Isopiestic Determination of the Osmotic Coefficients of NaNO3

Article pubs.acs.org/jced

Isopiestic Determination of the Osmotic Coefficients of NaNO3 + Eu(NO3)3 + H2O at 298.15 K and Representation with an Extended Ion-Interaction (Pitzer) Model Peter R. Zalupski* and Rocklan McDowell Idaho National Laboratory, Idaho Falls, Idaho 83415, United States

Simon L. Clegg* School of Environmental Sciences, University of East Anglia, Norwich NR4 7TJ, United Kingdom ABSTRACT: Isopiestic vapor pressures were measured at 298.15 K for aqueous NaNO3 + Eu(NO3)3 solutions, using NaCl(aq) as the reference standard. Measurements were made for both binary (single salt) solutions and for ternary solutions of the following NaNO3 ionic strength fractions: 0.05995, 0.08749, 0.16084, 0.27709, and 0.36313 over the water activity range 0.8951 ≤ aw ≤ 0.9832. (These ionic strength fractions correspond to NaNO3 molality fractions 0.27675, 0.36519, 0.53489, 0.69695, and 0.77381, respectively.) The results, and those of other studies for the two pure aqueous solutions, were used to determine the Pitzer model parameters for aqueous Eu(NO3)3 for molalities up to 3 mol kg−1 and the two ternary (mixture) parameters θEu,Na = 0.367 ± 0.0035 and ψEu,Na,NO3 = −0.0743 ± 0.0014. Some deviations of the measurements from the fitted model, of the order of +0.0075 in the osmotic coefficient, were noted for mixtures containing less than about 1 mol kg−1 total NO3−. The use of the mixture parameters in the Pitzer model yields predicted trace activity coefficients of Eu3+ in 1 mol kg−1 aqueous NaNO3 almost a factor of 2 greater than if they are omitted.

1. INTRODUCTION Accurate thermodynamic modeling of aqueous electrolyte solutions benefits numerous scientific applications, including the prediction of species activities in natural waters, the migration of radionuclides in geochemical environments, the understanding of chemical speciation in biochemical systems, and simulations of aerosol growth in the atmosphere. The semiempirical models, such as that of Pitzer,1 used to calculate the behavior of complex and often highly nonideal electrolyte mixtures must be based upon experimentally determined thermodynamic properties of the solvent and solutes. Isopiestic vapor pressure measurements,2 in which water activities are determined as a function of solution composition and concentration, offer an opportunity for a rigorous thermodynamic characterization of a chemical system. We have chosen this technique to study ternary electrolyte solutions of NaNO3 and Eu(NO3 )3 to support our efforts to construct a thermodynamic model of aqueous mixtures relevant to the liquid−liquid based separation of trivalent actinide ions from trivalent lanthanide ions. (A two-phase system containing an organophosphorous reagent in an aliphatic non-aqueous solution and a mixture of polyaminocarboxylate reagent, carboxylic acid buffer, and inorganic salt affords an efficient © XXXX American Chemical Society

separation of trivalent americium and curium from trivalent lanthanide ions.3) The thermodynamic characterization of both aqueous and nonaqueous environments is necessary in order to accurately predict the chemical speciation of all components in the two-phase system. The thermodynamic study described here focuses on an important mixture interaction in the aqueous phase which influences the activity coefficients of trivalent f-elements in aqueous NaNO3 media.

2. EXPERIMENTS All isopiestic measurements were carried out at 25.00 ± 0.005 °C using four laboratory built isopiestic chambers based on those described elsewhere.2 The chambers are made from Hastelloy C-22 (internal dimensions of 7.75 × 4.75 × 4.00 in.) and each hold 10 platinum (Pt) sample cups, housed inside gold-plated copper blocks. The chambers are immersed in an 18-gauge stainless steel water bath on a rocking apparatus designed to constantly mix the contents of the Pt cups with the help of small Pt pieces inside each sample cup. The water bath Received: January 7, 2014 Accepted: April 1, 2014

A

dx.doi.org/10.1021/je500016d | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Isopiestic Molalities of NaNO3 + Eu(NO3)3 Mixtures and NaCl Reference Solutions at 25 °Ca mT/mol·kg−1 yA = 0.08749

mT/mol·kg−1

yA = 0.16084

0.9023 ± 0.0007 0.9516 ± 0.0008 0.9842 ± 0.0011 1.1050 ± 0.0015 1.0218 ± 0.0012 1.1471 ± 0.0029 1.1241 ± 0.0008 1.2688 ± 0.0011 1.2952 ± 0.0008 1.4695 ± 0.0020 1.3440 ± 0.0016 1.5276 ± 0.0028 1.4012 ± 0.0016 1.5950 ± 0.0029 1.4618 ± 0.0008 1.6659 ± 0.0008 1.5017 ± 0.0007 1.7178b ± 0.0038 1.5623 ± 0.0008 1.7887 ± 0.0026 1.6073 ± 0.0007 1.8426 ± 0.0025 0.4401b ± 0.0005 0.4826b ± 0.0004 0.4558b ± 0.0005 0.5001 ± 0.0005 0.4641b ± 0.0008 0.5094b ± 0.0005 b 0.4768 ± 0.0008 0.5237b ± 0.0009 0.4839b ± 0.0007 0.5315b ± 0.0012 b 0.4967 ± 0.0006 0.5459b ± 0.0010 b 0.5067 ± 0.0006 0.5573b ± 0.0004 0.5189b ± 0.0006 0.5710b ± 0.0003 0.5304b ± 0.0010 0.5841b ± 0.0014 b 0.5473 ± 0.0009 0.6030b ± 0.0016 b 0.5601 ± 0.0010 0.6171b ± 0.0017 0.5707b ± 0.0019 0.6293b ± 0.0007 0.5860b ± 0.0009 0.6462b ± 0.0014 mT/mol·kg−1 yA = 0.0 0.7736 0.8113 0.8399 0.8793 0.9837 1.1537

