Isopiestic determination of the osmotic and activity coefficients of Cu(NO3)2(aq) at the temperature 298.15 K

J. Chem. Thermodynamics 1998, 30, 327]352

Isopiestic determination of the osmotic and activity coefficients of Cu( NO 3 ) 2( aq) at the temperature 298.15 K a John G. Albright, Paola Rizzo,b Department of Chemistry, Texas Christian Uni¨ ersity, Fort Worth, TX 76129, U.S.A.

and Joseph A. Rard c Geosciences and En¨ ironmental Technologies, Earth and En¨ ironmental Sciences Directorate, Lawrence Li¨ ermore National Laboratory, Uni¨ ersity of California, Li¨ ermore, CA 94550, U.S.A. The four previous isopiestic investigations of CuŽNO 3 . 2 Žaq. at the temperature 298.15 K exhibit a remarkable lack of agreement. Consequently, isopiestic vapor-pressure measurements were performed for CuŽNO 3 . 2 Žaq. solutions at T s 298.15 K both at the Texas Christian University and the Lawrence Livermore National Laboratory. These measurements extend from molality m s Ž0.0638 to 6.9235. mol . kgy1 . Under the conditions typically used for isopiestic experiments, it is found that solutions of CuŽNO 3 . 2 Žaq. at higher molalities lose HNO3 into the vapor phase, resulting in a gradual increase in the extent of hydrolysis of their solutions as the samples are re-equilibrated. This produces a progressive downward drift in the apparent osmotic coefficients. Consequently, most previous higher-molality isopiestic results for this system are believed to be unreliable. Experiments were performed to quantify and to minimize the effect of this hydrolysis on the resulting osmotic coefficients. These experiments indicate that the error in the osmotic coefficient from this HNO3 loss is insignificant at lower molalities of CuŽNO 3 . 2 Žaq.; at m s 4 mol . kgy1 it is ( 0.2 per cent, but above m f 5 mol . kgy1 it can become quite significant. Recommended values of the osmotic coefficients, water activities, and mean activity coefficients of CuŽNO 3 . 2 Žaq. are presented up to m s 3.00 mol . kgy1 , the maximum molality where we consider them to be completely accurate, and, with slightly lower accuracy, up to m s 6.9235 mol . kgy1 . Pitzer’s equation was found to represent reliably the experimental osmotic coefficients provided the third virial coefficient was ionic-strength dependent. KEYWORDS: isopiestic measurements; copper nitrate; osmotic coefficients; activity coefficients; Pitzer’s equation a This document was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government, nor the University of California, nor any of their employees makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference to any specific commercial products, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or the University of California, and shall not be used for advertising or product endorsement purposes. b Visiting Researcher on a Scholarship from the Dipartimento di Chimica, Universita ` Federico II di Napoli, 80134, Naples, Italy. c To whom correspondence should be addressed ŽE-mail: [email protected]..

0021]9614r98r030327 q 26 $25.00r0rct970307

328

J. G. Albright, P. Rizzo, and J. A. Rard

1. Introduction Aqueous solutions of YŽNO 3 . 3 , BaŽNO 3 . 2 , CuŽNO 3 . 2 , and other metal nitrates are frequently used as precursor solutions for the preparation of high-temperature superconducting mixed metal oxides including YBa 2 Cu 3 O 7y d . Thermodynamic properties are required in order to understand and model these solutions. We earlier reported the results from isopiestic and density measurements for YŽNO 3 . 3 Žaq. at the temperature 298.15 K,Ž1. although those experiments were performed before this class of superconductors had been discovered. These density measurements and isopiestic measurements extend into the supersaturated molality region to D m f 0.7 mol . kgy1 and D m f 2 mol . kgy1 , respectively.Ž2. Isopiestic measurements have been reported for CuŽNO 3 . 2 Žaq. at T s 298.15 K from m s Ž0.1091 to 2.415. mol . kgy1 with KClŽaq. as reference standard,Ž3. from m s Ž2.809 to 7.840. mol . kgy1 with H 2 SO4Žaq. as reference standard,Ž4. from m s Ž1.254 to 4.326. mol . kgy1 with an unknown reference standard,Ž5. and from m s Ž0.09443 to 2.2837. mol . kgy1 with KClŽaq. as reference standard and m s Ž0.8078 to 5.7689. mol . kgy1 with MgŽClO4 . 2 Žaq. as reference standard.Ž6. In the third of these studies Ž5. the reference standard was neither identified nor were its equilibrium molalities given. Goldberg Ž7. has compared the osmotic coefficients f of CuŽNO 3 . 2 Žaq. derived from three of these studies. His deviation plot indicates that values of f from Robinson et al.Ž3. and from BrownŽ4. do not approach each other smoothly but rather are offset by D f f 0.025. Brown did not acknowledge this inconsistency. Filippov et al.Ž8. reported that the water activity and molality of a saturated solution of CuŽNO 3 . 2 Žaq. in equilibrium with a solid phase of CuŽNO 3 . 2 . 3H 2 OŽcr. at T s 298.15 K were a w s 0.3459 and m s CuŽNO 3 . 2 4 s 8.072 mol . kgy1 , respectively. These values yield f s 2.433, which is roughly consistent with Brown’s results at lower molalities. Values of f from Sadowska and Libus´Ž6. are about Ž1 to 2. per cent above those of Robinson et al.,Ž3. are approximately 1 per cent above Brown’s values Ž4. at m f 3 mol . kgy1 , but fall about 1 per cent below Brown’s values at high molalities. Goldberg Ž7. found that f values derived from the study of Yakimov and GuzhavinaŽ5. were grossly discrepant from the other studies. An examination of the molalities of CuŽNO 3 . 2 Žaq. reported by Goldberg indicates they were calculated incorrectly from the reported ‘‘mole %’’ compositions of Yakimov and Guzhavina. We thus recalculated these molalities and the corresponding f values, but the corrected results were still extremely discrepant from the other isopiestic studies. Yakimov and Guzhavina did not provide any experimental details, so it is not possible to identify the source of their error or refine these calculations further. Goldberg Ž7. also derived values of f for CuŽNO 3 . 2 Žaq. from m s Ž0.010 to 0.508. mol . kgy1 from older determinations of freezing temperature depression. These values, after being corrected to T s 298.15 K, were quite scattered and were discrepant from the lower-molality isopiestic results. At least part of this discrepancy arose because of a lack of enthalpies of dilution and heat capacities for CuŽNO 3 . 2 Žaq.. Consequently, Goldberg estimated these corrections from available results for CuŽClO4 . 2 Žaq.. Heat capacities are now available Ž9. for CuŽNO 3 . 2 Žaq. at

f and g for CuŽNO 3 . 2 Žaq.

329

T s 298.15 K for m s Ž0.04882 to 0.14032. mol . kgy1 which could allow those calculations to be refined somewhat, but a large uncertainty remains because enthalpies of dilution are still lacking. The above survey of the available thermodynamic activity results for CuŽNO 3 . 2 Žaq. at T s 298.15 K indicates the general lack of consistency among them. Even the f values from studies in best agreement Ž3,4,6,8. are discrepant by about Ž1 to 2. per cent, compared with an agreement between isopiestic studies of Ž0.2 to 0.3. per cent in favorable cases.Ž10. Consequently, we performed isopiestic measurements over a wide molality range at T s 298.15 K using high-purity CuŽNO 3 . 2 to resolve these discrepancies and to characterize better the activities of the CuŽNO 3 . 2 Žaq. system.

2. Experimental Isopiestic vapor-pressure measurements were performed for CuŽNO 3 . 2 Žaq. at the temperature Ž298.15 " 0.005 . K, both at the Texas Christian University ŽTCU. and Lawrence Livermore National Laboratory ŽLLNL.. The isopiestic apparatuses have been described previously.Ž2,11,12. Both types have fan-like devices attached to their copper heat-transfer blocks. These provide some stirring of the vapor phase as the chambers are rotated Žat TCU. or rocked back-and-forth Žat LLNL. to keep the solutions well mixed during the equilibrations. Experiments at TCU were performed with NaClŽaq. and CaCl 2 Žaq. as reference standards, and those at LLNL with H 2 SO4 Žaq. and, in a few cases, NaClŽaq. as reference standards. Duplicate samples of CuŽNO 3 . 2 Žaq. and reference standards were used for the isopiestic experiments at LLNL and triplicate or quadruplicate samples for the experiments at TCU. Equilibrium molalities were determined to better than "0.1 per cent in nearly all cases and to better than "0.05 per cent in most cases, except for experiments with CuŽNO 3 . 2 Žaq. molalities (0.1125 mol . kgy1 where the agreement was within "0.0002 mol . kgy1 or "Ž0.15 to 0.3. per cent. Water used for solution preparations at TCU was purified by deionization, distillation, and then filtration with a Millipore filtering system, and at LLNL by double distillation. Molar masses used for molality calculations or gravimetric analysis of stock solutions are 58.443 g . moly1 for NaCl, 110.986 g . moly1 for CaCl 2 , 98.074 g . moly1 for H 2 SO4 , 136.138 g . moly1 for CaSO4 , 187.5558 g . moly1 for CuŽNO 3 . 2 , and 79.7454 g . moly1 for CuO. All apparent sample masses were converted to masses using buoyancy corrections. The first stock solution of CuŽNO 3 . 2 Žaq. was prepared at TCU by dissolution of a sample of Aldrich Žmass fraction s 0.99999. CuŽNO 3 . 2 . xH 2 OŽcr. in purified water, followed by filtration through a prewashed 0.2 m m Corning Nylon ‘‘Low Extractable Membrane’’ Filtering Unit. According to the ‘‘Certificate of Analysis’’ provided by Aldrich, the mass fractions of Ca and Mg were 5 . 10y6 and 1 . 10y7 , respectively. Part of this stock solution a1 was retained at TCU for use in the isopiestic experiments, and the remainder was shipped in a tightly-sealed all-glass container to LLNL for additional isopiestic experiments, molality analyses, and impurity analyses. The density of this stock solution was determined to be

