Thermodynamic Modeling of Apparent Molal Volumes of Metal Nitrate

Article pubs.acs.org/jced

Thermodynamic Modeling of Apparent Molal Volumes of Metal Nitrate Salts with Pitzer Model Mouad Arrad,*,† Mohammed Kaddami,† Hannu Sippola,‡,§ and Pekka Taskinen‡ †

Laboratory “Physical Chemistry of Processes and Materials” Faculty of Science and Technology, University Hassan 1, Settat, Morocco ‡ Department of Materials Science and Engineering, Metallurgical Thermodynamics and Modeling, Aalto University School of Chemical Technology, P.O. Box 16200, FI-00076 Aalto, Finland § FCG Design and Engineering, Osmontie 34, Helsinki, FI-00601, Finland ABSTRACT: The apparent molal volumes of selected metal nitrate salts, Al(NO3)3, Fe(NO3)3, and Mn(NO3)2, in water have been assessed from the available density measurements of their aqueous solutions at 25 °C over a wide molality range. The values of ϕV have been fitted to the Pitzer model using its volumetric contributions. The model parameters β(0)V, β(1)V, CφV, and V̅ 0 were determined for each aqueous electrolyte, over the composition range from 0 to about 3.5 mol·kg−1 H2O. The new experimental data and parameters obtained will be useful to extend the present database of electrolyte solutions as well as its application areas, allowing management of many physical properties of aqueous solutions in a numerical way in various end-uses.

found to be less than ± 0.0005 g·cm−3. The solutions of salts were prepared by dissolving the chemical in bi-distilled water.

1. INTRODUCTION The Pitzer model1 is one of the successful electrolyte solution models in the past 40 years. Its wide domain of applications and the relative simplicity of equations have led to series of papers dealing with volumetric properties of nitrate solutions: Kumar et al.,2 Krumgalz et al.,3 May et al.,4 and recently Rodriguez et al.5 All these papers present volumetric Pitzer parameters for electrolyte solutions fitted from the available literature data. To our knowledge, there is no previous modeling of these metal nitrate salts or a modeling of their volumetric properties such as density or apparent molar volume because of the huge lack of experimental data or the difficulty in accessing the original articles in old compilations such as ICT.6 To partially solve this problem, we provide more experimental density data for the investigated electrolytes and present Pitzer parameters at 25 °C and atmospheric pressure based on the best experimental data available in literature and our experimental data.

3. RESULTS The measurement method was identical to the method described by Sohnel et al.7 The only difference was that solutions were kept 30 min in the constant temperature bath using a thermostat with an accuracy of ± 0.1 °C. The density of pure water used in the calculations of the density of solution was taken from ref 8; the value used was 997.047 kg·m−3 at 25 °C. The apparent molal volume ϕV of the salt in the solution was calculated from the measured density of the solution using ϕ

(1)

where M is the molecular weight of the salt 212.996 g·mol−1, 241.86 g·mol−1, and 178.95 g·mol−1, respectively, for Al(NO3)3, Fe(NO3)3, and Mn(NO3)2, m is molality of the solution, ρ is density of the solution, and ρ0 is density of pure water. For each molality, three independent density measurements were conducted, and the obtained average value of density with the experimental uncertainty is presented in Tables 1 to 3 for aluminum nitrate, ferric nitrate, and manganese(II) nitrate, respectively.

2. EXPERIMENTAL SECTION All chemicals, Al(NO3)3·9H2O, Fe(NO3)3·9H2O and Mn(NO3)2·4H2O, were supplied by Sigma-Aldrich and used as delivered. According to the supplier, these reagents have purity higher than 99 %, water was distilled twice before use. Electrolyte solutions were prepared gravimetrically, considering the resolution of the balance. The relative uncertainty in the concentration is estimated to be less than ± 0.01 % for the investigated molalities. Densities of aqueous solutions were measured using a single-flask type pycnometer of 25 mL of volume. The uncertainty of the density measurements was © XXXX American Chemical Society

V = 1000(ρ0 − ρ)/(mρ0 ρ) + M /ρ

Received: October 15, 2014 Accepted: January 6, 2015

A

DOI: 10.1021/je5009894 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Measured Density Values at 25 °C as Function of Molality for Al(NO3)3 The Listed Density Is an Average Value of Three Measurementsa molality m mol kg