± ± ± ± ± ±

0.0011 0.0007 0.0007 0.0013 0.0012 0.0015

1.3110 1.3481 1.3759 1.4317 1.4849 0.3936 0.4124 0.4203 0.4321 0.4447 0.4556 0.4670 0.4784 0.4927 0.5073 0.5231 0.5392 0.5564

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.0021 0.0004 0.0006 0.0004 0.0026 0.0004 0.0003 0.0003 0.0007 0.0005 0.0004 0.0003 0.0002 0.0007 0.0013 0.0011 0.0008 0.0005

yA = 0.16084 1.0772 1.1342 1.1786 1.2418 1.4085 1.6846 1.9368 1.9496 2.0094 2.0569 2.1566 2.2447 0.5172 0.5437 0.5543 0.5712 0.5889 0.6043 0.6205 0.6366 0.6573 0.6783 0.7010 0.7249 0.7493

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.0013 0.0007 0.0007 0.0013 0.0008 0.0014 0.0018 0.0020 0.0005 0.0004 0.0011 0.0022 0.0002 0.0004 0.0002 0.0006 0.0004 0.0005 0.0003 0.0003 0.0006 0.0007 0.0007 0.0008 0.0005

−1

ϕ*

0.0008 0.0008 0.0014 0.0018 0.0013 0.0013 0.0030 0.0031 0.0015 0.0016 0.0016 0.0017 0.0002 0.0002 0.0003 0.0005 0.0005 0.0003 0.0003 0.0002 0.0007 0.0008 0.0009 0.0006 0.0008

0.9502 0.9539 0.9563 0.9591 0.9673 0.9819 0.9863 0.9915 0.9972 1.0011 1.0069 1.0114 0.9242 0.9248 0.9251 0.9256 0.9259 0.9265 0.9269 0.9274 0.9279 0.9287 0.9293 0.9299 0.9306

m*/mol·kg 1.3001 1.3764 1.4254 1.4831 1.6432 1.9129 1.9901 2.0802 2.1790 2.2442 2.3407 2.4139 0.6133 0.6358 0.6482 0.6662 0.6762 0.6952 0.7096 0.7277 0.7440 0.7686 0.7868 0.8038 0.8255

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

m*/mol·kg−1

ϕ*

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.9544 0.9581 0.9610 0.9652 0.9772 0.9982 1.0198 1.0197 1.0249 1.0289 1.0370 1.0449 0.9254 0.9263 0.9267 0.9274 0.9281 0.9288 0.9295 0.9302 0.9311 0.9320 0.9331 0.9343 0.9355

1.3870 1.4626 1.5214 1.6033 1.8277 2.1946 2.5504 2.5481 2.6324 2.6953 2.8215 2.9431 0.6570 0.6909 0.7047 0.7264 0.7494 0.7693 0.7907 0.8114 0.8378 0.8649 0.8943 0.9261 0.9579

0.0013 0.0006 0.0005 0.0021 0.0013 0.0022 0.0043 0.0028 0.0008 0.0005 0.0008 0.0056 0.0001 0.0002 0.0002 0.0004 0.0003 0.0002 0.0002 0.0001 0.0004 0.0004 0.0005 0.0007 0.0005

yA = 0.05995

yA = 0.27709

0.8378 ± 0.0005 1.1157 0.8717 ± 0.0005 1.1638 0.8842 ± 0.0004 1.1825 0.9162 ± 0.0010 1.2288 0.9994 ± 0.0005 1.3543 1.1216 ± 0.0006 1.5397 1.1529 ± 0.0026 1.5925 1.1859 ± 0.0022 1.6410 1.2244 ± 0.0020 1.6994 1.2627 ± 0.0005 1.7604 1.3094 ± 0.0004 1.8336 1.3510 ± 0.0024 1.9023 0.3918 ± 0.0002 0.4935 0.4025 ± 0.0004 0.5079 0.4072 ± 0.0004 0.5141 0.4158 ± 0.0005 0.5257 0.4285 ± 0.0006 0.5425 0.4376 ± 0.0007 0.5547 0.4468 ± 0.0004 0.5668 0.4568 ± 0.0006 0.5798 0.4686 ± 0.0008 0.5963 0.4805 ± 0.0009 0.6122 0.4895 ± 0.0006 0.6242 0.5038 ± 0.0007 0.6432 0.5167b ± 0.0012 0.6606 mT/mol·kg−1 yA = 0.36313 0.9915 1.0361 1.0684 1.1272 1.2429 1.4371 1.5026 1.5752 1.6364 1.6996 1.7721 1.8395 0.4917 0.5141 0.5252 0.5398 0.5562 0.5695 0.5831 0.5988 0.6161 0.6357 0.6484 0.6661 0.6845

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.0011 0.0011 0.0006 0.0006 0.0015 0.0009 0.0009 0.0007 0.0009 0.0014 0.0007 0.0010 0.0010 0.0012 0.0010 0.0008 0.0009 0.0009 0.0006 0.0003 0.0012 0.0010 0.0002 0.0004 0.0005