330

J. G. Albright, P. Rizzo, and J. A. Rard

1.35092 g . cmy3 at T s 298.15 K using the Mettler]Parr DMAr40 vibrating densimeter at TCU. The molality of the CuŽNO 3 . 2 Žaq. stock solution a1 was determined at LLNL by measuring the masses of residues formed from conversion of mass aliquots of the stock solution to CuOŽs.. Two separate analyses were performed. Triplicate samples of stock solution were used for each analysis, and the masses of the residues were determined after heating them to temperatures of Ž973, 1023, and 1073. K followed by cooling in a desiccator. Six or seven mass determinations were done for each sample with each different furnace temperature. In the first analytical procedure the samples of CuŽNO 3 . 2 Žaq. were evaporated to near dryness in crucibles after addition of excess HClŽaq. to decompose the nitrate ions, excess H 2 SO4 Žaq. was added and the solutions evaporated to dryness to eliminate the chloride ions and convert the samples to CuSO4 Žs., which were then decomposed thermally to CuOŽs. in a box furnace.Ž13. In the second analytical procedure, the CuŽNO 3 . 2 Žaq. samples were evaporated to dryness in crucibles, and the CuŽNO 3 . 2 Žs. was decomposed directly to CuO in the box furnace. For both analytical procedures, the stock solution molalities calculated from the weighings carried out following heating of the samples to T s Ž1023 and 1073. K were completely consistent, whereas those calculated from previous weighings carried out following heating to T s 973 K were slightly higher by Ž0.017 to 0.042. per cent. However, this difference is less than the approximately 0.06 per cent uncertainty of the analyses. A stock solution molality of Ž2.7710 " 0.0018. mol . kgy1 was obtained from the first analysis and the second analysis yielded Ž2.7702 " 0.0016. mol . kgy1 , where these uncertainties are Ž n y 1. standard deviations. These values are in excellent agreement, and their average was accepted for molality calculations. We note that some precautions are necessary when using these methods for gravimetric analysis of the molalities of CuŽNO 3 . 2 Žaq. solutions or of other soluble CuŽII. salts. First, solutions of CuCl 2 Žaq., such as are formed when the CuŽNO 3 . 2 Žaq. samples are evaporated with excess HCl, exhibit a tendency to ‘‘creep’’ out of the porcelain crucibles as the solutions are about to become dry. This problem can be prevented by adding the H 2 SO4Žaq. to the samples while a small amount of water still remains. Second, evaporation of CuŽNO 3 . 2 Žaq. solutions yields various hydrated copperŽII. nitrates, CuŽNO 3 . 2 . xH 2 OŽs.. However, there appears to be at least partial formation of anhydrous CuŽNO 3 . 2 Žs. as the temperature is increased further but before decomposition to CuOŽs. occurs, and CuŽNO 3 . 2 Žs. is slightly volatile below its decomposition temperature.Ž14,15. Addison and Hathaway Ž15. reported that although CuŽNO 3 . 2 Žs. began to decompose below T s 463 K, CuŽNO 3 . 2 Žg. is stable up to T s 499 K, whereupon it decomposes rapidly, apparently to CuOŽs.. A small amount of a black sooty deposit of CuOŽs. was found on the inside walls of our crucibles after the CuŽNO 3 . 2 . xH 2 OŽs. was decomposed thermally in our box furnace. Significant loss of CuŽNO 3 . 2 due to volatility can be avoided during the gravimetric analysis by covering the porcelain crucibles with lids that are opened only very slightly to vent water vapor and fumes from the nitrate decomposition, and by raising the temperature of the furnace quickly enough to ensure rapid decomposition of the CuŽNO 3 . 2 Žs. to CuOŽs..

f and g for CuŽNO 3 . 2 Žaq.

331

The CuOŽs. formed from decomposition of the CuSO4 Žs. was analysed for impurities at LLNL using direct current arc optical emission spectroscopy ŽDCAOES.. Eight impurity elements ŽSi, Al, Ca, Fe, Li, Na, K, and Mg. were detected. Twenty other elements were analysed for, including other second and third transition series metals, but not found. The impurities Si and Al were found at relatively high and nearly equal amounts, which implies that they could have been introduced into the sample by a slight reaction of the CuOŽs. with the kaolinite coatings of the porcelain crucibles during the thermal decomposition of the CuSO4Žs. at the high furnace temperatures Žup to 1073 K., rather than having been present in the original CuŽNO 3 . 2 Žaq. solution. It is also possible that the Fe and some of the alkali metal impurities were introduced in the same manner. More meaningful analyses for these impurities were obtained by direct analysis of the CuŽNO 3 . 2 Žaq. stock solution a1 at LLNL using inductively-coupled plasma optical emission spectroscopy ŽICPrOES. and inductively-coupled plasma atomic emission spectroscopy ŽICPrAES. with calibration standards. Five of the potential impurities ŽAl, Fe, Li, Na, and K. were not detected in the solution, which confirms that they were introduced during the thermal decomposition of the CuSO4 Žs. and were not present in the CuŽNO 3 . 2 Žaq. stock solution a1. However, even though they were present in CuO, they were not present in large enough amounts to invalidate the molality analysis. Three of the impurities found in the CuOŽs. were also detected in the CuŽNO 3 . 2 Žaq. solution. Based upon the ICP analyses, our CuŽNO 3 . 2 was found to have a mole fraction purity of 0.999917, with mole fractions of 3 . 10y6 of MgŽNO 3 . 2 , 5.5 . 10y5 of CaŽNO 3 . 2 , and 2.5 . 10y5 of SiO 2 also being present. A second stock solution of CuŽNO 3 . 2 Žaq. was prepared at TCU from a separate batch of Aldrich Žmass fraction s 0.99999. CuŽNO 3 . 2 . xH 2 OŽcr., and was used there for some additional isopiestic experiments at intermediate and high molalities. Although we did not have it analysed for its impurity content, it was presumably comparable in purity to the first batch. Its stock solution density was determined to be 1.52560 g . cmy3 at T s 298.15 K using the Mettler]Parr DMAr40 vibrating densimeter at TCU. Part of this stock solution a2 was shipped in a tightly-sealed, all-glass container to LLNL for a molality analysis. Its molality was determined by conversion of mass aliquots to CuOŽs., using the first method described above with a furnace temperature of 1023 K. Analysis using triplicate samples gave m s Ž4.5578 " 0.0020. mol . kgy1 . Both NaClŽaq. isopiestic reference standard stock solutions were prepared by mass from oven-dried analytical reagent grade NaClŽcr. and purified water. The molality of the NaClŽaq. solution prepared at LLNL was determined to be Ž2.92433 " 0.0008 2 . mol . kgy1 based on dehydration of three samples at T s 773 K. See Rard and Archer Ž16. for a more detailed description of this molality analysis and for the impurity content of the NaCl. For the NaClŽaq. solution prepared at TCU, the molality was calculated from the masses of NaClŽcr. and of water assuming the NaCl contained a mass fraction Ž0.0013 " 0.0002. of residual water.Ž17. The m s Ž0.44998 6 " 0.000278 . mol . kgy1 H 2 SO4Žaq. reference standard stock solution used at LLNL is the same as described elsewhere.Ž12. Samples of it were weighed directly into the isopiestic sample cups, and were then concentrated in a

332

J. G. Albright, P. Rizzo, and J. A. Rard

desiccator to achieve the desired initial molalities for the isopiestic experiments. The CaCl 2 Žaq. reference stock solution was prepared at TCU from Mallinckrodt analytical reagent grade CaCl 2 . 2H 2 OŽcr. and purified water. A portion of this solution was shipped to LLNL in a tightly-sealed, all-glass container, where its molality was determined by conversion of samples to anhydrous CaSO4 , as described elsewhere.Ž13. The analysis was performed in triplicate. Weighings of the crucibles were done after heating the residues to various temperatures, followed by cooling the samples to room temperature in a desiccator. The calculated molality was m s Ž6.9701 " 0.0036. mol . kgy1 from the six weighings after heating the residues to T s 823 K, m s Ž6.9720 " 0.0030. mol . kgy1 from the six weighings after heating the residues to T s 873 K, and m s Ž6.9714 " 0.0028. mol . kgy1 from the six weighings after heating the residues to T s 923 K. There is no trend in these results with the furnace temperature, and the average of m s Ž6.9712 " 0.0033. mol . kgy1 was accepted for molality calculations. Tables 1 through 3 contain the equilibrium molalities and times for the isopiestic experiments with samples of CuŽNO 3 . 2 Žaq. stock solution a1 with NaClŽaq., CaCl 2 Žaq., and H 2 SO4Žaq., respectively, as reference standards. Table 4 contains additional isopiestic results for experiments with CuŽNO 3 . 2 Žaq. stock solution a2, with CaCl 2 Žaq. as reference standard. Values of the molal Žor ‘‘practical’’. osmotic coefficient f of CuŽNO 3 . 2 Žaq. were calculated from these equilibrium molalities using the fundamental equation for isopiestic equilibrium:

f s n *m*f *rn m,

Ž 1.

where n s 3 is the stoichiometric ionization number of CuŽNO 3 . 2 Žaq. assuming complete dissociation and m its equilibrium molality. Corresponding quantities for isopiestic reference standards are denoted with asterisks: n * s 2 for NaCl and n * s 3 for CaCl 2 and H 2 SO4 . Osmotic coefficients of the reference standards f * at T s 298.15 K were calculated for NaClŽaq. from Archer’s extended Pitzer model,Ž18. for CaCl 2 Žaq. from the extended Pitzer model of Rard and Clegg,Ž19. for H 2 SO4 Žaq. at m* ( 6.1 mol . kgy1 from the extended Pitzer model of Clegg et al.,Ž20. and for H 2 SO4 Žaq. at m* ) 6.1 mol . kgy1 from the empirical equation of Rard et al.Ž21. These two equations for H 2 SO4 Žaq. are quite consistent at the switch-over molality. Isopiestic experiments were performed to fairly low molalities of CuŽNO 3 . 2 Žaq. because such results are required for a reliable extrapolation of f values to the region where the Debye]Huckel limiting law is obeyed. This is especially important ¨ for CuŽNO 3 . 2 Žaq. because of the lack of reliable activity values at low molalities from other methods. We attribute the good quality of the isopiestic results at the lowest molalities to two factors. First, fan-like devices were present in the isopiestic chambers Žexcept for some of the results presented in table 3. to provide stirring of the vapor phase as the solutions were equilibrated.Ž11,12. At higher molalities the rate of approach of the solutions to isopiestic equilibrium is controlled mainly by heat transport through the copper heat-transfer blocks and walls of the sample cups. In contrast,

f and g for CuŽNO 3 . 2 Žaq.