−1

2.7927 2.0982 1.5073 1.0069 0.8667 0.5413

reported more recently another set of experimental data which are more consistent on the molal volume scale. Experimental observations on the volumetric properties of aqueous ferric nitrate are scarce. The only literature data available comes from Doan et al.14 In this study we have used reliable data from the literature in addition to our experimental data in the modeling of apparent molal volume with Pitzer equations. Tables 4 to 6 summarize the experimental data points used in the assessments:

density ρ g cm−3 1.3557 1.2887 1.2133 1.1484 1.1288 1.0816

Table 4. Apparent Molal Volume Data Used in the Assessment for Al(NO3)3

a Standard uncertainties u are u(m) = 0.001 mol kg−1, u(T) = 0.1 K, and the expanded uncertainties of measured densities are u(ρ) = 0.0005 g·cm−1.

m/(mol kg−1)

mol kg

−1

2.4423 1.9070 1.4761 1.1826 0.4672 0.1102

density ρ g cm−3 1.3636 1.2938 1.2355 1.1942 1.0791 1.0174

a Standard uncertainties u are u(m) = 0.001 mol kg−1, u(T) = 0.1 K, and the expanded uncertainties of measured densities are u(ρ) = 0.0005 g·cm−1.

density ρ

mol kg−1

g cm−3

3.4838 2.0057 1.3726 0.5661 0.1948 0.0287

1.3590 1.2240 1.1621 1.0699 1.0230 1.0009

62.09 57.07 56.94 54.22 53.56 52.11 51.84 51.01 50.28 49.60 49.31 48.03 47.72 47.05

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Table 5. Apparent Molal Volume Data Used in the Assessment for Fe(NO3)3 m/(mol kg−1)

Table 3. Measured Density Values at 25 °C as Function of Molality for Mn(NO3)2 The Listed Density Is an Average Value of Three Measurementsa molality m

V/(cm3 mol−1)

2.7927 2.0982 1.5073 1.0069 0.8667 0.5413 0.4446 0.2924 0.1903 0.1394 0.1134 0.09067 0.05163 0.04245

Table 2. Measured Density Values at 25 °C as Function of Molality for Fe(NO3)3 The Listed Density Is an Average Value of Three Measurementsa molality m

ϕ

ϕ

V/(cm3 mol−1)

2.4423 1.9071 1.4761 1.1826 0.4672 0.1102 0.5 1.0 1.5 2.0 2.5 3.0

Standard uncertainties u are u(m) = 0.001 mol kg−1, u(T) = 0.1 K, and the expanded uncertainties of measured densities are u(ρ) = 0.0005 g·cm−1. a

66.95 66.30 64.62 62.54 60.85 55.55 61.31 62.31 63.71 65.05 66.86 68.15

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Table 6. Apparent Molal Volume Data Used in the Assessment for Mn(NO3)2

4. A REVIEW OF PUBLISHED VOLUMETRIC DATA Densities of metal nitrate solutions with water have been determined in the literature by a few experimental groups only. Pearce et al.9 presented density measurements for aluminum nitrate. Their data seem to lead to huge numerical values when we calculated the apparent molal volumes, since this quantity is very sensitive to experimental uncertainties. More recently, a precise study from Hovey et al.10 using a vibrating tube densimeter reported accurate density values at low electrolyte molalities. We notice that the method used by them is more accurate and sensitive in dilute solutions than pycnometry. Concerning manganese(II) nitrate, Herz11,12 published experimental data dealing with density and viscosity. Those density observations, however, provide a large scatter when they are converted to apparent molal volumes. Spitzer et al.13

m/(mol kg−1) 3.4838 2.0057 1.3726 0.5661 0.1948 0.0287 0.04939 0.06607 0.0869 0.09925 0.13062 0.13245 0.17439 B

ϕ

V/(cm3 mol−1) 55.01 53.50 50.21 46.58 44.37 42.33 42.3 43.3 43.5 43.2 43.6 43.6 44.0

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Article

Table 7. Pitzer Model Parameters at 25 °C Obtained for the Investigated Electrolytesa electrolyte Al(NO3)3 Fe(NO3)3 Mn(NO3)2 a

β(0)V

β(1)V

CφV

σ

−0.00016211 −0.00016622 0.00047753

−0.0004844 0.0036609 −0.00057558

0.000092473 0.000060724 −0.000100605

0.16 0.22 0.07

V̅ 0 10

43.1 47.38 40.713

Units: V̅ 0 in cm3·mol−1; β(0)V and β(1)V in kg·mol−1·bar−1; CφV in kg2·mol−2·bar−1.