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.0005 0.0007 0.0004 0.0007 0.0004 0.0006 0.0014 0.0009 0.0015 0.0004 0.0002 0.0021 0.0002 0.0002 0.0003 0.0005 0.0004 0.0006 0.0002 0.0004 0.0006 0.0007 0.0003 0.0003 0.0005

yA = 1.0 1.1931 1.2513 1.2915 1.3694 1.5218 1.7788 1.8684 1.9658 2.0531 2.1387 2.2405 2.3353 0.5741 0.6021 0.6144 0.6320 0.6521 0.6682 0.6846 0.7036 0.7256 0.7505 0.7641 0.7868 0.8098

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.0005 0.0011 0.0003 0.0005 0.0007 0.0008 0.0003 0.0006 0.0008 0.0009 0.0006 0.0009 0.0003 0.0004 0.0004 0.0002 0.0003 0.0005 0.0003 0.0003 0.0006 0.0009 0.0001 0.0004 0.0005

m*/mol·kg−1

ϕ*

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.9491 0.9516 0.9526 0.9551 0.9621 0.9730 0.9760 0.9790 0.9826 0.9864 0.9910 0.9952 0.9232 0.9236 0.9237 0.9240 0.9245 0.9249 0.9253 0.9257 0.9262 0.9267 0.9272 0.9278 0.9285

1.2744 1.3287 1.3497 1.4017 1.5425 1.7498 1.8056 1.8611 1.9256 1.9919 2.0726 2.1448 0.5691 0.5855 0.5926 0.6057 0.6250 0.6391 0.6529 0.6681 0.6864 0.7045 0.7185 0.7400 0.7600

0.0005 0.0003 0.0004 0.0007 0.0006 0.0010 0.0022 0.0004 0.0025 0.0006 0.0004 0.0026 0.0001 0.0002 0.0001 0.0003 0.0002 0.0002 0.0001 0.0003 0.0003 0.0003 0.0003 0.0001 0.0004

m*/mol·kg−1

ϕ*

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.9402 0.9422 0.9436 0.9462 0.9519 0.9617 0.9651 0.9690 0.9724 0.9758 0.9798 0.9835 0.9226 0.9231 0.9234 0.9238 0.9242 0.9245 0.9249 0.9254 0.9259 0.9265 0.9269 0.9275 0.9281

1.0731 1.1201 1.1532 1.2121 1.3360 1.5350 1.6007 1.6759 1.7394 1.8018 1.8749 1.9416 0.5416 0.5663 0.5779 0.5937 0.6116 0.6258 0.6406 0.6572 0.6763 0.6972 0.7108 0.7301 0.7502

0.0004 0.0015 0.0003 0.0006 0.0009 0.0014 0.0006 0.0010 0.0016 0.0018 0.0013 0.0018 0.0002 0.0002 0.0003 0.0002 0.0002 0.0003 0.0002 0.0002 0.0005 0.0007 0.0001 0.0003 0.0004

a

A small number of results, fewer than ten, were discarded as grossly in error and are not listed here. bThese values are means of two replicate samples (some sample cups were inadvertently tipped over and the contents lost), all other results are the means of three samples.

is insulated with rigid fiberglass insulation (approximately R20). The bath is cooled with a copper coil connected to a closed-loop refrigerated bath (VWR refrigerated circulator model 1150S) and heated with an immersion heater (Watlow,

Firerod Immersion Heater, 1000 W, 120 V). A high precision water bath temperature controller (Hart Scientific, model 2100) is used to control the output of the heater. The temperature of the water bath is monitored with a calibrated B



Article

Eu(NO3)3 stock was determined to be 3.0463 ± 0.0027 mol· kg−1, and that of NaNO3 stock was 4.8889 ± 0.0041 mol·kg−1. The sample solutions were prepared from the stock solutions by weighing both mixture components according to the ionic strength fractions listed in Table 1. Samples of both binary aqueous solutionsEu(NO3)3 and NaNO3were included in the isopiestic study as well as the ternary NaNO3 + Eu(NO3)3 aqueous mixtures. Each isopiestic chamber contained six sample solutions (at two different ionic strength fractions) and four reference standard solutions. Equilibrations were typically 7 days for solutions at higher concentrations; however, at low concentrations equilibrations of up to 90 days were used in order to reach isopiestic equilibrium. After each chamber opening, the sample cups were quickly capped and weighed on an OHAUS Discovery DV215CD balance calibrated to yield a ± 0.00023 g uncertainty in the measurements. After each chamber opening the molalities of the standard solutions were found to agree to within ± 0.15 %, and in most cases to less than ± 0.05 %. After 12 equilibrations the samples were diluted by adding deionized water, and then an additional 13 equilibrations were carried out. The experimental results are listed in Table 1, adopting a methodology previously used by Rard and Miller.4 Electrolyte A is NaNO3, and electrolyte B is Eu(NO3)3. The table lists the equilibrated molalities for the binary and ternary mixtures included in the study, together with the molalities of the reference solutions (m*) and their osmotic coefficients (ϕ*). Total molalities mT are reported for the NaNO3 and Eu(NO3)3 single-solute solutions and mixtures, where mT = mA + mB. Solution composition is indicated by the ionic strength fraction of NaNO3, yA, according to

Figure 1. Range of molalities (m) of pure aqueous and mixed solutions of NaNO3 and Eu(NO3)3 studied in this work. The points represent the measured molalities of all the isopiestic solutions.