333

TABLE 1. Isopiestic molalities m of CuŽNO 3 . 2 Žaq. and m* of the NaClŽaq. reference standard solutions and the osmotic coefficients f of CuŽNO 3 . 2 Žaq. at the temperature T s 298.15 K for experiments performed at TCU a m* Ž NaCl. mol . kgy1

5.4100 5.0431 4.6671 4.2579 3.9374 3.6791 3.3451 3.0420 2.7770 2.5685 2.3828 2.6711 2.5256 2.3980 2.2367 2.0338 1.8256 1.6421 1.1991 1.1945 0.9760 0.8445 0.7093 0.5956 0.5591 0.4849 0.4426 0.3898 0.3383 0.2519 0.1555 0.1285 0.0899 0.0962 0.0882 0.0923

m  Cu Ž NO 3 . 2 4 mol . kgy1 Series 1-TCU 2.9939 2.8091 2.6170 2.4081 2.2444 2.1115 1.9395 1.7829 1.6444 1.5351 1.4370 Series 2-TCU 1.5843 1.5119 1.4438 1.3581 1.2483 1.1313 1.0342 Series 3-TCU 0.7815 0.7790 0.6490 0.5689 0.4844 0.4119 Series 4-TCU 0.3879 0.3392 0.3112 0.2757 0.2406 0.1810 Series 5-TCU 0.1125 0.0932 0.0653 0.0699 0.0638 0.0668

f CuŽNO 3 . 2 4 b

ta d

1.4736 1.4304 1.3871 1.3396 1.3021 1.2720 1.2325 1.1961 1.1643 1.1388 1.1160

8 6 7 7 8 8 6 8 14 10 10

1.1548 Ž w s 0. 1.1340 1.1188 1.0987 1.0740 1.0512 Ž w s 0. 1.0238

7 7 7 8 8 6 23

0.9673 0.9664 0.9386 0.9216 0.9048 0.8905

35 35 62 34 64 52

0.8869 0.8783 0.8733 0.8677 0.8629 0.8551

68 63 34 64 53 139

0.8535 0.8535 0.8571 0.8558 0.8609 0.8598

126 199 95 23 27 30

a A fan-like device was present in the chamber, which provided some stirring of the vapor phase as the chamber was rotated during the equilibrations. Different samples of CuŽNO 3 . 2 Žaq. stock solution a1 and of NaClŽaq. were used for each series of experiments. The lengths of the equilibration periods t are given in days. b Osmotic coefficients of the NaClŽaq. reference standard were calculated from the equation and parameters of Archer.Ž18. Values of f CuŽNO 3 . 2 4 given zero weight in the least-squares fits to equation Ž5. are indicated by Ž w s 0..

334

J. G. Albright, P. Rizzo, and J. A. Rard TABLE 2. Isopiestic molalities m of CuŽNO 3 . 2 Žaq. and m* of the CaCl 2 Žaq. reference standard solutions and the osmotic coefficients f of CuŽNO 3 . 2 Žaq. at the temperature T s 298.15 K for experiments performed at TCU a m* Ž CaCl 2 . mol . kgy1

m  Cu Ž NO 3 . 2 4 mol . kgy1

3.8425 3.8179 3.5376 3.3001 3.1067 2.9287 2.7589 2.5918 2.4610 4.5307

4.5226 4.4989 4.1202 3.8014 3.5452 3.3117 3.0941 2.8817 2.7181 5.6249

4.5075 4.4943 3.5323

5.4806 5.4695 4.1353

f CuŽNO 3 . 2 4 b

ta d

Series 6-TCU 1.7977 Ž w s 0. 1.7872 1.7112 1.6463 1.5923 1.5420 1.4927 Ž w s 0. 1.4449 Ž w s 0. 1.4075 Ž w s 0. 1.9275 Ž w s 0.

8 8 15 9 10 7 8 21 9 131

1.9605 Ž w s 0. 1.9544 Ž w s 0. 1.7005 Ž w s 0.

9 6 17

1.9218 Ž w s 0. 1.8907 Ž w s 0. 1.8738 Ž w s 0.

14 12 12

1.8418 1.7298 1.6335 Ž w s 0. 1.5519 1.4740 1.4129 1.3617

4 3 4 3 4 3 3

Series 7-TCU

Series 8-TCU 4.3598 4.2581 4.2058

5.2738 5.1434 5.0788 Series 9-TCU c

4.0172 3.5943 3.2426 2.9518 2.6826 2.4700 2.2899

4.7693 4.1886 3.7177 3.3348 2.9902 2.7238 2.5021

a At some of the higher molalities, especially for the 131 d equilibration, there was a slow loss of HNO3 from the solutions of CuŽNO 3 . 2 Žaq. as they were equilibrated. Thus those equilibrium molalities are for nitrate-deficient Žand higher pH. samples of variable composition. In those cases it is likely that some of the HNO3 being lost from the CuŽNO 3 . 2 Žaq. solutions was absorbed by the CaCl 2 Žaq. solutions, thereby contaminating them. A fan-like device was present in the chamber to provide stirring of the vapor phase as the chamber was rotated during the equilibrations. Different samples of CuŽNO 3 . 2 Žaq. stock solution a1 and of CaCl 2 Žaq. were used for each series of experiments. The lengths of the equilibration periods t are given in days. b Osmotic coefficients of the CaCl 2 Žaq. reference standard were calculated from the equation and parameters of Rard and Clegg.Ž19. Values of f CuŽNO 3 . 2 4 given zero weight in the least-squares fits to equation Ž5. are indicated by Ž w s 0.. c The desiccator was back-filled with HeŽg. during these equilibrations.

at low molalities the rate of approach to isopiestic equilibrium is controlled mainly by mass transport of water through the vapor phase. Vapor stirring significantly improves this mass transport.Ž10. Second, exceptionally long equilibration times were generally used to allow the solutions to reach equilibrium at the lowest molalities.

f and g for CuŽNO 3 . 2 Žaq.

335

TABLE 3. Isopiestic molalities m of CuŽNO 3 . 2 Žaq. and m* of the H 2 SO4 Žaq. reference standard solutions and the osmotic coefficients f of CuŽNO 3 . 2 Žaq. at the temperature T s 298.15 K for experiments performed at LLNLa m* Ž H 2 SO4 . mol . kgy1

m  Cu Ž NO 3 . 2 4 mol . kgy1

m*  NaCl. mol . kgy1 Series 1-LLNL

7.35875 " 0.0011 7.5534 " 0.0025 7.7169 " 0.0028 7.8782 " 0.0050 6.8303 " 0.0053 7.0871 " 0.0072

5.8711 " 0.0017 6.0680 " 0.0013 6.2188 " 0.0023 6.3848 " 0.0015 5.5256 " 0.0003 5.7507 " 0.0014

f CuŽNO 3 . 2 4 b

f H 2 SO4 4 b

2.0287 Ž w s 0. 2.0434 Ž w s 0. 2.0605 Ž w s 0. 2.0714 Ž w s 0. 1.9204 Ž w s 0. 1.9541 Ž w s 0.

1.6186 1.6416 1.6605 1.6788 1.5536 1.5857

ta d

c

Series 3-LLNLd equilibrated with a reservoir of a solution saturated with NaClŽcr.4 4.25735 " 0.0014 3.2912 " 0.0023 1.5391 1.1898 4.3355 " 0.0021 3.3585 " 0.0008 1.5519 1.2022 4.3422 " 0.0021 3.3642 " 0.0006 1.5530 1.2032 4.3426 " 0.0000 3.3669 " 0.0000 1.5520 1.2033 4.3454 " 0.0013 3.3675 " 0.0000 1.5532 1.2037 4.3455 " 0.0004 3.37035 " 0.0002 1.5520 Ž w s 0. 1.2037 4.3430 " 0.0013 6.1324 " 0.0002 1.2049 e 4.3461 " 0.0011 Series 4-LLNL f equilibrated with a reservoir of a solution saturated with SrCl 2 . 6H 2 OŽcr.4 4.9007 " 0.0010 3.8230 " 0.0014 1.6534 1.2898 4.9015 " 0.0018 3.8261 " 0.0007 1.6525 1.2899 4.9022 " 0.0001 3.8280 " 0.0000 1.6520 1.2900

21 21 17 19 20 13

14 14 16 21 18 25 14 14

18 22 14

a Samples of Cu ŽNO 3 . 2 Žaq. stock solution a1 were used for these experiments. The lengths of the equilibration periods t are given in days. b Osmotic coefficients of the H 2 SO 4Žaq. reference standard were calculated from the equation and parameters of Rard et al.Ž21. for m* H 2 SO 44 ) 6.1 mol . kgy1 , of Clegg et al.Ž20. for m* H 2 SO 4 4 - 6.1 mol . kgy1 , and of NaClŽaq . from the equation of Archer.Ž18. Values of f Cu ŽNO 3 . 2 4 given zero weight in the least-squares fits to equation Ž5. are indicated by Ž w s 0 .. c Because of the loss of HNO 3 from the solutions of Cu ŽNO 3 . 2Žaq . as they were equilibrated, these six equilibrium molalities are for nitrate-deficient Žand higher pH . samples of variable composition. It is also likely that some of the HNO 3 being lost from the Cu ŽNO 3 . 2 Žaq . solutions was absorbed by the H 2 SO 4Žaq . solutions, thereby contaminating them. The values of f Cu ŽNO 3 . 2 4 from this series are thus unreliable and were not included in the least-squares fits. A fan-like device was present in the chamber during these equilibrations to provide some stirring of the vapor phase as the chamber was rocked back-and-forth. d After the series 1 experiments were completed, the samples of Cu ŽNO 3 . 2 Žaq . and of H 2 SO 4Žaq . were discarded and replaced with fresh ones. An attempt was made ŽSeries 2 . to equilibrate them with a reservoir cup containing both saturated NaClŽaq. and solid NaClŽcr., but the gasket under the lid of the isopiestic chamber was not sealed properly and water leaked into the chamber. Afterward the chamber and sample cups were cleaned and dried, new samples were weighed out, and the equilibrations restarted ŽSeries 3 .. See the text for more details. The fan-like device was removed from the chamber during the first six of these equilibrations in order to avoid dispersing any HNO 3 that might have been present in the vapor phase, and a sheet of thick copper metal foil was positioned above the sample cups to act as a chemical trap for the HNO 3. However, the copper foil was removed from the chamber during the last two experiments of this series, which involved solutions of H 2 SO 4Žaq. and NaClŽaq. only, and the vapor-stirring fan-like device was also reinstalled. During the last of these experiments crystallization occurred in both samples of the NaClŽaq. reference standard so no molality is reported. e This value of f s 1.2049 was calculated from the equilibrium molalities with f * of NaClŽaq. from the equation of Archer.Ž18. The equation of Clegg et al.Ž20. predicts that f s 1.2033 for H 2 SO 4Žaq . at this molality. f After the series 3 experiments were completed, the sample of Cu ŽNO 3 . 2 Žaq . were discarded and replaced with fresh ones. The fan-like device was removed from the chamber during these equilibrations and the sheet of thick copper metal foil was repositioned above the sample cups to act as a chemical trap for the HNO3 . These samples were equilibrated with a reservoir containing both saturated SrCl 2Ž aq. and SrCl 2 . 6H 2 O Žcr..

