J . Phys. Chem. 1989, 93, 4630-4636
4630
important than the loss or gain in the free volume. it was found that the magnitude of the excess volume depends exclusively on B2X,2relative to Cfrf$~~P*~, becau_se a-positive value of X I 2increases T for the mixture, making V > P ' and hence > 0. The difference in the molecular sizes, the nature of intermolecular interactions, and the r-meric relationship seem to play a vital role in determining the excess volume of mixture. Inconsistency in the experimental as well as theoretical results may arise from several factors that may be of equal or greater significance than the size difference, such as molecular shape, viz., the modes of molecular energy and the mechanism of flow. The interactions involving more than three bodies might be more appropriate when the value of ( V I /V,)li3 = 1.5 is used. The study of excess volume
data is associated with steric hindrance, but its contribution is not observable in the case of linear alkanes as detailed out by Delmas et a1.32,33
Acknowledgment. W e are extremely grateful to Dr. D. N . Rihani, Head, Research and Development Centre, Engineers India Limited, Gurgaon, and Dr. K . Misra, Reader, Chemistry Department, University of Allahabad, for their valuable suggestions and keen interest during the work. ( 3 2 ) Nguyen, H. P.; Delmas, G. Can. J . Chem. 1986, 64, 681. (33) Delmas, G.; De Saint-Romain, P.; Purves, P. J . Chem. Soc., Faraday Trans. Z1975, 71, 1181.
Ion Interaction Model Applied to Equilibria in the NiS04-H2S04-H20 System E . J . Reardon Department of Earth Science, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 (Received: July I I , 1988; In Final Form: December 2, 1988)
The Pitzer ion interaction model has been applied to describe chemical equilibria in the NiS04-H2S04-H20 system as a function of temperature. The available activity coefficient, enthalpy, and mineral solubility data have been analyzed to derive the pertinent ion interaction parameters and their temperature derivatives. Additional solubility measurements of a-NiS04.6H20 in sulfuric acid were made at 25 O C to refine parameter values describing the Ni-HS04 interaction. The parameters derived in this study provide an excellent representation of nickel sulfate hydrate solubility relations over the temperature range from 0 to 70 O C and sulfuric acid concentrations from 0 to 6 m. Thermodynamic quantities derived from the model results are in good agreement with values determined from experiments and those calculated from published thermodynamic data.
1. Introduction Parameterization of thermochemical data in binary salt systems provides important reference data that enable accurate predictions of solution/mineral equilibria in multicomponent solutions. Over the past decade, the ion interaction model as developed by Pitzer and his co-workers has been the most widely utilized theoretically based framework with which to perform this parameterization. Although important aspects of the interaction model are still being developed, the principal relationships among the colligative properties of electrolyte solutions are given in a review by Pitzer.' Our attention was drawn to analyzing thermochemical data in the NiS04-H2S04-H20 system as a result of our earlier work with the FeSO4-H2SO4-H20 system2 In that study, we found that the parameterization model, developed from regression analysis of isopiestic and solubility data, gave only fair agreement between model-predicted and experimentally measured thermodynamic quantities. At that time, we indicated that a major contributor to the disparity was probably uncertainties in the thermodynamic database for Fe(II), especially Fe2+ ion. Because of the high susceptibility of Fe(I1) to oxidation, acquisition of accurate thermochemical data for Fe(I1) compounds can be particularly difficult. Ni2+ is not subject to these oxidation problems, and we considered that the thermodynamic database for nickel sulfate compounds would be more accurate and serve as a better test of the consistency between model-derived and experimentally measured thermodynamic quantities. In addition, an analysis of this system contributes to a growing ion interaction parameter database that will enable an accurate description of ( I ) Pitzer, K. S. Theory: Ion interaction approach. In Actitiity Coefficients in Electrolyte Solutions; Pytkowicz, R. M . , Ed.; CRC Press: Cleveland. 1979; Vol. I . pp 157-208. ( 2 ) Reardon, E. J.; Beckie, R. D. Modelling chemical equilibria of acid
mine-drainage: The FeS0,-H2S04-H20 system. Geochim. Cosmochim. Acta 1987, Si. 2355-2368.