thermocouple thermometer (Hart Scientific, model 1504). Each sample cup is fitted with a Teflon cover, which is used to close every cup after chamber opening. Aqueous NaCl (Aldrich, 99.999 %, and used without further purification) solutions were used as isopiestic standards. The concentration of the NaCl stock solution was determined gravimetrically to be 5.7160 ± 0.0050 mol·kg−1, after dehydration in a muffle furnace. Five determinations were performed, using Coors Ceramic crucibles (Coorstek AD-998 Al2O3). The NaCl samples were heated at 2 °C·min−1 to 600 °C, held at this maximum temperature for 2 h, followed by cooling at the same rate to 250 °C. The crucibles were transferred to the desiccator filled with layers of dry alumina beads and silica gel. After an overnight cooling the crucibles were weighed to determine the mass of NaCl present. The calculated molality of the NaCl stock solution, based only upon the initial mass of solid NaCl dissolved (and without drying or other treatment), was 5.7110 mol·kg−1. This agrees with the value obtained gravimetrically to within the stated uncertainty, and suggests that the solid NaCl used contained a negligible amount of residual water and that there was no significant loss of chloride during the heating of the NaCl solutions in the muffle furnace. Solid Eu2O3 (American Elements, 99.999 %) was converted to Eu(NO3)3 by dissolution into Optima grade HNO3 (Aldrich, 99.999 %), using 5.9 equiv of acid diluted with deionized water to approximately 35 % v/v. The remaining undissolved solid was filtered out using a 0.2 μm filter membrane. The NaNO3 stock solution was prepared by dissolving solid NaNO3 (Aldrich, 99.999 %) in water. HPLCgrade water was used throughout. Concentrated stocks of both Eu(NO3)3 and sodium nitrate were standardized using purified Dowex 50X8 cation exchange resin in H+ form. Aliquots of the stocks were diluted with water and deposited on a resin bed. The eluent (collected after multiple slow rinses of the column bed) was titrated using standardized NaOH. The stock solution of Eu(NO3)3 was adjusted to its equivalence pH value with dilute HNO3 to prevent hydrolysis. The concentration of

yA = mA /(mA + 6mB)

(1)

The corresponding fraction of Eu(NO3)3, yB, is given by yB = 6mB /(mA + 6mB)

(2)

The tabulated osmotic coefficients of the NaCl reference solutions were calculated using the equations of Archer,5 and those of the test solutions (ϕ) determined using the following relationship: ϕ = v*m*ϕ*/(∑ vm i i)

(3)

i

where i is either NaNO3 or Eu(NO3)3, νi is the number of ions formed by the complete dissociation of one molecule of solute i (2 for NaNO3 and 4 for Eu(NO3)3), and ν* is equal to 2. The experimental isopiestic molalities of all of the solutions are shown in Figure 1.

3. ANALYSIS The Pitzer equation for the osmotic coefficient of aqueous Eu3+−Na+−NO3− mixtures, which includes the ionic strength dependent third virial coefficient of Archer5 as generalized by Clegg et al.,6 is given below: ϕ − 1 = (2/Σimi)[−AϕI 3/2/(1 + 1.2I1/2) + ϕ )+ m Eu 3 +m NO3−(BϕEu,NO3 + ZCTEu,NO 3 ϕ )+ m Na +m NO3−(BϕNa,NO3 + ZC TNa,NO 3

m Eu 3 +m Na +(ΦϕEu,Na + m NO3−ψEu,Na,NO )] 3

C

(4)



Article

broad classes of electrolytes, but may also be fitted individually. The parameters for ternary interactions in the model, which are determined from the measurements made in this study, are ψEu,Na,NO3 (as noted above) and θEu,Na. Equations for cation and anion activity coefficients and the excess Gibbs energy of the solution, which are consistent with eq 4 for the osmotic coefficient, are given in the Appendix of Clegg et al.6 for the general case of arbitrary numbers of cations and anions, as is the equation for the osmotic coefficient. In the subsections below we determine the binary interation parameters for Eu(NO3)3 and NaNO3 from literature data, and then the ternary parameters from the measurements made in this study. 3.1. Aqueous NaNO3. Sources of data for osmotic and activity coefficients of aqueous NaNO3 at 25 °C are listed in Table 2. We have redetermined values of ϕ from the published isopiestic molalities using modern values of the osmotic coefficients of the isopiestic standards NaCl,5 and KCl.8 These values were then fitted using eq 4 for molalities up to 9.0 mol kg−1, to obtain the interaction parameters listed in Table 3. The corresponding equations for cation and anion activity coefficients (eq AI2 and AI3 of Clegg et al.6) were used to fit the activity measurements of Harned and Shropshire.9 In general, the weights used (and omission of points that are apparently in error) were the same as used by Clegg et al.10 The results are shown in Figure 2, for the osmotic coefficients only. Our own measurements, which were not included in the fit, are compared with the fitted model in Figure 2b. There is good agreement at about 1 mol·kg−1 NaNO3, but small negative deviations at higher molalities which are up to a factor of ∼2 greater than the scatter in the other data about the fitted model. The effects of this deviation, and a similar one found for aqueous Eu(NO3)3 solutions, are examined in section 3.3 below. The equation of Pitzer and Mayorga,11 using only (0) (0) , β(1) parameters βca ca , and Cca and based upon osmotic coefficients tabulated by Robinson and Stokes,12 is also compared with the fitted eq 4 in Figure 2b. The differences are due in part to the new data that have become available both for aqueous NaNO3 and the isopiestic standards since their work, and in part due to the use of only three fitted parameters (and a consequent upper limit to the validity of their equation of ∼6 mol·kg−1). The thermodynamic properties of aqueous NaNO3, from (236 to 425) K, have also been critically reviewed by Archer13 and represented using a Pitzer model. The data for osmotic and activity coefficients at 25 °C used by this author (see Archer’s Table 3) are essentially the same as those fitted here, though with the addition of some measured water vapor pressures that show quite large deviations from the fitted model and also the omission of the study of Bezboruah et al.14 Deviations of Archer’s fitted equation from our eq 4 are plotted in Figure 2b,

