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Mutual Diffusion Coefficients and Refractive Index Increments of K2SO4(aq) at 298.15 K from Rayleigh Interferometry

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Donald G. Miller: Deceased.

Abstract

Isothermal mutual diffusion coefficients (interdiffusion coefficients) were measured for K2SO4(aq) at 298.15 ± 0.005 K, at numerous concentrations ranging from dilute solutions to near saturation (0.59648 mol·dm–3; 0.61349 mol·kg–1) under free diffusion boundary conditions, using high precision Rayleigh interferometry. Under the experimental conditions these diffusion coefficients are on the volume-fixed reference frame Dv. Two series of experiments were performed, the first using the traditional experimental approach with a mercury lamp source and with the interference patterns being recorded on glass photographic plates, and the second with a He–Ne laser light source and computerized data acquisition using a photodiode array. The results from both series of experiments are in excellent agreement, and generally yield diffusion coefficients precise to at least 0.002 × 10–9 m2·s–1 (0.15% to 0.19%) and in most cases to 0.001 × 10–9 m2·s–1 (0.07% to 0.1%). These experiments also yield accurate values of the refractive index differences for the solution pairs used in the diffusion experiments. The new diffusion coefficients are compared to two sets of published values of diffusion coefficients for K2SO4(aq) which are somewhat discrepant from each other. This study extends and complements our earlier work on the diffusion coefficients of the most common brine salts: NaCl(aq), KCl(aq), MgCl2(aq), CaCl2(aq), Na2SO4(aq),]MgSO4(aq), NaHCO3(aq), and KHCO3(aq) at 298.15 K.

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References

  1. Rard, J.A., Miller, D.G.: The mutual diffusion coefficients of NaCl–H2O and CaCl2–H2O at 25 °C from Rayleigh interferometry. J. Solution Chem. 8, 701–716 (1979)

    Article  CAS  Google Scholar 

  2. Rard, J.A., Miller, D.G.: Mutual diffusion coefficients of BaCl2–H2O and KCl–H2O at 25 °C from Rayleigh interferometry. J. Chem. Eng. Data 25, 211–215 (1980)

    Article  CAS  Google Scholar 

  3. Miller, D.G., Rard, J.A., Eppstein, L.B., Albright, J.G.: Mutual diffusion coefficients and ionic transport coefficients lij of MgCl2–H2O at 25 °C. J. Phys. Chem. 88, 5739–5748 (1984)

    Article  CAS  Google Scholar 

  4. Rard, J.A., Miller, D.G.: The mutual diffusion coefficients of Na2SO4–H2O and MgSO4–H2O at 25 °C from Rayleigh interferometry. J. Solution Chem. 8, 755–766 (1979)

    Article  CAS  Google Scholar 

  5. Albright, J.G., Mathew, R., Miller, D.G.: Measurement of binary and ternary mutual diffusion coefficients of aqueous sodium and potassium bicarbonate solutions at 25 °C. J. Phys. Chem. 91, 210–215 (1987)

    Article  CAS  Google Scholar 

  6. Albright, J.G., Mathew, R., Miller, D.G., Rard, J.A.: Isothermal diffusion coefficients for NaCl–MgCl2–H2O at 25 °C. 1. Solute concentration ratio of 3:1. J. Phys. Chem. 93, 2176–2180 (1989)

    Article  CAS  Google Scholar 

  7. Paduano, L., Mathew, R., Albright, J.G., Miller, D.G., Rard, J.A.: Isothermal diffusion coefficients for NaCl–MgCl2–H2O at 25 °C. 2. Low concentrations of NaCl with a wide range of MgCl2 concentrations. J. Phys. Chem. 93, 4366–4370 (1989)

    Article  CAS  Google Scholar 

  8. Mathew, R., Paduano, L., Albright, J.G., Miller, D.G., Rard, J.A.: Isothermal diffusion coefficients for NaCl–MgCl2–H2O at 25 °C. 3. Low MgCl2 concentrations with a wide range of NaCl concentrations. J. Phys. Chem. 93, 4370–4374 (1989)

    Article  CAS  Google Scholar 

  9. Mathew, R., Albright, J.G., Miller, D.G., Rard, J.A.: Isothermal diffusion coefficients for NaCl–MgCl2–H2O at 25 °C. 4. Solute concentration ratio of 1:3. J. Phys. Chem. 94, 6875–6878 (1990)