336

J. G. Albright, P. Rizzo, and J. A. Rard TABLE 4. Isopiestic molalities m of CuŽNO 3 . 2 Žaq. and m* of the CaCl 2 Žaq. reference standard solutions and the osmotic coefficients f of CuŽNO 3 . 2 Žaq. at the temperature T s 298.15 K for experiments performed at TCU a m* Ž CaCl 2 . mol . kgy1

5.5022 5.5097 5.5176 4.9486 4.9553 4.9373 4.9411 4.9401 4.9817 4.9877 4.9921 4.2986 4.3104 4.3205 4.3316 3.5183 3.5064 3.5131 3.5159 3.0636 3.1033 3.1199 2.8967 2.9068 2.9210 2.4565 2.4997 2.5140

m  Cu Ž NO 3 . 2 4 mol . kgy1 Series 10-TCU c 6.8829 6.9020 6.9235 Series 11-TCU c 6.1010 6.1125 Series 12-TCU c 6.0800 6.0883 6.0923 Series 13-TCU c 6.1460 6.1579 6.1680 Series 14-TCU c 5.1723 5.1921 Series 15-TCU c 5.2043 5.2239 Series 16-TCU c 4.0797 4.0719 4.0811 4.0870 3.4837 3.5384 3.5589 Series 17-TCU c 3.2588 3.2765 3.2942 2.7056 2.7617 2.7782

f CuŽNO 3 . 2 4 b

ta d

2.1972 2.1961 2.1944

2 1 1

2.0726 2.0735

2 1

2.0715 2.0714 2.0694

2 1 2

2.0811 2.0815 2.0812

2 1 1

1.9116 1.9135

2 1

1.9168 1.9182 Ž w s 0.

2 1

1.7120 Ž w s 0. 1.7054 1.7071 1.7069 1.5823 1.5923 1.5976

2 1 1 2 3 8 3

1.5382 Ž w s 0. 1.5390 1.5433 1.4098 1.4209 1.4257

2 1 2 3 7 4

a At the higher molalities there was a slow loss of HNO3 from the solutions of CuŽNO 3 . 2 Žaq. as they were equilibrated. Thus those equilibrium molalities are for nitrate-deficient Žand higher pH. samples of variable composition. Some of the HNO3 being lost from the CuŽNO 3 . 2 Žaq. solutions was absorbed by the CaCl 2 Žaq. solutions, thereby contaminating them slightly. A fan-like device was present in the chamber to provide stirring of the vapor phase as the chamber was rotated during the equilibrations. Different samples of CuŽNO 3 . 2 Žaq. stock solution a2 and of CaCl 2 Žaq. were used for each series of experiments. The lengths of the equilibration periods t are given in days. b Osmotic coefficients of the CaCl 2 Žaq. reference standard were calculated from the equation and parameters of Rard and Clegg.Ž19. Values of f CuŽNO 3 . 2 4 given zero weight in the least-squares fits to equation Ž5. are indicated by Ž w s 0.. c The desiccator was back-filled with HeŽg. during these equilibrations.

f and g for CuŽNO 3 . 2 Žaq.

337

Isopiestic equilibration times used in the earlier experiments at CuŽNO 3 . 2 Žaq. molalities of m ) 2.7 mol . kgy1 were typically Ž6 to 21. d for TCU Series 6 through 8, and good agreement between the molalities of replicate samples could be achieved with any of these times. However, for one of the high molality experiments performed at TCU, an unusually long equilibration time of 131 d was used Žthe last experiment of TCU Series 6., which yielded a value of f for CuŽNO 3 . 2 Žaq. that was over 3 per cent below results determined with shorter equilibration times. At essentially the same time, the LLNL Series 1 experiments were being performed, with the molalities being increased for each re-equilibration. It was noticed that the resulting values of f for CuŽNO 3 . 2 Žaq. exhibited progressively larger negative deviations from the values of BrownŽ4. with each re-equilibration. The solutions were then diluted slightly and equilibrated twice more. Values of f for these last two experiments were much lower than those obtained by extrapolation of the trend for the first four experiments. It was also noticed that the brass vapor-stirring ‘‘fan’’ had tarnished much more than those in our other isopiestic chambers where no CuŽNO 3 . 2 Žaq. was present. Furthermore, although the agreement between the equilibrium molalities of the duplicate CuŽNO 3 . 2 Žaq. samples remained good, those for the H 2 SO4Žaq. reference standard solutions became slightly more discrepant with each re-equilibration. A similar downward drift in the isopiestic values of f had been observed for CuCl 2 Žaq. at T s 298.15 K,Ž13. which was conclusively shown to result from continuous loss of HCl from the solutions during the isopiestic experiments and the resulting progressively increasing hydrolysis of CuŽII.. A similar effect, loss of HNO 3 from the CuŽNO 3 . 2 Žaq. samples during isopiestic experiments, is undoubtedly the origin of the downward drift and hysteresis in the values of f when the solutions are re-equilibrated. Those experiments with CuCl 2 Žaq. were performed in the isopiestic chambers at LLNL which are constructed from stainless steel. The stainless steel lid of these chambers acted as a highly efficient chemical trap for the HClŽg., thereby removing it from the vapor phase and preventing contamination of the reference standard samples. In contrast, stainless steel is passive to HNO3 , and the isopiestic chambers at TCU are constructed from plastic desiccators which also do not react with HNO3 Žg. under the experimental conditions. A portion of the HNO3 Žg. apparently reacted with brass vapor-stirring ‘‘fans’’ since they had become tarnished. However, because they were designed to stir the vapor phase, most of the HNO3 Žg. undoubtedly was dispersed throughout the chamber. Consequently, much of the HNO3 lost from the CuŽNO 3 . 2 Žaq. samples could have migrated to those sample cups containing reference standard solutions and contaminated them. It was noted earlier that the discrepancy between the molalities of the H 2 SO4Žaq. reference standard solutions for the LLNL Series 1 increased slightly each time the solutions were re-equilibrated. The four cups containing solutions were located in the four retainers nearest to the center of the heat-transfer block, which positioned them closest to the vapor-stirring ‘‘fan.’’ The two sample cups containing CuŽNO 3 . 2 Žaq. were located diagonally to each other, as were the cups containing

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J. G. Albright, P. Rizzo, and J. A. Rard

the H 2 SO4Žaq. reference standard solutions. The isopiestic chamber was rocked back-and-forth during the equilibrations to keep the individual solutions mixed and eliminate concentration gradients caused by solvent transport. This motion produces a back-and-forth but slightly asymmetric rotation of the fans. This increasing but small discrepancy in the molalities of the H 2 SO4 Žaq. solutions could mean that the two samples absorbed HNO3 Žg. at slightly different rates, presumably due to the slight asymmetry in the vapor stirring as the ‘‘fans’’ reversed direction. However, this is not certain because the effect is so small. No such discrepancies in reference solution molalities were observed for the higher-molality experiments at TCU. This probably results from the much more rapid and continuous vapor stirring produced by the rotation of the isopiestic desiccators, which would produce more uniform concentrations of HNO3 Žg.. Vaporization of nitric acid from the CuŽNO 3 . 2 Žaq. solutions undoubtedly occurs because of the presence of small amounts of undissociated HNO3 Žaq. which form in these acidic solutions: Hq Ž aq . q NOy 3 Ž aq . s HNO 3 Ž aq, undissoc. . s HNO 3 Ž g . .

Ž 2.

The pH of the m s Ž4.5578 " 0.0020. mol . kgy1 CuŽNO 3 . 2 Žaq. stock solution a2 was determined with a pH meter to be approximately 0.6, which is quite low. However, the stoichiometric ionic strength of this solution is I s 13.7 mol . kgy1 , which is considerably higher than that of the pH s 2.00 buffer solution used to calibrate the pH meter. There was undoubtedly a large liquid junction potential present in the electrode system when the CuŽNO 3 . 2 Žaq. solution was studied, which is not entirely compensated for by the calibration with a relatively dilute buffer. This makes the interpretation of the pH f 0.6 reading of the pH meter highly uncertain. However, this measurement was adequate to establish that CuŽNO 3 . 2 Žaq. solutions at high molalities are quite acidic. Nitric acid is nearly completely dissociated at low molalities Ž22. and HNO3 Žaq, undissoc.. is likely to be present in significant amounts only in relatively concentrated solutions of CuŽNO 3 . 2 Žaq.. Thus, we do not expect loss of HNO3 from CuŽNO 3 . 2 Žaq. solutions to occur at low and intermediate molalities, and the osmotic coefficients for those experiments should be reliable and accurate. This is supported by the excellent agreement between values of f for CuŽNO 3 . 2 Žaq. from TCU Series 1 and 2. The molalities for the tenth and eleventh experiments of Series 1 overlapped with those of the first four experiments of Series 2 and the resulting f values agree within their experimental scatter. To reduce the effect of HNO3 loss on f for CuŽNO 3 . 2 Žaq. solutions at high molalities for some subsequent experiments performed at TCU, the equilibration times were reduced to Ž1 to 4. d. For some of those equilibrations with shorter times, and a few other experiments performed at TCU, the desiccator was back-filled with helium gas, since the improved thermal conductivity in the vapor phase and the resulting more vigorous vapor stirring enhanced the rate at which the solutions reached isopiestic equilibrium. This was done by removing most of the air from the desiccator with a

f and g for CuŽNO 3 . 2 Žaq.