Table 2. Sources of Data for Osmotic and Activity Coefficients of Aqueous NaNO3 at 25 °Ca m min.

max.

no.

zero wt.

data type

1.382 0.7573 5.02·10−4 0.105 1.00 0.100 0.513

9.889 6.164 0.0201 6.025 10.00 10.83 2.34

29 12 7 49 10 18 78

0 0 0 2 1 14 all

iso iso act iso vp vp iso

std.

source

NaCl NaCl, KCl

18, 19 14 9 20 21 22 this study

KCl

NaCl

a

The headings of the columns are as follows: m, molality (minimum and maximum); no., number of data points; zero wt., the number of points within the fitted range of molality that were assigned zero weight; data type, iso (isopiestic), act (activity coefficient of NaNO3), vp (equilibrium vapor pressure); std., the isopiestic reference standard used. The 78 values of the osmotic coefficient determined in this study are reported in Table 1 (as the means of each set of three replicate samples, omitting one set of that was obviously in error). Water activities for very high concentrations (including solutions supersaturated with respect to solid NaNO3) have been measured by Tang and Munkelwitz23 and Chan et al.24 but are not used here. See also Table 3 of Archer13 for some additional sources of data, which at 25 °C are chiefly water vapor pressures above saturated solutions and differences between the vapor pressures over aqueous solutions and that of pure water.

where prefix m denotes molality, the summation is over all cations and anions i, I is the molality based ionic strength (equal to 0.5 Σi mizi2), Aϕ is the molality-based Debye−Huckel constant (0.3915 at 25 °C),1 and ψEu,Na,NO3 is a parameter for the interaction of the ions Eu3+, Na+, and NO3−. Equation 4 also contains the following functions:

Z=

∑ mi|zi|

(5a)

i

Bcaϕ = βca(0) + βca(1) exp( −αcaI1/2)

(5b)

(0) (1) CcaTϕ = Cca + Cca exp( −ωcaI1/2)

(5c)

Φijϕ = θij + θijE(I ) + IθijE ′(I )

(5d)

where “c” indicates a cation, and “a” an anion. The unsymmetrical mixing functions θEij (I) and θE’ ij (I) for dissimilar ions i and j of the same charge type but differing charge, and which do not contain any fitted parameters, are given by Pitzer7 and by Clegg et al.6 and are not reproduced here. The fitted parameters in the model which are determined from data for (1) (0) (1) single electrolyte solutions are β(0) ca , βca , Cca , and Cca . The coefficients αca and ωca are generally set to single values for

Table 3. Fitted Values of the Pitzer Model Parameters for Pure Aqueous NaNO3 and Eu(NO3)3 at 298.15 K.a β(0)

β(1) −1

kg·mol

−0.001264 ± 0.00043 0.34142 ± 0.00029

kg·mol

C(0) −1

0.13529 ± 0.0061 4.0450 ± 0.014

kg ·mol 2

C(1) −2

0.0002009 ± 0.000025 −0.0041280 ± 0.000016

kg ·mol−2 2

0.08652 ± 0.0060 −4.7918 ± 0.065

α

ω

both kg1/2·mol−1/2 2.0 1.4

2.5 3.0

solute NaNO3b Eu(NO3)3

These parameters were obtained by fitting osmotic coefficients of the two pure aqueous solutions (and including activity coefficients in the case of NaNO3(aq)) to maximum molalities of 9.0 mol·kg−1 (NaNO3), and 3.0 mol·kg−1 (Eu(NO3)3). bAt 298.15 K the interaction parameters in the model of Archer,13 calculated using the coefficients in his Table 4, are β(0) = 0.002305, β(1) = 0.21103, C(0) = 4.126·10−6, and C(1) = 0.02461. Both α and ω have the same values as above. a

D



Article

Figure 3. (a) Measured and fitted osmotic coefficients (ϕ) of aqueous Eu(NO3)3 at 25 °C, plotted against the square root of Eu(NO3)3 molality (m). Key: plus, from the equation of Rard and Spedding;15 circle, measurements of Rard and Spedding15 (KCl(aq) isopiestic standard); dot, measurements of Rard and Spedding15 (CaCl2(aq) isopiestic standard); line, our fitted model with parameters in Table 3. (b) Deviations of measured osmotic coefficients from the fitted model (observed minus fitted). Symbols and lines are the same as in panel a except: star, measurements made in this study (and not fitted); line, calculated using the equation given by Rard and Spedding.15