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solution/mineral equilibria in acid mine-drainage waters. 2. Experimental Section In this study, a-NiS04.6H20 solubility measurements in sulfuric acid were made at 25 O C . Solubility was approached from undenaturation by dissolving excess Baker reagent-grade (YNiS04.6H20 in H 2 S 0 4solutions of various concentrations. The reaction vessels were 40-mL glass vials with Teflon septum stoppers. The vessels were mounted in a Plexiglass carousel that was suspended in a temperature bath maintained to within 0.1 OC of 25 "C. A rotational speed of between 10 and 20 rpm to the carousel was achieved by directing the effluent stream from the circulating pump toward the carousel assembly. Although cu-NiS04.6H20 has been reported to require several hours to dissolve to ~ a t u r a t i o na, ~total ~ of 3 days was allowed for equilibrium. As a check on the attainment of equilibrium, a number of supersaturated solutions at 25 "C were prepared by cooling the supernatant of solutions saturated at 35 "C. a-NiS04.6H20 appeared in these reaction vessels after an incubation period of approximately 24 h. The solubility measurements made on these solutions were within the 1% experimental uncertainty of the solubility measurements made on solutions that attained equilibrium from undersaturated conditions. The solubility measurements were made by analyzing the solutions for nickel with a Varian Model 1475 atomic absorption spectrophotometer. N o matrix interference from the presence of H 2 S 0 4 in the samples was observed.
3. System Parameterization 3.1. The NiSOCH,O System. Mean molal activity coefficients (ya) for NiS04 in aqueous solution have been reported by Pitzer' over the concentration range 104-2.5 m. He corrected the osmotic (3) Pitzer, K. S.Thermodynamic properties of aqueous solutions of bivalent sulfates. J . Chem. Soc., Faraday Trans. 2 1972, 68, 101-1 13.
C 1989 American Chemical Society
Equilibria in the NiS04-H2S04-H20 System
The Journal of Physical Chemistry, Vol. 93, No. 11, 1989 4631 TABLE I: Regression Analysis Results for the Single Electrolyte Parameters of NiSO, from the Isopiestic Data Presented in Figure lo
* -0.6
0
2 z
;1-g
0 A +
--
LEQEND
Pltzrr (1972) Llbua et al. (1980) = Harlng and Boachr (1929)
parameter
Pitzerl value
this study value
std error
pW
0.1702 2.907 -40.06 0.0366
0.1594 2.926 -42.76 0.0406
0.0089 0.060 1.48 0.0038
p(I) p(2)
CQ -1.2
"Standard errors refer only to this study.
-1.8 I 0
, 0.4
I
0.8
1.2
I
6
1.6
m0.6
Figure 1. Summary of experimental data for the mean molal activity coefficient of N i S 0 4 based on isopiestic measurements. Solid curve shows the representation of these values from the Pitzer equations and the single electrolyte parameters for N i S 0 4 determined in this study.
6
I
h
- 4 Y
Y
$
0
9
A +
2
coefficient data ($) of Brown and Prue' obtained from freezing point data to a temperature of 25 OC and combined them with the isopiestic measurements tabulated by Robinson and Stokese5 Pitzer3 thus provided absolute values for y,(NiS04) at this temperature for all concentrations up to the saturation limit with respect to NiS04.7H20. Data for ya(NiS04) from emf measurements at low concentrations (6H20 & N i S 0 4 . 6 H 2 0 + Ni2+ + SO>- + 6 H 2 0 NiS04.7H20 Ni2+ SO-: 7H20 NiS04.7H20 + a-NiS04.6H20 H 2 0 a-NiS04.6H20 + @-NiS04.6H20
+
.=
+
+ +
AGRo,bkJ 12.41 1 1.84 12.70 0.29 0.57
11.47 f 1.5 11.52 i 1.5 0.05 i 0.3
AHRo,bkJ 6.56 0.0 13.65 7.09 6.56
4.81 f O . l l c 12.49 f 0.22d 7.68 f 0.1 I C
" T h e literature AGRo values have been calculated from free energy data tabulated by Robie et al.34 whereas AHRovalues are directly measured quantities. *First column entry is calculated from KSpdata in this study. Second column entry is from published thermodynamic data. CGoldberg et aI.l4 dStout et al." 'Calculated by combining literature AHRovalues for reactions 2 and 1.
Because no entropy data exist for P-NiSO4.H20, this comparison can only be made for reactions 1, 3, and 4 in Table IV. The model-predicted values for these reactions are -19.6, 3.2, and 22.8, respectively. These can be compared with those calculated from data in Robie et of -23.8 f 1.7, 1.8 f 1.7, and 24.1 f 1.8 J mol-' K-',respectively. Again, the model-predicted values compare favorably, close t o the uncertainty of the thermodynamic data.
The accuracy of the parameterization model for the combined NiS04-H2S04-H20 system can be tested by comparing model-calculated water activities with those derived from the isopiestic measurements of Awakura et al.3s These authors graphically (35) Awakura, Y . ;Park, S. K.; Morinaga, S.; Majima, H. (1986) Determination of the activities of mixed aqueous H,SO, solutions containing MnSO,, NiS04 or CoS04. Denki Kagaku 1986, 54, 240-244.