339

vacuum pump until the pressure was f4 kPa, filling the desiccator with HeŽg. until the pressure reached f0.1 MPa, followed by re-evacuation and refilling of the desiccator with HeŽg. twice more. It was found that with this procedure isopiestic equilibrium was easily achieved in Ž3 or 4. d with excellent consistency between the replicate samples, and good agreement was obtained even with Ž1 to 2. d equilibrations. Series 9 through 17 experiments at TCU were done in this manner. During several of the TCU experiments a thin scum formed on the surface of the CuŽNO 3 . 2 Žaq. solutions. We do not report the results for these experiments because the purity of the solution was compromised. This scum was not identified, but it is possibly CuŽII. hydroxynitrate formed by hydrolysis resulting from the loss of HNO3 . Even with these short equilibration times, there seemed to be a very slight downward drift in f for CuŽNO 3 . 2 Žaq. at intermediate and high molalities. However, it was quite insignificant at and below m f 3 mol . kgy1 and was only very slightly outside experimental error at m f 4 mol . kgy1 . This was established as follows. The isopiestic molality ratios m CuŽNO 3 . 2 4 rmŽCaCl 2 . for the TCU Series 16 and 17 were found to be a linear function of m CuŽNO 3 . 2 4 , and were described by the least-squares equation: m  Cu Ž NO 3 . 2 4 rm Ž CaCl 2 . s 0.98513 q 0.043304 . m  Cu Ž NO 3 . 2 4 rm8 ,

Ž 3.

with a correlation coefficient of 0.99881. Here m8 s 1 mol . kgy1 . This equation is valid for m CuŽNO 3 . 2 4 s Ž2.7056 to 4.0870. mol . kgy1 . The maximum deviation of any value of the molality ratio from this equation is Dw m CuŽNO 3 . 2 4 rmŽCaCl 2 .x s y0.0022Žy0.19 per cent. and the average deviation is 0.0008 Ž0.07 per cent.. Deviations of individual values of m CuŽNO 3 . 2 4 rmŽCaCl 2 . from this equation at the lower molalities, TCU Series 17 experiments, tended to be smaller and showed no correlation with the number of times the samples were re-equilibrated. This implies that there is no systematic drift in this molality ratio due to loss of HNO3 from the CuŽNO 3 . 2 Žaq. samples. In contrast, at the higher molalities, TCU Series 16 experiments, there was a very small but systematic drift in this ratio as the samples were equilibrated. Differences between equation Ž3. and the experimental values of m CuŽNO 3 . 2 4 rmŽCaCl 2 . from the first to the last experiment of that series were y0.0022, y0.0002, y0.0002, 0.0003, 0.0011, 0.0018, and 0.0015. The total change after seven equilibrations was approximately 0.3 per cent, which is slightly outside the precision of measurement of the molality ratio and is in the direction expected from loss of HNO3 from the CuŽNO 3 . 2 Žaq. samples. Most TCU Series 9 experiments fall in the molality range for which equation Ž3. is valid, but were not included in the calculations for the following reason. The initial two equilibrations of that series involved molalities )4.1 mol . kgy1 , where loss of HNO3 from the CuŽNO 3 . 2 Žaq. samples should have been more rapid and extensive. Thus, when those samples were diluted to lower molalities, the extent of hydrolysis was slightly greater than for samples which had not been concentrated as much.

340

J. G. Albright, P. Rizzo, and J. A. Rard

As described below, two additional series of experiments were performed at LLNL to quantify the effect of this experimental difficulty on the f values at intermediate molalities. These are analogous to those reported in our earlier isopiestic study Ž13. of CuCl 2 Žaq.. In the CuCl 2 Žaq. study Ž13. the solutions underwent progressive loss of HCl as they were re-equilibrated. Their apparent molalities also showed a systematic upward drift, and their apparent osmotic coefficients showed a systematic downward drift. This is exactly the type of behavior exhibited by CuŽNO 3 . 2 Žaq.. In some experiments, solutions of CuCl 2 Žaq. and CaCl 2 Žaq. reference standard were also equilibrated with a reservoir cup containing a saturated solution of CuCl 2 Žaq. in contact with a solid phase of CuCl 2 . 2H 2 OŽcr.. Although the apparent molalities of CuCl 2 Žaq. in the isopiestic sample cups showed a continuous increase due to increasing hydrolysis as the samples were re-equilibrated, the water activity of the saturated solution as calculated from the reference standard solution molalities was essentially constant for equilibrations of Ž14, 16, 17, and 20. d. A 41 d experiment using an air-filled chamber and different solution samples also gave a consistent water activity. This indicates that the water activity of the reservoir solution was controlled solely by the Gibbs energy of formation of CuCl 2 . 2H 2 OŽcr. and did not depend on time or on the extent of hydrolysis of the CuCl 2 Žaq. solutions in the sample cups or hydrolysis of the solution phase present in the reservoir cup. A constant water activity is guaranteed by the condition of thermodynamic equilibrium provided CuCl 2 . 2H 2 OŽcr. is the only solid phase present in the reservoir solution. The solubility of CuŽNO 3 . 2 . 3H 2 OŽcr. at T s 298.15 K is quite large, about 8.072 mol . kgy1 ,Ž8. and is high enough that loss of HNO3 should be severe even during a single isopiestic equilibration. However, there is no need for isopiestic measurements at fixed water activity to be performed only at the water activity of the saturated solution of the electrolyte being investigated. Any saturated solution will be satisfactory as long as its water activity occurs in a useful region. In addition, the HNO3 migrating from the CuŽNO 3 . 2 Žaq. solutions through the vapor phase needs to be trapped to avoid migration to the reference standard solutions, so that they remain uncontaminated and their equilibrium molalities can be used to calculate the correct water activity. We decided to perform these equilibrations Žat LLNL. by using a reservoir solution cup containing saturated NaClŽaq. in equilibrium with a solid phase of NaClŽcr., and one containing a saturated solution of SrCl 2 Žaq. in equilibrium with a solid phase of SrCl 2 . 6H 2 OŽcr.. According to Robinson and Stokes,Ž23. the water activities of these saturated solutions at T s 298.15 K are a w s 0.7528 and a w s 0.7083, respectively. The vapor-stirring ‘‘fan’’ was removed from the copper block during these experiments to avoid dispersing the HNO3 Žg. throughout the chamber. In addition, a sheet of thick copper foil was placed above the solution cups to react chemically with, and thus trap, the HNO3 from the CuŽNO 3 . 2 Žaq. solutions. An attempt was made to attach the copper foil to the lower side of the lid of the isopiestic chamber using an APIEZON wax, but it would not adhere to the highly-polished surface. We avoided using glue or cement, because they might have contained a solvent or other volatile organic components, which have the potential

f and g for CuŽNO 3 . 2 Žaq.

341

for contamination of our solutions during the experiments. We then attempted to secure the copper foil by putting its edges between the lid of the chamber and the neoprene gasket used to form a waterproof seal. Unfortunately, the gasket no longer sealed properly, and water leaked from the constant temperature water-bath into the chamber during the next equilibration. These isopiestic samples were discarded since they were contaminated, the sample cups and chamber were cleaned and dried, and new samples were weighed out. For the next experiment the copper foil was bent to form a tent over the isopiestic cups. This approach was more successful. However, some water had seeped between the threads of two of the brass retainers and the copper block during the earlier water leak, and it slowly bled out during the next two equilibrations after a vacuum was applied to remove air from the chamber. This water did not have any direct contact with the isopiestic samples, but it was absorbed into them through the vapor phase. This water diluted the samples to a water activity higher than that of saturated NaClŽaq., but these two experiments still yield reliable osmotic coefficients. All eight retainers were removed subsequently, cleaned, dried, and then returned to the chamber. Four additional equilibrations were then performed with the reservoir of saturated NaClŽaq. without further problems and yielded an average molality of CuŽNO 3 . 2 Žaq. of Ž3.3672 " 0.0024. mol . kgy1 . This was followed by two equilibrations without the CuŽNO 3 . 2 Žaq. samples; see below for details. These samples were then discarded, and fresh samples weighed out for an additional series of equilibrations with a reservoir solution of saturated SrCl 2 Žaq.. The third, fourth, fifth, and sixth equilibrations of solutions of CuŽNO 3 . 2 Žaq. and H 2 SO4 Žaq. with a reservoir of saturated NaClŽaq., LLNL Series 3 of table 3, should, in principle, yield constant molalities and constant osmotic coefficients for CuŽNO 3 . 2 Žaq. if no time-dependent hydrolysis had occurred. A very slight but regular increase in the molalities was observed with each subsequent equilibration: a total of 0.076 per cent for H 2 SO4 Žaq. and 0.182 per cent for CuŽNO 3 . 2 Žaq. during these four experiments. However, m CuŽNO 3 . 2 4 rmŽH 2 SO4 . only varied from 0.77477 to 0.77560, and f for CuŽNO 3 . 2 Žaq. from 1.5520 to 1.5532. These variations are smaller than the typical imprecision of Ž0.1 to 0.2. per cent for the isopiestic molality ratio, and provide no evidence for significant systematic changes due to loss of HNO3 from the CuŽNO 3 . 2 Žaq. solutions. Thus, osmotic coefficients obtained from all of the isopiestic experiments with Cu ŽNO 3 . 2 Žaq. molalities (3.37 mol . kgy1 may be presumed to be free of systematic error from this source, at least beyond the 0.002 . f level. Three equilibrations were then performed using fresh samples of CuŽNO 3 . 2 Žaq. and the same samples of H 2 SO4Žaq., all equilibrated with a reservoir of saturated SrCl 2 Žaq. solution. A very slight but regular increase in the molalities was again observed with each subsequent equilibration, totaling 0.030 per cent for H 2 SO4Žaq. and 0.13 per cent for CuŽNO 3 . 2 Žaq.. However, m CuŽNO 3 . 2 4 rmŽH 2 SO4 . only varied from 0.78009 to 0.78088, and f for CuŽNO 3 . 2 Žaq. from 1.6520 to 1.6534. These molality variations, although appearing to be systematic, are smaller than the typical imprecision of isopiestic experiments. We therefore conclude that for