Figure 2. (a) Measured and fitted osmotic coefficients (ϕ) of aqueous NaNO3 at 25 °C, plotted against the square root of NaNO3 molality (m). Key: circle, Kirgintsev and Luk’yanov;18,19 times (×), Bezboruah et al.;14 dot, Robinson;20 plus, Kangro and Groeneveld;21 triangle, Pearce and Hopson;22 line, the fitted model given by eq 4. (b) Deviations of measured osmotic coefficients from the fitted model (observed minus fitted). Symbols and lines are the same as in panel a except: star, measurements made in this study (and not fitted); solid line, calculated using the NaNO3 interaction parameters given by Pitzer and Mayorga;11 dash-dot line, calculated using the model of Archer.13

and are small above about 1 mol·kg−1. The differences at lower molalities are due to the fact that eq 4 more closely represents the single osmotic coefficient data set at 25 °C in this region, whereas the model of Archer is influenced by data for other temperatures. 3.2. Aqueous Eu(NO3)3. Osmotic coefficients of aqueous Eu(NO3)3 at 25 °C have been measured by Rard and Spedding.15 Osmotic coefficients were recalculated from their original isopiestic molalities using osmotic coefficients of the

reference solutions KCl(aq) and CaCl2(aq) from Archer8 and Rard and Clegg,16 respectively. Equation 4 was then fitted to the data up to a maximum molality of 3 mol kg−1. The results are shown in Figure 3, and the fitted parameters listed in Table 3. Our own measurements, which were not included in the fit, again show small negative deviations from the fitted model, as does the Rard and Spedding equation (based upon osmotic coefficients obtained using values of the isopiestic standard available at the time of their work). E



Article

Figure 4. (a) Plot of Δϕ, multiplied by the term in ion molalities given by eq 6, against the molality of NO3− (m) in the solution mixtures. The value of Δϕ is the difference between the measured osmotic coefficient and that calculated using the Pitzer model with ternary interaction parameters (θNa,Eu and ψNa,Eu,NO3) set to zero. Key: circle, data below 1.0 mol·kg−1 NO3− (which were not fitted); dot, data for all other molalities (which were included in the fit); line, the best fit model (eq 6). (b) The same as in panel a, but calculated using the NaNO3 interaction parameters of Archer,13 given in the notes to Table 3. (c) The same as in panel a, for mNO3− > 1.0 mol·kg−1 only. Key: dot, data for isopiestic equilibrations which included sample cup(s) containing either pure aqueous NaNO3 or Eu(NO3)3 in addition to the mixtures; circle, data for isopiestic equilibrations which included sample cup(s) containing pure aqueous NaNO3, adjusted to the osmolalities suggested by the data for pure NaNO3(aq) (the star symbols in Figure 2b); triangle, data for isopiestic equilibrations which included sample cup(s) containing pure Eu(NO3)3(aq), adjusted to the osmolalities suggested by the data for pure Eu(NO3)3(aq) (the star symbols in Figure 3b).

3.3. Aqueous Eu(NO3)3−NaNO3 Mixtures. The ternary interation parameters θEu,Na and ψEu,Na,NO3 can be determined from the results listed in Table 1 using the following equation:17

ψEu,Na,NO3 set to zero. Values of the left-hand side of eq 6 are plotted in Figure 4a. In the calculation of the error bars we assumed uncertainties in the measured ϕ of ± 0.0015, which is representative of the scatter in the measurements overall, rather than the smaller values obtained only from the weighing statistics (section 2). We have also used the results for each individual sample (excluding those points based upon measurements that were clearly in error) rather than the averaged values listed in Table 1. The plotted points in Figure 4a are close to linear with respect to NO3− molality for total NO3−

Δϕ(Σimi)/(2m Eu 3 +m Na +) = θEu,Na + m NO3−ψEu,Na,NO

3

(6)

where Δϕ is the difference between the measured osmotic coefficient and that calculated using eq 4 with both θEu,Na and F



Article

Figure 5. Measured and calculated osmotic coefficients (ϕ) of the aqueous mixtures at mNO3− = 1.0 mol·kg−1, plotted against the ionic strength fraction of Eu(NO3)3 (yEu(NO3)3) in the mixture. Key: dot, measured values; dash-dot line, calculated using the Pitzer model without the fitted θNa,Eu and ψNa,Eu,NO3 determined in this study; solid line, calculated using the Pitzer model with θNa,Eu = 0.367 and ψNa,Eu,NO3 = −0.0743 (determined in this work).

molalities above about 1 mol kg−1 NO3−, as expected, but rise at lower molalities. These isopiestic solutions are from all chambers, but especially chamber three for which the values of the left-hand side of eq 6 are highest and mNO3− lowest. The reason for this deviation from expected behavior at low molalities is not known. If, for example, significant complexation of NO3− by Eu3+ were occurring in solution then the stoichiometric ϕ (i.e., −ln(aw)/(0.0180152·[4mEu(NO3)3 + 2mNaNO3]), where aw is the water activity) would be expected to be too low rather than too high. We have fitted eq 6 to our measurements, for mNO3− > 1.0 mol kg−1, and obtained θEu,Na = 0.367 ± 0.0035 and ψEu,Na,NO3 = −0.0743 ± 0.0014. The fitted line is shown in Figure 4a. We have repeated the analysis using the NaNO3 Pitzer model parameters of Archer in eq 4 (they are listed in the notes to Table 3), and the results are plotted in Figure 4b. The fitted straight line corresponds to θEu,Na = 0.350 ± 0.0033 and ψEu,Na,NO3 = −0.0714 ± 0.0013, which are close to the values obtained using the NaNO3 parameters determined in this work. The only notable difference between the results plotted in Figure 4a,b is in the maximum values of the ordinate at the lowest molalities (which were not fitted). Next, we examined the possible influence on the result of the small systematic errors apparent in our data for the two pure aqueous electrolytes, on the assumption that they might also occur in the mixtures. This was done in the following way. First, the Δϕ shown in Figures 2 and 3 were converted to deviations in osmolality (Δϕ·(m{Eu3+, Na+} + mNO3−)), and fitted by straight lines. Next, for the subset of measurements for the mixtures for which one of the sample cups contained either pure aqueous NaNO3 or Eu(NO3)3, we adjusted the osmolality of the standard solution (NaCl(aq)) on the assumption that the