5. DISCUSSION AND CONCLUSIONS We have fitted the experimental apparent molal volume ϕV data to the following eqs 2 to 4 based on the Pitzer extended virial coefficient equation for aqueous electrolyte solutions:1,4 ϕ

V = V̅ 0 + ν|z Mz X|(AV /2b) ln(1 + bI1/2) φV V ] + νMνXRT[2mBMX + m2(νMνX)1/2 CMX

(2)

where V (0)V (1)V (2)V BMX = βMX + βMX g (α1I1/2) + βMX g (α2I1/2)

(3)

g (x) = 2[1 − (1 + x) exp(−x)]/x 2

(4) Figure 1. Experimental points and calculated values of apparent molal volume for Al(NO3)3 against molality at 25 °C.

In eq 2 to 4 the symbols zM and zX are the charges of the cation and anion in the electrolyte, νM and νX are the stoichiometric coefficients of the ions in the salt, with the notation ν = νM + νX, and I is the stoichiometric ionic strength of the solution, R = 8.314 J·K−1·mol−1 is the gas constant. Since we have only electrolyte of the type 1−2 and 1−3, α2 and β(2)V are not included in the Pitzer expressions used in this work. The internal parameters used in this work, b = 1.2 (kg· mol−1)1/2, α1 = 2.0 (kg·mol−1)1/2, are the standard values proposed by Pitzer.1 The theoretical Debye−Hückel slope, AV calculated using the formulation of Fernandez et al.,15 is Av = 1.8743 cm3·kg−1·mol −3/2 at 25 °C, and V̅ 0 in eq 3 is the partial molal volume of the electrolyte at infinite dilution, at the prevailing temperature and pressure. The Pitzer volume parameters β(0)V, β(1)V, CφV, and V̅ 0 determined in this work at 25 °C are given in Table 7. The obtained values were calculated using an unweighted leastsquare method, and the experimental data are given in Tables 4 to 6. The only case where the partial molal volume at infinite dilution V̅ 0 was fitted as an adjustable parameter was ferric nitrate since the available data in the literature6,16−18 are less consistent. The variation between two compilations6,18 is from 36.5 cm3·mol−1 to 49.7 cm3·mol−1, and an average value was proposed by Couture et al.17 For both aluminum nitrate and manganese nitrate, we decided to adopt the values provided respectively by Hovey et al.10 and Spitzer et al.13 Figures 1 to 3 show the experimental apparent molal volumes of the electrolytes according to various authors as a function of molality, and the assessed value fitted with parameters of the Pitzer model, using eqs 2 to 4. The leastsquares fitting result are depicted as the solid line in each figure. The data from Herz11,12 were omitted in the fitting procedure of Mn(NO3)2 because those data are not consistent. The data from Pearce et al.9 were not included in the fitting of aluminum nitrate salt, because the conversion from density to apparent molal volume led to large values (more than 10 cm3/ mol of deviation at low concentrations) and no information was available concerning the accuracy of the measurements. The partial molal volume at infinite dilution for ferric nitrate obtained in this work V̅ 0 = 47.38 cm3 mol−1 is in fair agreement with the value (43.7 cm3 mol−1) reported by Millero,16 using

Figure 2. Experimental points and calculated values of apparent molal volume for Fe(NO3)3 against molality at 25 °C.

Figure 3. Experimental points and calculated values of apparent molal volume for Mn(NO3)2 against molality at 25 °C.

the additivity rule, while the value tabulated by ICT6 is somewhat higher at 49.7 cm3 mol−1. Concerning aluminum nitrate and manganese nitrate, the value provides by Hovey et al.10 and Spitzer et al.13 are in good agreement with the calculated apparent molal volume value at low concentration. The experimental data for Mn(NO3)2 by Jones et al.19 are in good agreement with our measurements regardless that their C



Article

(14) Doan, T. H.; Sangster, J. Viscosities of Concentrated Aqueous Solutions of Some 1:1, 2:1, and 3:1 Nitrates at 25 °C. J. Chem. Eng. Data 1981, 26, 141−144. (15) Fernandez, P.; Goodwin, A. R. H.; Lemmon, E. W.; Levelt Sengers, J. M. H.; Williams, R. C. A Formulation for the Static Permittivity of Water and Steam at Temperatures from 238 to 873 K at Pressures up to 1200 MPa, Including Derivatives and Debye− Hückel Coefficients. Phys. Chem. Ref. Data 1997, 26, 1125−1166. (16) Millero, F. J. In Water and Aqueous Solutions; Horne, R. A., Ed.; Wiley-Interscience: New York, 1972; Chapters 13 and 14. (17) Couture, A. M.; Laidler, K. J. The Partial Molal Volumes of Ions in Aqueous Solution I. Dependence on Charge and Radius. Can. J. Chem. 1956, 34, 1209−1216. (18) Landolt-Bö rnstein. Physikalisch Chemische Tabellen; Julius Springer Verlag: Berlin, 1923; pp 395−402. (19) Jones, J. S.; Ziemer, S. P.; Brown, B. R.; Woolley, E. M. Apparent molar volumes and apparent molar heat capacities of aqueous magnesium nitrate, strontium nitrate, and manganese nitrate at temperatures from 278.15 to 393.15 K and at the pressure 0.35 MPa. J. Chem. Thermodyn. 2007, 39, 550−560. (20) Rogers, P. S. Z.; Pitzer, K. S. Volumetric Properties of Aqueous Sodium Chloride Solutions. J. Phys. Chem. Ref. Data 1982, 11, 15−81.