342

J. G. Albright, P. Rizzo, and J. A. Rard

molalities of CuŽNO 3 . 2 Žaq. ( 3.83 mol . kgy1 , loss of HNO3 from the CuŽNO 3 . 2 Žaq. solutions and the concomitant hydrolysis produces an error in the osmotic coefficients of (0.0015 . f even after three equilibrations lasting a total of 54 d. However, the LLNL Series 1 experiments of table 3, in which the HNO3 was not ‘‘trapped’’ with copper foil, indicate that errors in the osmotic coefficients of CuŽNO 3 . 2 Žaq. resulting from this HNO3 loss can be very large for molalities )5 mol . kgy1 , with increasing low values of f of CuŽNO 3 . 2 Žaq. being obtained if the same solution samples are re-equilibrated. The isopiestic molality ratios m CuŽNO 3 . 2 4 rmŽH 2 SO4 . for the experiments of LLNL Series 3 and 4 were approximately a linear function of m CuŽNO 3 . 2 4 and were represented by the least-squares equation: m  Cu Ž NO 3 . 2 4 rm Ž H 2 SO4 . s 0.73298 q 0.012440 . m  Cu Ž NO 3 . 2 4 rm8 , Ž 4 . with a correlation coefficient of 0.9880. This equation is valid for m CuŽNO 3 . 2 4 s Ž3.2912 to 3.8280. mol . kgy1 . The maximum deviation of any of the experimental values from this equation is Dw m CuŽNO 3 . 2 4 rmŽH 2 SO4 .x s 0.00087 Ž0.11 per cent., and the average deviation is 0.00033 Ž0.043 per cent., which indicates that these isopiestic results are very consistent internally. Experiments for LLNL Series 3 lasted a total of 108 d, but the maximum systematic change in Dw m CuŽNO 3 . 2 4 rmŽH 2 SO4 .x from equation Ž4. between the first and the last equilibration was only 0.10 per cent. Corresponding experiments for LLNL Series 4 lasted 54 d during which time Dw m CuŽNO 3 . 2 4 rmŽH 2 SO4 .x showed a systematic variation of 0.10 per cent. These changes are smaller than the typical imprecision of Ž0.1 to 0.2. per cent in the molality ratio for isopiestic experiments, but they are meaningful because of the high precision of these experiments. This further supports our contention that the effect of hydrolysis on the osmotic coefficients of CuŽNO 3 . 2 Žaq. solutions for m CuŽNO 3 . 2 4 - 4 mol . kgy1 is essentially negligible compared with the typical uncertainty of isopiestic measurements. Water activities of saturated solutions of NaClŽaq. and SrCl 2 Žaq. were calculated from the NaClŽaq. or H 2 SO4 Žaq. reference solution molalities, and are a w s 0.7538 and a w s 0.7106, respectively. These activities are slightly higher than the values reported by Robinson and StokesŽ23. and from previous measurements at LLNL.Ž2. The significance of this difference is unclear. The following two experiments were then performed to check whether the copper foil was interfering with the vapor diffusion of water between sample cups, and whether the solutions were truly equilibrating with the saturated solution reservoir. After the first six equilibrations of LLNL Series 3 were completed with the reservoir of saturated NaClŽaq., the CuŽNO 3 . 2 Žaq. samples and the copper foil were removed from the chamber, the vapor-stirring fan was put back in, and a pair of fresh samples of NaClŽaq. was equilibrated with the same pair of H 2 SO4 Žaq. reference solution samples and the same saturated NaClŽaq. solution reservoir. The average of the H 2 SO4Žaq. molalities from two such equilibrations was Ž4.3445 " 0.0023. mol . kgy1 , which agrees almost exactly with the average from the previous four experiments of Ž4.3439 " 0.0021. mol . kgy1 , which were performed when copper foil and CuŽNO 3 . 2 Žaq. solutions were present. Thus the presence of the

f and g for CuŽNO 3 . 2 Žaq.

343

copper foil and CuŽNO 3 . 2 Žaq. solutions did not affect the molality of the reference standard or the equilibrium with the reservoir solution. In addition, the osmotic coefficient of H 2 SO4 Žaq. calculated from the equilibrium molalities, f s 1.2049, using the equation of Archer Ž18. for NaClŽaq., is in excellent agreement with the value of f s 1.2033 calculated from the extended Pitzer equation of Clegg et al.Ž20. for H 2 SO4 Žaq.. Although the water activities of the saturated reservoir solutions are slightly higher than those usually obtained, the osmotic coefficient of H 2 SO4Žaq. obtained from these experiments is completely consistent with other values obtained at LLNL and elsewhere.Ž20.

3. Results and analysis with Pitzer’s equations A graphical comparison was made of values of f obtained in this study and those from previous isopiestic investigations. Osmotic coefficients from Robinson et al.Ž3. are 0.005 to 0.017 lower than our results, those from BrownŽ4. are typically about 0.02 to 0.03 higher, and those from Sadowska and Libus´Ž6. are lower than our results at m - 0.3 mol . kgy1 , are close to our results from m f Ž0.33 to 0.71. mol . kgy1 , and are systematically higher at all higher molalities. The discrepancy between our results and those of Sadowska and Libus´ increases with increasing molality. Robinson et al.Ž3. described their CuŽNO 3 . 2 as having been ‘‘ . . . purified by a three-fold recrystallization from water . . . ’’ Given that recrystallization normally involves heating of a solution to increase the solubility, the higher temperatures should have enhanced the rate of loss of HNO3 and produced a hydrolysed and nitrate-deficient stock solution of CuŽNO 3 . 2 Žaq.. Based on our observations that hydrolysis causes the value of the apparent osmotic coefficient to fall below that for the corresponding unhydrolysed solution at the same molality, the deviations of Robinson et al.’s results from ours are in the expected direction. Sadowska and Libus´Ž6. described their CuŽNO 3 . 2 as ‘‘ . . . purified by several crystallizations from redistilled water.’’ They then added 0.002 mol of HNO3 for each mol of CuŽNO 3 . 2 to suppress hydrolysis, so their acidified solution had a nitrate excess. We expect the apparent osmotic coefficient of a  0.998CuŽNO 3 . 2 q 0.002HNO34Žaq. solution to be greater than that for the corresponding solution of the stoichiometric salt, which is consistent with their osmotic coefficients being higher than ours at m ) 0.7 mol . kgy1 . Values of the osmotic coefficients reported by BrownŽ4. are also higher than ours. However, since Brown did not give any experimental details, the origin of this difference is uncertain. Our experimental osmotic coefficients were represented with Pitzer’s equationŽ24. and Archer’s extension Ž18. of Pitzer’s equation. These equations can be written in the general form for the osmotic coefficient of CuŽNO 3 . 2 Žaq.:

f y 1 s y z Ž Cu . z Ž NO 3 . A f I 1r2r Ž 1 q b I 1r2 . q 2 m  n Ž Cu . n Ž NO 3 . rn 4 B f Ž Cu, NO 3 . q 4 m2  n Ž Cu . n Ž NO 3 . z Ž Cu . rn 4 C Tf Ž Cu, NO 3 . , 2

Ž 5.

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J. G. Albright, P. Rizzo, and J. A. Rard

where n Ži. denotes the number of ions of type i formed by dissociation of one molecule of CuŽNO 3 . 2 , z Ži. the valence of an ion of type i, m the stoichiometric molality, and I s 3m the stoichiometric ionic strength. Also, n ŽCu. s 1, n ŽNO 3 . s 2, n s n ŽCu. q n ŽNO 3 . s 3, z ŽCu. s 2, z ŽNO 3 . s y1, and b s 1.2 kg 1r2 . moly1 r2 . At T s 298.15 K, A f s 0.391475 kg 1r2 . moly1 r2 .Ž20,25. The quantities B f ŽCu, NO 3 . and C Tf ŽCu, NO 3 . are defined as: B f Ž Cu, NO 3 . s b Ž0. Ž Cu, NO 3 . q b Ž1. Ž Cu, NO 3 . exp  ya Ž Cu, NO 3 . I 1r2 4 , Ž 6 . and C Tf Ž Cu, NO 3 . s C Ž0. Ž Cu, NO 3 . q C Ž1. Ž Cu, NO 3 . exp  yv Ž Cu, NO 3 . I 1r2 4 , Ž 7 . where a is usually fixed at the value 2.0 kg 1r2 . moly1 r2 , except for the divalent metal sulfates.Ž24. Mean activity coefficients g" of CuŽNO 3 . 2 Žaq. are given by: ln g"s y z Ž Cu . z Ž NO 3 . Af  I 1r2r Ž 1 q b I 1r2 . q Ž 2rb . ln Ž 1 q b I 1r2 . 4 q 2 m  n Ž Cu . n Ž NO 3 . rn 4 2 b Ž0. Ž Cu, NO 3 . q

ž

2

2  b Ž1. Ž Cu, NO 3 . ra Ž Cu, NO 3 . I 4 1 y  1 q a Ž Cu, NO 3 . I 1r2 y 2

a Ž Cu, NO 3 . Ir2 4 exp  ya Ž Cu, NO 3 . I 1r2 4 2

/q

2 m2  n Ž Cu . n Ž NO 3 . z Ž Cu . rn 4 3C Ž0. Ž Cu, NO 3 . q 4C Ž1. Ž Cu, NO 3 .

ž

2

3

6 y  6 q 6 v Ž Cu, NO 3 . I 1r2 q 3 v Ž Cu, NO 3 . I q v Ž Cu, NO 3 . I 3r2 y 4

4

v Ž Cu, NO 3 . I 2r2 4 exp  yv Ž Cu, NO 3 . I 1r2 4 r  v Ž Cu, NO 3 . I 2 4 .

/

Ž 8.

TABLE 5. Least-squares parameters and standard errors for Archer’s extended version of Pitzer’s equation for CuŽNO 3 . 2 Žaq. at the temperature T s 298.15 K, where sŽ f . is the standard deviation of the fit Ž m8 s 1 mol . kgy1 . Parameter

b Cu, NO 3 .Ž m8. b Ž1. ŽCu, NO 3 .Ž m8. C Ž0. ŽCu, NO 3 .Ž m8. 2 C Ž1. ŽCu, NO 3 .Ž m8. 2 a ŽCu, NO 3 .Ž m8.1r2 v ŽCu, NO 3 .Ž m8.1r2 mrm8 b sŽ f . Ž0. Ž

a b

Value

Standard Error

Value

Standard Error

0.2052637 1.7476229 0a 0.2783228 2.0 1.5 3.00 0.00098

0.000317 0.005673

0.2483145 1.7145322 y0.0022996 0.1616900 2.0 1.5 6.9235 0.00194

0.000761 0.010417 0.000026 0.003483

0.001900

This value of C Ž0. ŽCu, NO 3 . was set equal to zero. Maximum molality to which these parameters apply.

f and g for CuŽNO 3 . 2 Žaq.

345

The standard forms of Pitzer’s equations for f and ln g" are obtained by setting the parameter C Ž1. ŽCu, NO 3 . s 0, in which case C Tf ŽCu, NO 3 . s C Ž0. ŽCu, NO 3 .. We note that C Ž0. ŽCu, NO 3 . is equivalent to Pitzer’s Ž24. CŽMX. parameter. However, the parameter usually reported is C f ŽMX.. These two parameters are related by: C f Ž MX. s 2 z Ž M . z Ž X.