Figure 6. Measured and fitted osmotic coefficients (ϕ) of the aqueous mixtures, plotted against the molality (m) of the NO3− anion, for different cation molality ratios R (where R = mEu3+/(mEu3+ + mNa+)). (a) Symbols: osmotic coefficients for R = 0.22619 (dot), R = 0.46512 (circle); R = 0.72324 (plus). The lines show the fitted model, including ternary interaction parameters, and also osmotic coefficients for the two pure aqueous solutions (as marked). (b) The same as panel a, for molality ratios R = 0.30305 (dot), R = 0.63481 (circle).

osmolality of the mixture deviated from that of the standard by the same amount as the pure aqueous solution. Both the original and adjusted values of the left-hand side of eq 6 are plotted in Figure 4c. The adjustment results in only a small change and we conclude, therefore, that the differences between the osmotic coefficients of the two pure aqueous salts measured in this study and other datawhich may indicate a lack of complete isopiestic equilibrium within the chamberdo not significantly affect the fitted values of θEu,Na and ψEu,Na,NO3. The absolute values of the two ternary parameters are large, as much as an order of magnitude greater than typical for G



Article

mixtures of 1:1 and 2:1 electrolytes for example.1 The influence of these parameters is illustrated in Figure 5 which shows measured and fitted osmotic coefficients at 1.0 mol·kg−1 total NO3− molality, as a function of the ionic strength fraction of Eu(NO3)3. In the figure, the values of the osmotic coefficient calculated without using the fitted ternary parameters, i.e., only from the properties of the pure aqueous solutions, have an almost linear relationship with yEu(NO3)3. The measurements deviate quite strongly from this. The fitted model agrees most closely with the measurements at high fractions of Eu(NO3)3. The poorer agreement for solutions containing mostly NaNO3 reflects the deviations from the fitted straight line (eq 6) in Figure 4a for the least concentrated solutions. The reason for this is not known. In Figure 6 we plot osmotic coefficients for each of the five Eu(NO3)3:NaNO3 ratios for which measurements were made and include calculated values for the two pure aqueous solutions. Viewed in this way, the agreement of the fittted model with the measurements is generally good, with obvious deviations visible only for ratios 0.22619 and 0.30305 at low mNO3− (the solid dots in Figure 6a,b), and for the ratio 0.46512 at moderate and high molalities (the open circles in Figure 6a).

activities in NaNO3 media (which may be used in the TALSPEAK process). Figure 7 shows calculated values of the activity coefficient of Eu3+ (γEu(trace)) for trace concentrations of Eu3+ in aqueous NaNO3, calculated using eq (AI2) of Clegg et al.6 both with and without the ternary parameters determined in this study. It is clear from the figure, first, that γEu(trace) varies strongly with NaNO3 molality, falling as low as 0.0048 at 4 mol· kg−1 NaNO3. Second, the effect of the ternary interactions is large: the value of γEu(trace) at 1.0 mol·kg−1 NaNO3 is almost a factor of 2 greater than that calculated with these interactions set to zero. It is therefore likely that, despite some differences between measured and fitted osmotic coefficients at low concentrations, the use of the Pitzer parameters determined here will result in increased accuracy in calculated osmotic and activity coefficients in solutions containing the ions Eu3+, Na+, and NO3−.

■

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

4. SUMMARY AND CONCLUSION In this work we have determined osmotic coefficients of pure aqueous NaNO3 and Eu(NO3)3, and their mixtures, for five

■

ACKNOWLEDGMENTS The work by P.R.Z. and R.M. was supported by the U.S. Department of Energy, Office of Nuclear Energy, under DOE Idaho Operations Office Contract DE-AC07-05ID14517. The work by S.L.C. was supported under Subcontract No. 108186 with the Idaho National Laboratory, Fuel Cycle Research and Development program (FCR&D), U.S. DOE, Office of Nuclear Energy.