values were measured under a total pressure of 0.35 MPa, while all our measurement were done in prevailing atmospheric pressure. According to this correlation, we can confirm that the effect of pressure over narrow pressure ranges is minor in the measurement of volumetric properties of electrolyte solutions. The same conclusion was made also by Rogers et al.20 We would like to mention that the parameters published earlier by Krumgalz et al.3 were attributed erroneously to ferrous nitrate Fe(NO3)2, due to a typing error in the original experimental paper.14 Therefore, in the current calculations of apparent molal volume the molecular weight of ferrous nitrate Fe(NO3)2 instead of ferric nitrate Fe(NO3)3 was used when assessing the data.3 As one can notice in Figures 1 to 3, a very good agreement is obtained between the calculated values of apparent molal volume and the selected experimental data used in the fitting in the three electrolyte systems investigated in this work. We should note, however, that new experimental data at wide temperature and concentration ranges are highly recommended in these systems.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Pitzer, K. S. Activity Coefficient in Electrolyte Solutions; CRC Press: Boca Raton, FL, 1991; Chapter 1. (2) Kumar, A. J. Densities and Apparent Molal Volumes of Aqueous Concentrated Calcium Chloride Solutions from 50 to 200 at 20.27 bar. J. Solution Chem. 1986, 15, 409−412. (3) Krumgalz, B. S.; Pogorelsky, R.; Pitzer, K. S. Volumetric Proprieties of Single Aqueous Electrolyte from Zero to Saturation Concentration at 298.15 K Represented by Pitzer’s Ion-Interaction Equations. J. Phys. Chem. Ref. Data 1996, 25, 663−689. (4) May, P. M.; Rowland, D.; Hefter, G.; Königsberger, E. A generic and updatable Pitzer characterization of aqueous binary electrolyte solutions at 1 bar and 25 °C. J. Chem. Eng. Data 2011, 56, 5066−6077. (5) Rodriguez, C.; Prugger, K.; Millero, F. J. Apparent molal volumes of some aqueous rare earth salt solutions fit to the Pitzer equation. J. Chem. Eng. Data 2013, 58, 1833−1838. (6) International Critical Tables; McGraw-Hill Book Company, Inc.: New York, 1928; Vol. 3, pp 51−95. (7) Sohnel, O.; Novotny, P.; Solc, Z. Densities of Aqueous Solutions of 18 Inorganic Substances. J. Chem. Eng. Data 1984, 29, 379−382. (8) Wagner, W.; Pruß, A. The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use. J. Phys. Chem. Ref. Data 2002, 31, 395−535. (9) Pearce, J. N.; Blackman, L. E. The Vapor Pressures and Activity Coefficients of Aqueous Solutions of Calcium and Aluminum Nitrate at 25 °C. J. Am. Chem. Soc. 1935, 57, 24−27. (10) Hovey, J. K.; Tremaine, P. R. Thermodynamics of Aqueous Aluminum: Standard Partial Molar Heat Capacities of Al3+ from 10 to 55 °C. Geochim. Cosmochim. Acta 1986, 50, 453−459. (11) Herz,W. Die innere Reibung von Salzlösungen. Z. Anorg. Chem. 1914, 89, Issue1 (5 November), 393−396. (12) Herz,W. Zur Kenntnis der Inneren Reibung Wässeriger Salzlösungen. Z. Anorg. Allg. Chem. 1917, 99, Issue 1 (16 August), 132−136. (13) Spizer, J. J.; Olofsson, L. V.; Singh, P. P.; Hepler, G. L. Apparent Molar Heat Capacities and Volumes of Aqueous Electrolytes at 298.15 K: Ca(NO3)2, Co(NO3)2, Cu(NO3)2, Mg(NO3)2, Mn(NO3)2, Ni(NO3)2, and Zn(NO3)2. J. Chem. Thermodyn. 1979, 11, 233−238. D


Thermodynamic Modeling of Apparent Molal Volumes of Metal Nitrate

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