1r2

C Ž MX. .

Ž 9.

For CuŽNO 3 . 2 Žaq., C f ŽCu, NO 3 . s 2 3r2 CŽCu, NO 3 .. Because of experimental difficulties with the isopiestic measurements, a somewhat larger than usual number of the experimental f values were judged to be unreliable. Some experiments had been performed to elucidate the magnitude of the resulting error on f from the loss of HNO3 from CuŽNO 3 . 2 Žaq. solutions in different molality regions, or were performed before this problem was identified. The rejected experiments include all of TCU Series 7 and 8 and LLNL Series 1,

FIGURE 1. Differences Žresiduals. between experimental osmotic coefficients f and least-squares fit values f Žcalc. of CuŽNO 3 . 2 Žaq. as a function of m at T s 298.15 K, for fits with the molality region Ž0 to 3.00. mol . kgy1 using equation Ž5. with b Ž0. ŽCu, NO 3 ., b Ž1. ŽCu, NO 3 ., and C Ž1. ŽCu, NO 3 . parameters. The parameter C Ž0. ŽCu, NO 3 . was set equal to zero since it was not significant. v, isopiestic results with NaClŽaq. reference standard; B, isopiestic results with CaCl 2 Žaq. reference standard first CuŽNO 3 . 2 Žaq. stock solution4; ', isopiestic results with CaCl 2 Žaq. reference standard second CuŽNO 3 . 2 Žaq. stock solution4.

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J. G. Albright, P. Rizzo, and J. A. Rard

five experiments from TCU Series 6, along with a few individual values of f from several of the other series. Twenty-four values of f that were consequently given zero weight in the least-squares fits with equation Ž5. are indicated with Ž w s 0. in tables 1 through 4; the other 78 values of f were assigned equal weights. Test fits of equation Ž5. with the experimental osmotic coefficients for the molality range m ( 3.00 mol . kgy1 indicated that the standard form of Pitzer’s equationŽ24. was able to represent the experimental results moderately well, but with systematic cyclic deviations of D f s Ž0.002 to 0.004. in certain molality regions. However, Archer’s extension Ž18. of Pitzer’s equation, which has an ionstrength-dependent third virial coefficient, was able to represent the same results much more accurately and without systematic deviations. Thus it was chosen to represent our isopiestic results. Table 5 contains the least-squares coefficient values and their standard errors

FIGURE 2. Differences Žresiduals. between experimental osmotic coefficients f and least-squares fit values f Žcalc. of CuŽNO 3 . 2 Žaq. as a function of m at T s 298.15 K, for fits with the molality region Ž0 to 6.9235. mol . kgy1 using equation Ž5. with b Ž0. ŽCu, NO 3 ., b Ž1. ŽCu, NO 3 ., C Ž0. ŽCu, NO 3 ., and C Ž1. ŽCu, NO 3 . parameters. v, isopiestic results with NaClŽaq. reference standard; ', isopiestic results with CaCl 2 Žaq. reference standard first CuŽNO 3 . 2 Žaq. stock solution4; B, isopiestic results with CaCl 2 Žaq. reference standard second CuŽNO 3 . 2 Žaq. stock solution4; %, isopiestic results with H 2 SO4 Žaq. reference standard.

f and g for CuŽNO 3 . 2 Žaq.

347

for fits of the parameters of equation Ž5. to two different molality regions. The first set of coefficients is based on a least-squares fit to the molality region Ž0.0638 to 3.00. mol . kgy1 , where there is essentially no error in the osmotic coefficients due to loss of HNO3 and where equation Ž5. gives a highly accurate representation of the experimental f values for CuŽNO 3 . 2 Žaq. with nearly random deviations. When all four parameters of this equation  b Ž0. ŽCu, NO 3 ., b Ž1. ŽCu, NO 3 ., C Ž0. ŽCu, NO 3 ., and C Ž1. ŽCu, NO 3 .4 were determined simultaneously, it was found that the C Ž0. ŽCu, NO 3 . coefficient had a very large relative uncertainty of 0.53 . C Ž0. ŽCu, NO 3 .. It was consequently set equal to zero, and the other three parameters were re-evaluated. We believe that the resulting smoothed values of f from this three-parameter model are accurate to "0.002 . f for this molality region, which is comparable to the usual accuracy of isopiestic measurements for electrolytes not having such experimental difficulties. When the molality range being represented by equation Ž5. was increased above 3.00 mol . kgy1 , then small but systematic deviations were present between the experimental and calculated values of f . The second set of coefficients of table 5 is based on a model fit to the more expanded molality region of Ž0.0638 to 6.9235. mol . kgy1 . Smoothed values of f TABLE 6. Smoothed values of the molality-based osmotic coefficients f , water activities a w , and mean activity coefficients g" for CuŽNO 3 . 2 Žaq. at rounded values of the molality m at the temperature 298.15 K a mrŽmol . kgy1 . 0.01 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.60 0.70 0.80 0.90 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60 2.80 3.00 a

f

aw

g"

0.9071 0.8624 0.8531 0.8537 0.8580 0.8643 0.8718 0.8801 0.8891 0.8985 0.9083 0.9287 0.9500 0.9718 0.9941 1.0166 1.0621 1.1079 1.1539 1.1999 1.2459 1.2919 1.3379 1.3839 1.4300 1.4762

0.999510 0.997672 0.995400 0.993104 0.990769 0.98839 0.98596 0.98349 0.98096 0.97839 0.97576 0.97033 0.96470 0.95885 0.95280 0.94654 0.93344 0.91959 0.90503 0.8898 0.8740 0.8576 0.8407 0.8233 0.8054 0.7871

0.7276 0.5769 0.5175 0.4879 0.4700 0.4586 0.4510 0.4461 0.4433 0.4419 0.4417 0.4442 0.4495 0.4570 0.4663 0.4772 0.5029 0.5334 0.5683 0.6076 0.6512 0.6996 0.7528 0.8113 0.8756 0.9461

These values were calculated from the first set of parameters in table 5.

348

J. G. Albright, P. Rizzo, and J. A. Rard

calculated with those parameters should be reliable to about 0.004 . f . This larger uncertainty results from the experimental difficulties above m s 4 mol . kgy1 due to loss of HNO3 during the isopiestic equilibrations, and to slight systematic cyclic deviations of D f ( 0.003 between the fitting equation and experimental values of TABLE 7. Smoothed values of the molality-based osmotic coefficients f , water activities a w , and mean activity coefficients g" for CuŽNO 3 . 2 Žaq. at rounded values of the molality m at the temperature 298.15 K a mrŽmol . kgy1 . 0.01 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.60 0.70 0.80 0.90 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60 2.80 3.00 3.20 3.40 3.60 3.80 4.00 4.20 4.40 4.60 4.80 5.00 5.20 5.40 5.60 5.80 6.00 6.20 6.40 6.60 6.80 6.9235 a

f

aw

g"

0.9073 0.8634 0.8545 0.8551 0.8593 0.8653 0.8724 0.8803 0.8888 0.8978 0.9072 0.9270 0.9478 0.9693 0.9915 1.0140 1.0601 1.1069 1.1539 1.2010 1.2479 1.2944 1.3405 1.3861 1.4311 1.4755 1.5192 1.5624 1.6048 1.6465 1.6875 1.7278 1.7674 1.8062 1.8442 1.8815 1.9180 1.9537 1.9886 2.0227 2.0560 2.0884 2.1201 2,1509 2.1808 2.1989

0.999510 0.997670 0.995393 0.993092 0.990755 0.98838 0.98595 0.98349 0.98097 0.97840 0.97578 0.97039 0.96478 0.95896 0.95292 0.94667 0.93356 0.91966 0.90503 0.8897 0.8738 0.8574 0.8404 0.8230 0.8053 0.7872 0.7689 0.7504 0.7318 0.7131 0.6943 0.6756 0.6569 0.6382 0.6198 0.6014 0.5833 0.5654 0.5478 0.5305 0.5134 0.4967 0.4803 0.4643 0.4487 0.4392

0.7279 0.5781 0.5192 0.4898 0.4720 0.4605 0.4528 0.4477 0.4447 0.4431 0.4427 0.4447 0.4497 0.4569 0.4660 0.4768 0.5026 0.5334 0.5689 0.6089 0.6533 0.7024 0.7561 0.8146 0.8783 0.9474 1.022 1.103 1.189 1.283 1.383 1.490 1.605 1.728 1.860 1.999 2.148 2.306 2.474 2.652 2.840 3.038 3.248 3.469 3.701 3.850

These values were calculated using the second set of parameters in table 5.

f and g for CuŽNO 3 . 2 Žaq.

349

FIGURE 3. Smoothed values of the osmotic coefficients f and the mean activity coefficient g" as a function of m1r 2 : }}}, g"; ] ] ] ], f .

f for molalities -3.3 mol . kgy1 . Above m s 3.3 mol . kgy1 , however, equation Ž5. represents the experimental f values without any systematic bias. Figures 1 and 2 show the differences Žresiduals. between the experimental values of f and the least-squares fit values f Žcalc. from equation Ž5. for CuŽNO 3 . 2 Žaq. at T s 298.15 K, for these two different molality ranges. See table 5 for the corresponding least-squares coefficients. Minor differences between the experimental values of f resulting from use of the different reference standards NaClŽaq., CaCl 2 Žaq., and H 2 SO4Žaq. are -0.002 . f , which is well within the uncertainty of their osmotic coefficients.Ž18-21. Tables 6 and 7 contain calculated values of f , a w Žwater activity., and g" at selected molalities from use of these two sets of parameters, respectively. Values given in table 6 are more accurate, but are limited to m ( 3.00 mol . kgy1 . Figure 3 is a plot of f and g" for CuŽNO 3 . 2 Žaq. as a function of m1r2 . These values fall within the range observed for other 1:2 strong electrolytes.Ž23.

