 0.755 5.577 0.756 7.209 0.752 9.187 0.744
1.811 1.584 1.406 1.270 1.169 1.099 1.055 1.033 1.029
5978 5845 5713 5580 5448 5315 5183 5050 4918
2.302 2.268 2.235 2.204 2.174 2.146 2.119 2.093 2.080
Ca(CH3 CO2 )2 (aq) 0.685 0.785 0.797 0.797 1.380 0.809 1.920 0.821 2.637 0.832 3.578 0.843 4.801 0.853 6.372 0.863 8.371 0.873
1.946 1.848 1.752 1.657 1.565 1.474 1.386 1.300 1.209
5644 5616 5588 5561 5533 5506 5478 5451 5423
278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15
0.5890 0.6356 0.6841 0.7345 0.7866 0.8406 0.8964 0.9538
Ni(CH3 CO2 )2 (aq) 0.817 0.937 1.165 0.949 1.627 0.954 2.228 0.953 2.994 0.945 3.953 0.931 5.135 0.913 6.566 0.890
2.053 1.525 1.270 1.225 1.337 1.568 1.887 2.269
5657 5517 5377 5236 5096 4956 4815 4675
283.15 288.15 293.15 298.15 303.15 308.15 313.15
1.662 1.741 1.829 1.925 2.031 2.146 2.272
Zn(CH3 CO2 )2 (aq) 1.118 0.910 1.554 0.912 2.138 0.914 2.908 0.918 3.918 0.923 5.225 0.929 6.907 0.936
1.049 0.985 0.909 0.823 0.732 0.637 0.540
5383 5383 5383 5383 5383 5383 5383
T K
m mol · kg−1
283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15
3.88 4.03 4.20 4.37 4.55 4.73 4.92 5.11 5.32
278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15
p kPa
a1
119
120
A. Apelblat and E. Korin
The authors appreciate the technical assistance of Mrs Mary Mamana. REFERENCES 1. The Merck Index, An Encyclopedia of Chemicals, Drugs and Biologicals: 11th edition. Budavari, S.: editor. Merck Co., Inc.: Rahway, NJ. 1989. 2. O’Brien, F. E. M. J. Sci. Instruments 1948, 25, 73–76. 3. Beggerow, G. Heat of Mixing and Solution, Landdolt-B¨ornstein, New Ser. IV/2. Hellwege, K. H.: editor. Springer-Verlag: Berlin. 1976. 4. Smith-Magowan, D.; Goldberg, R. N. A Bibliography of Sources of Experimental Data Leading to Thermal Properties of Binary Aqueous Electrolyte Solutions. U.S. Nat. Bureau of Standards. Special Publ. 537. Washington, D.C. March 1979. 5. Berthelot, M. Ann. Chim. Phys. 1875, 4, 90–95. 6. Marignac, M. C. Ann. Chim. Phys. 1878, 8, 410–430. 7. Thomsen, J. Thermochemische Untersuchungen, Vol. III. Barth Verlag: J. A. Leipzig. 1883. 8. Plake, E. Z. Physik. Chem. (Leipzig) 1932, A162, 257–280. 9. Apelblat, A.; Manzurola, E. J. Chem. Thermodynamics 1999, 31, 1347–1357. 10. Apelblat, A.; Manzurola, E. J. Chem. Thermodynamics (in press) [WE-221]. 11. Apelblat, A.; Manzurola, E. J. Chem. Thermodynamics 1997, 29, 1527–1533. 12. Apelblat, A.; Korin, E. J. Chem. Thermodynamics 1998, 30, 59–71. 13. Apelblat, A.; Korin, E. J. Chem. Thermodynamics 1998, 30, 459–471. 14. Apelblat, A. J. Chem. Thermodynamics 1998, 25, 1191–1198. 15. Apelblat, A.; Korin, E. J. Chem. Thermodynamics 1998, 30, 1263–1269. 16. Apelblat, A.; Manzurola, E. J. Chem. Thermodynamics 1999, 31, 85–91. 17. Montgomery, R. L.; Melaugh, R. A.; Lau, C. C.; Meier, G. H.; Chan, H. H.; Rossini, F. D. J. Chem. Thermodynamics 1977, 9, 915–936. 18. Kilday, M. V. J. Res. Nat. Bur. Stand. (U.S.) 1980, 85, 467–481. 19. Modell, M.; Reid, R. C. Thermodynamics and its Applications. Prentice-Hall: Englewood Cliffs, NJ. 1974, 338–339. 20. Saul, S.; Wagner, W. J. Phys. Chem. Ref. Data 1987, 16, 893–901. (Received 21 February 2000; in final form 9 July 2000)
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