■

REFERENCES

(1) Pitzer, K. S. Ion interaction approach: theory and data correlation. In Activity Coefficients in Electrolyte Solutions, 2nd ed.; Pitzer, K. S., Ed.; CRC Press: Boca Raton, FL, 1991; pp 75−153. (2) Rard, J. A.; Platford, R. F. Experimental Methods: Isopiestic. In Activity Coefficients in Electrolyte Solutions, 2nd ed.; Pitzer, K. S., Ed.; CRC Press: Boca Raton, FL, 1991; pp 209−277. (3) Nilsson, M.; Nash, K. L. A review of the development and operational characteristics of the TALSPEAK process. Solvent Extr. Ion Exch. 2007, 25, 665−701. (4) Rard, J. A.; Miller, D. G. Isopiestic determination of the osmotic and activity coefficients of aqueous mixtures of NaCl and MgCl2 at 25 °C. J. Chem. Eng. Data 1987, 32, 85−92. (5) Archer, D. G. Thermodynamic properties of the NaCl + H2O system II. Thermodynamic properties of NaCl(aq), NaCl.2H2O(cr), and phase equilibria. J. Phys. Chem. Ref. Data 1992, 21, 793−829. (6) Clegg, S. L.; Rard, J. A.; Pitzer, K. S. Thermodynamic properties of 0 - 6 mol kg−1 aqueous sulfuric acid from 273.15 to 328.15 K. Faraday Trans. Chem. Soc. 1994, 90, 1875−1894. (7) Pitzer, K. S. Thermodynamics of electrolytes V: effects of higher order electrostatic terms. J. Solution Chem. 1975, 4, 249−265. (8) Archer, D. G. Thermodynamic properties of the KCl + H2O system. J. Phys. Chem. Ref. Data 1999, 28, 1−17. (9) Harned, H. S.; Shropshire, J. The activity coefficients of alkali metal nitrates and perchlorates in dilute aqueous solutions from diffusion coefficients. J. Am. Chem. Soc. 1958, 80, 2967−2968. (10) Clegg, S. L.; Brimblecombe, P.; Liang, Z.; Chan, C. K. Thermodynamic properties of aqueous aerosols to high supersaturation. II. A model of the system Na+ - Cl− - NO3− - SO42− H2O at 298.15 K. Aerosol Sci. Technol. 1997, 27, 345−366.

Figure 7. Calculated trace activity coefficients of Eu3+ (γEu(trace)) in aqueous NaNO3 solutions at 25 °C, plotted against the square root of NaNO3 molality (m). Key: solid line, Pitzer model including the ternary parameters θNa,Eu and ψNa,Eu,NO3 determined in this study; dashdot line, Pitzer model not including the ternary parameters.

different ratios of the salts and for total salt molalities of up to 2.25 mol·kg−1. The measured osmotic coefficients of the mixtures have been fitted with an extended Pitzer model to obtain values of the ternary interaction parameters θEu,Na and ψEu,Na,NO3. Practical applications of the Pitzer model with the parameters presented here include, for example, calculations of Eu3+ H



Article

(11) Pitzer, K. S.; Mayorga, G. Thermodynamics of electrolytes II: activity and osmotic coefficients for strong electrolytes with one or both ions univalent. J. Phys. Chem. 1973, 77, 2300−2308. (12) Robinson, R. A.; Stokes, R. H. Electrolyte Solutions, 2nd ed. (revised); Butterworths: London, 1965. (13) Archer, D. G. Thermodynamic properties of the NaNO3 + H2O system. J. Phys. Chem. Ref. Data 2000, 29, 1141−1156. (14) Bezboruah, C. P.; Covington, A. K.; Robinson, R. A. Excess Gibbs energies of aqueous mixtures of alkali metal chlorides and nitrates. J. Chem. Thermodyn. 1970, 2, 431−437. (15) Rard, J. A.; Spedding, F. H. Isopiestic determination of the activity coefficients of some aqueous rare-earth electrolyte solutions at 25 °C. 6. Eu(NO3)3, Y(NO3)3, and YCl3. J. Chem. Eng. Data 1982, 27, 454−461. (16) Rard, J. A.; Clegg, S. L. Critical evaluation of the thermodynamic properties of aqueous calcium chloride. 1. Osmotic and activity coefficients of 0 - 10.77 mol kg−1 aqueous calcium chloride solutions at 298.15 K, and correlation with extended Pitzer models. J. Chem. Eng. Data 1997, 42, 819−849. (17) Pitzer, K. S.; Kim, J. S. Thermodynamics of electrolytes IV: activity and osmotic coefficients of mixed electrolytes. J. Am. Chem. Soc. 1974, 96, 5701−5707. (18) Kirgintsev, A.; Luk’yanov, A. V. Isopiestic investigations of ternary solutions. III. NaCl-NaNO3-H2O, NaCl-NaBr-H2O, NH4ClNH4Br-H2O. Russ. J. Phys. Chem. 1964, 38, 867−869. (19) Kirgintsev, A.; Luk’yanov, A. V. Isopiestic investigation of ternary solutions. VI. Aqueous ternary solutions containing sodium nitrate with the nitrates of lithium, potassium, ammonium, rubidium, and caesium respectively. Russ. J. Phys. Chem. 1965, 39, 653−655. (20) Robinson, R. A. The activity coefficients of alkali nitrates, acetates and p-toluenesulphonates in aqueous solution from vapor pressure measurements. J. Am. Chem. Soc. 1935, 57, 1165−1168. (21) Kangro, W.; Groeneveld, A. Konzentrierte waBrige Losungen, I. Z. Phys. Chem. (Neue Folge) 1962, 32, 110−126. (22) Pearce, J. N.; Hopson, H. The vapor pressure of aqueous solutions of sodium nitrate and potassium thiocyanate. J. Phys. Chem. 1937, 41, 535−538. (23) Tang, I. N.; Munkelwitz, H. R. Water activities, densities, and refractive indices of aqueous sulphates and sodium nitrate droplets of atmospheric importance. J. Geophys. Res. 1994, 99, 18801−18808. (24) Chan, C. K.; Liang, Z.; Zheng, J.; Clegg, S. L.; Brimblecombe, P. Thermodynamic properties of aqueous aerosols to high supersaturation: I−measurements of water activity of the system Na+ Cl− - NO3− - SO42− - H2O at ∼298.15 K. Aerosol Sci. Technol. 1997, 27, 324−344.

I


Isopiestic Determination of the Osmotic Coefficients of NaNO3

Recommend Documents