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4636
agreement between the model-predicted and the measured data is relatively good. The maximum total difference in water activities is less than 0.003 and is generally within 0.001. Full details of the concentration conditions of the data points shown in Figure 8, although not the actual values, are given in Awakura et al.3s
0'925
I //
I
Id 0.900
0.925
0.850
0.875
1
aw (pred)
Figure 8. Plot of model-calculated and experimental measurements of water activity in solution mixtures of nickel sulfate and sulfuric acid. Experimental data is from Awakura et Perfect agreement between model-calculated and experimental data would plot along the solid line. report a series of water activity measurements for solution mixtures of 0-2.5 m H2SO4 in 0-2.5 m NiS04. The water activity of each plotted data point was read from the graph and compared to model-calculated values in Figure 8. Figure 8 is a scatter diagram of /la, versus N i S 0 4 concentration, where Aa, is the difference between experimental and model-calculated water activities. The
5. Conclusions The parameterization of the NiS0,-H2S0,-H20 system performed in this paper with use of the relations developed by Pitzer and co-workers allows an accurate description of nickel sulfate hydrate solubility, phase transitions, and solute activities over a temperature range from 0 to 5 5 "C, sulfuric acid concentration from 0-6 m, and nickel sulfate concentrations up to the solubility limit. The usefulness of the parameterization model is further demonstrated by the agreement of model-derived thermodynamic quantities with those that have been either measured directly or calculated from published thermodynamic data. The upper temperature limit of 5 5 "C for the applicability of the model is cited above because this is the maximum temperature reported by Pitzer et aL30 for the applicability of their parameters for the H2S04-H20 system. Simulations performed in this study, however, yield good agreement between measured and predicted mineral solubilities to temperatures of 70 "C. Registry No. NiS04, 7786-81-4; H2S04.7664-93-9; NiS04*6H20, 10101-97-0.
Thermodynamics of a Quadrupolar Hard Diatomic Fluid Using a Perturbation Theory with Nonspherlcal Reference System M. Lombardero,* C. Martin, E. Lomba, Instituto de Qu fmica F h c a Rocasolano, CSIC, Serrano I 1 9, 28006 Madrid. Spain, and Departamento de Qu fmica Fisica, Facultad de Quimicas, Universidad Complutense, 28040 Madrid, Spain
and J. L. F. Abascal Departamento de Quimica Fisica, Facultad de Qu fmicas, Universidad Complutense, 28040 Madrid, Spain (Receiued: August 11, 1988)
A nonspherical reference perturbation theory for free energy was used to compute the thermodynamic properties of a fluid
made up of hard diatomic molecules with point (ideal) quadrupoles at the molecular centers. Our scheme combined the usual perturbation approach and the RAM perturbation technique, which was used to approximate the molecular distribution function for the reference system. Two options were examined by taking both the Percus-Yevick integral equation solution and molecular dynamics data for the radial distribution function of the RAM reference potential. To check the theory, new Monte Carlo calculations were performed for the quadrupolar system. Comparison of the theoretical and simulation results indicated good agreement for the main thermodynamic quantities.
I. Introduction Following the progress achieved in describing and explaining atomic and simple molecular fluids, theoretical interest has, in recent years, increasingly focused on the most general cases of systems with electrostatic interactions in which both molecular structure and electrostatic forces are anisotropic. Specifically, dipolar and quadrupolar molecules have received special attention, in view of their theoretical and practical interest. In the context of perturbation theory, two different types of approximations have been put forward for fluids consisting of nonspherical molecules,' depending upon whether the reference potential is spherical ( u expansion and f expansion, both of which utilize angle-averaged reference potentials) or nonspherical. However, it now seems clear that approximations based on the former method are incapable *To whom correspondence should be addressed at lnstituto de Quimica Flsica Rocasolano.
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of accurately describing nonspherical molecules with orientation-dependent electrostatic interactiom2 Nonspherical reference approaches for hard quadrupolar diatomic molecules have been examined by several all of whom have used simulated data for the molecular pair distribution function for the reference fluid. In this study we have considered an alternative route in which the structure of the reference fluid is approximated by the reduced form of the R A M perturbation (1) Gray, C. G.; Gubbins, K. E. Molecular Theory of Fluids; Clarendon Press: Oxford, U.K., 1984. ( 2 ) Wojcik, M. C.; Gubbins, K. E. J . Phys. Chem. 1984,88,6559. Wojcik, M. C. Ph.D. Thesis, Cornell University, 1984. (3) Sandler, S. I . Mol. Phys. 1974, 28, 1207. (4) Martina, E.; Stell, G.; Deutch, J . M . J . Chem. Phys. 1979, 70,5751. (5) Valderrama, J. 0.;Sandler, S. I. Mol. Phys. 1983, 49, 925. (6) Williams, C. P.; Gupta, S.; McLaughlin, E. Chem. Phys. Lert. 1987. 140. 250.
0 1989 American Chemical Society