4. Examination of other aqueous chloride and nitrate electrolytes for hydrolysis during isopiestic equilibrations Rard and Platford Ž10. summarized literature reports of the few other aqueous

350

J. G. Albright, P. Rizzo, and J. A. Rard

electrolytes, such as UO 2 Cl 2 Žaq., that undergo irreversible hydrolysis during isopiestic equilibrations. At the time, the only other divalent metal salts reported to undergo such hydrolysis under isopiestic conditions were NiCl 2 Žaq. and CoCl 2 Žaq. at elevated temperatures. Holmes and Mesmer Ž26. reported that CoCl 2 Žaq. underwent slow hydrolysis at T s 413.36 K which eventually resulted in the precipitation of CoŽOH. 2 Žs., and that both NiCl 2 Žaq. and CoCl 2 Žaq. underwent rapid and extensive hydrolysis at T s 443.92 K. We have since found that both CuCl 2 Žaq.Ž13. and Žpresent report. CuŽNO 3 . 2 Žaq. lose HCl or HNO3 , respectively, into the vapor phase during isopiestic experiments at T s 298.15 K, which results in the progressive hydrolysis of the dissolved copper salts and systematic shifts in the water activities and osmotic coefficients of their solutions. However, this hydrolysis occurs slowly enough that it was overlooked in all previous investigations of these systems. The possibility thus exists that other previously studied divalent metal chloride and nitrate salts undergo similar slow hydrolysis during isopiestic experiments. In the recent isopiestic investigation of CaCl 2 Žaq. at T s 298.15 K and high molalities,Ž19. experiments were performed in which the samples were equilibrated numerous times, with the molalities generally being increased from one experiment to the next. However, in several cases, these samples were diluted with water to reinvestigate a molality region previously investigated, and in all cases the later results were completely consistent with the earlier results. Thus, solutions of CaCl 2 Žaq. undergo no hydrolysis during isopiestic experiments lasting several months. Isopiestic experiments for MnCl 2 Žaq.,Ž27. NiCl 2 Žaq.,Ž28. CdCl 2 Žaq.,Ž29. and ZnCl 2 Žaq.Ž30. at T s 298.15 K were performed in a similar manner with the same solutions being used for numerous experiments. Some later experiments were performed with the same samples in a previously investigated molality region and those results were completely consistent with the earlier experiments. These electrolytes likewise show absolutely no evidence for hydrolysis due to loss of HCl during the isopiestic experiments. ŽThis is not obvious from the presentation of the isopiestic results for those systems, since the isopiestic equilibrium molalities in their tables were listed either in increasing or in decreasing order rather than the actual order that the experiments were performed.Ž27 ] 30. . We have not performed isopiestic measurements for any other divalent metal nitrates. However, we have performed isopiestic measurements for various trivalent rare-earth nitrates and chlorides at T s 298.15 K, e. g. LaŽNO 3 . 3 Žaq.,Ž31. PrŽNO 3 . 3 Žaq.,Ž28. EuŽNO 3 . 3 Žaq.,Ž1. YŽNO 3 . 3 Žaq.,Ž1. and YCl 3 Žaq..Ž1. Also see earlier papers cited in those studies for isopiestic results for other rare-earth salts. The isopiestic equilibrium molalities in those studies were reported in the order of increasing molality. However, for each system, several series of experiments were performed in which pairs of samples were used for numerous equilibrations. In each series, most of the experiments were performed with the molalities of these solutions being increased or decreased from experiment to experiment. In several cases, these same samples were then diluted or concentrated to reinvestigate a previously studied molality region. Values of the osmotic coefficients for the later experiments were always completely consistent with those from the earlier

f and g for CuŽNO 3 . 2 Žaq.

351

experiments. These rare-earth nitrates and chlorides show absolutely no evidence for hydrolysis occurring due to loss of HNO3 or HCl during the isopiestic experiments. As described in the experimental section, the ‘‘natural’’ pH of our m s Ž4.5578 " 0.0020. mol . kgy1 CuŽNO 3 . 2 Žaq. stock solution a2 is approximately 0.6. Aqueous solutions of the stoichiometric rare-earth nitrates at this molality have pH values around 3, and have pH values 02.5 at m s 6 mol . kgy1 .Ž32. The higher acidity of the CuŽNO 3 . 2 Žaq. solutions, with the resulting greater extent of formation of HNO3 Žaq, undissoc.., is undoubtedly the reason why CuŽNO 3 . 2 Žaq. solutions at higher molalities lose HNO3 during isopiestic equilibrations at T s 298.15 K, whereas the less acidic rare-earth nitrates do not. At a pH somewhere between 2.5 and 0.6, solutions of nitrate salts begins to lose HNO3 into the vapor phase during isopiestic equilibrations at T s 298.15 K, and this problem will undoubtedly begin to occur at slightly higher pH for isopiestic experiments performed at higher temperatures. We recommend that before isopiestic experiments are undertaken for solutions of nitrate salts, the pH of a highly concentrated or saturated solution be measured. If that pH is less than f2, then test experiments should be performed to determine whether or not these solutions undergo HNO3 loss and irreversible hydrolysis at the higher molalities. Examination of plots of changes in speciation of metal ions with changes in pH Ž33. indicates that the only divalent metal nitrate solutions that should undergo more extensive HNO3 loss than CuŽNO 3 . 2 Žaq. at T s 298.15 K are PbŽNO 3 . 2 Žaq., BeŽNO 3 . 2 Žaq., and HgŽNO 3 . 2 Žaq..

Note added in proof We have been in correspondence with R. H. Stokes. The isopiestic molalities of CuŽNO 3 . 2 Žaq. from the study of Robinson et al.Ž3. were taken from the Master’s thesis of his wife, Jean M. ŽWilson. Stokes. Prof. Stokes provided us with the following information: Ž1. the CuŽNO 3 . 2 Žaq. for that study was prepared by dissolving analytical reagent grade copper metal in nitric acid. The resulting CuŽNO 3 . 2 . xH 2 OŽcr. was recrystallized twice from water, which probably involved boiling of the solutions; Ž2. the molality of the CuŽNO 3 . 2 Žaq. stock solution was determined by addition of excess KI under acidic conditions, followed by titration of the resulting I 2 Žaq. with a standard thiosulfate solution; Ž3. calculated values of f at m s Ž0.1211 and 0.4241. mol . kgy1 show large deviations from a curve drawn through the other results from that study, whereas plots given in the thesis indicate better consistency. Thus either these two molalities, or their corresponding reference solution molalities, contain misprints. The contribution of J. G. A. was supported by TCURF Grant 5-23758 and of J. A. R. was performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under contract No. W-7405-ENG-48. P. R. thanks the Universita ` Federico II di Napoli for a scholarship to perform

352

J. G. Albright, P. Rizzo, and J. A. Rard

research at TCU. We thank Michelle Yang and Christopher Borrego at TCU for some assistance with the measurements. The authors thank Dr Donald G. Miller for helpful suggestions and Dr Donald G. Archer for supplying us with a copy of his computer program for calculation of the thermodynamic properties of NaClŽaq. and for access to his evaluation for KClŽaq. prior to publication. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33.

Rard, J. A.; Spedding, F. H. J. Chem. Eng. Data 1982, 27, 454]461. Rard, J. A. J. Solution Chem. 1985, 14, 457]471. Robinson, R. A.; Wilson, J. M.; Ayling, H. S. J. Am. Chem. Soc. 1942, 64, 1469]1471. Brown, J. B. Trans. R. Soc. N.Z. 1948, 77, 19]23. Yakimov, M. A.; Guzhavina, E. I. Russ. J. Inorg. Chem. 1971, 16, 934]936. Sadowska, T.; Libus, ´ W. J. Solution Chem. 1982, 11, 457]468. Goldberg, R. N. J. Phys. Chem. Ref. Data 1979, 8, 1005]1050. Filippov, V. K.; Barkov, D. S.; Fedorov, Ju. A. Z. Phys. Chem. ŽLeipzig. 1985, 266, 129]134. Spitzer, J. J.; Olofsson, I. V.; Singh, P. P.; Helper, L. G. J. Chem. Thermodynamics 1979, 11, 233]238. Rard, J. A.; Platford, R. F. Acti¨ ity Coefficients in Electrolyte Solutions: 2nd edition. Pitzer, K. S.: editor. CRC Press: Boca Raton, FL. 1991, Chap. 5. Mitchell, J. P.; Butler, J. B.; Albright, J. G. J. Solution Chem. 1992, 21, 1115]1129. Rard, J. A. J. Chem. Thermodynamics 1997, 29, 533]555. Rard, J. A. J. Chem. Eng. Data 1992, 37, 433]442. Addison, C. C.; Hathaway, B. J. J. Chem. Soc. 1958, 3099]3106. Field, B. O.; Hardy, C. J. Quart. Re¨ . 1964, 28, 361]388. Rard, J. A.; Archer, D. G. J. Chem. Eng. Data 1995, 40, 170]185. Rard, J. A. J. Chem. Thermodynamics 1996, 28, 83]110. Archer, D. G. J. Phys. Chem. Ref. Data 1992, 21, 793]829. Rard, J. A.; Clegg, S. L. J. Chem. Eng. Data 1997, 42, 819]849. Clegg, S. L.; Rard, J. A.; Pitzer, K. S. J. Chem. Soc. Faraday Trans. 1994, 90, 1875]1894. Rard, J. A.; Habenschuss, A.; Spedding, F. H. J. Chem. Eng. Data 1976, 21, 374]379. Young, T. F.; Maranville, L. F.; Smith, H. M. The Structure of Electrolytic Solutions. Hamer, W. J.: editor. Wiley: New York. 1959, pp. 35]63. Robinson, R. A.; Stokes, R. H. Electrolyte Solutions: 2nd edition Žrevised.. Butterworths: London. 1965, Appendix 8.11. Pitzer, K. S. Acti¨ ity Coefficients in Electrolyte Solutions: 2nd edition. Pitzer, K. S.: editor. CRC Press: Boca Raton, FL. 1991, Chap. 3. Archer, D. G.; Wang, P. J. Phys. Chem. Ref. Data 1990, 19, 371]411. Holmes, H. F.; Mesmer, R. E. J. Chem. Thermodynamics 1981, 13, 131]137. Rard, J. A. J. Chem. Eng. Data 1984, 29, 443]450. Rard, J. A. J. Chem. Eng. Data 1987, 32, 334]341. Rard, J. A.; Miller, D. G. J. Solution Chem. 1985, 14, 271]299. Rard, J. A.; Miller, D. G. J. Chem. Thermodynamics 1989, 21, 463]482. Rard, J. A. J. Chem. Eng. Data 1987, 32, 92]98. Rard, J. A.; Spedding, F. H. J. Phys. Chem. 1975, 79, 257]262. Baes, Jr., C. F.; Mesmer, R. E. The Hydrolysis of Cations. Wiley Interscience: New York. 1976.

(Recei¨ ed 1 August 1997; in final form 29 September 1997)

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