    Article  CAS  Google Scholar 

  10. Miller, D.G., Albright, J.G., Mathew, R., Lee, C.M., Rard, J.A., Eppstein, L.B.: Isothermal diffusion coefficients of NaCl–MgCl2–H2O at 25 °C. 5. Solute concentration ratio of 1:1 and some Rayleigh results. J. Phys. Chem. 97, 3885–3899 (1993)

    Article  CAS  Google Scholar 

  11. Rard, J.A., Albright, J.G., Miller, D.G., Zeidler, M.E.: Ternary mutual diffusion coefficients and densities of the system {z1NaCl + (1–z1)Na2SO4}(aq) at 298.15 K and a total molarity of 0.5000 mol dm–3. J. Chem. Soc. Faraday Trans. 92, 4187–4197 (1996)

    Article  CAS  Google Scholar 

  12. Albright, J.G., Gillespie, S.M., Rard, J.A., Miller, D.G.: Ternary solution mutual diffusion coefficients and densities of aqueous mixtures of NaCl and Na2SO4 at 298.15 K for six different solute fractions at a total molarity of 1.000 mol·dm–3. J. Chem. Eng. Data 43, 668–675 (1998)

    Article  CAS  Google Scholar 

  13. Annunziata, O., Rard, J.A., Albright, J.G., Paduano, L., Miller, D.G.: Mutual diffusion coefficients and densities at 298.15 K of aqueous mixtures of NaCl and Na2SO4 for six different solute fractions at a total molarity of 1.500 mol·dm–3 and of aqueous Na2SO4. J. Chem. Eng. Data 45, 936–945 (2000)

    Article  CAS  Google Scholar 

  14. Fu, J., Paduano, L., Rard, J.A., Albright, J.G., Miller, D.G.: Mutual diffusion coefficients and densities at 298.15 K of aqueous mixtures of NaCl and Na2SO4 at high concentrations with NaCl solute fractions of 0.9000. J. Chem. Eng. Data 46, 601–608 (2001)

    Article  CAS  Google Scholar 

  15. Fu, J., Rard, J.A., Paduano, L., Albright, J.G., Miller, D.G.: Mutual diffusion coefficients and densities at 298.15 K of aqueous mixtures of NaCl and Na2SO4 with NaCl solute fractions of 0.9500, trace diffusion coefficients of SO42– in NaCl(aq), and trace refractive index increments and partial molar volumes of Na2SO4 and NaCl. J. Chem. Eng. Data 47, 496–512 (2002)

    Article  CAS  Google Scholar 

  16. Miller, D.G., Sartorio, R., Paduano, L., Rard, J.A., Albright, J.G.: Effects of different sized concentration differences across free diffusion boundaries and comparison of Gouy and Rayleigh diffusion measurements using NaCl–KCl–H2O. J. Solution Chem. 25, 1185–1211 (1996)

    Article  CAS  Google Scholar 

  17. Ptacek, C., Blowes, D.: Predicting sulfate-mineral solubility in concentrated waters. In: Alpers, C.N., Jambor, J.L., Nordstrom, D.K. (eds.) Sulfate minerals—crystallography, geochemistry, and environmental significance. Reviews in mineralogy and geochemistry, vol. 40. Mineralogical Society of America, Washington, D.C (2000)

    Google Scholar 

  18. Mullin, J.W., Nienow, A.W.: Diffusion coefficients of potassium sulfate in water. J. Chem. Eng. Data 9, 526–527 (1964)

    Article  CAS  Google Scholar 

  19. Leaist, D.G., Hao, L.: Binary mutual diffusion coefficients of aqueous ammonium and potassium sulfates at 25 °C. J. Solution Chem. 21, 345–350 (1992)

    Article  CAS  Google Scholar 

  20. Anderson, D.E., Graf, D.L.: Ionic diffusion in naturally-occurring aqueous solutions: use of activity coefficients in transition-state models. Geochim. Cosmochim. Acta 42, 251–262 (1978)

    Article  CAS  Google Scholar 

  21. Felmy, A.R., Weare, J.H.: Calculation of multicomponent ionic diffusion from zero to high concentration: I. The system Na–K–Ca–Mg–Cl–SO4–H2O at 25 °C. Geochim. Cosmochim. Acta 55, 113–131 (1991)

    Article  CAS  Google Scholar 

  22. Steefel, C.I., Lichtner, P.C.: Diffusion and reaction in rock matrix bordering a hyperalkaline fluid-filled fracture. Geochim. Cosmochim. Acta 58, 3595–3612 (1994)

    Article  CAS  Google Scholar 

  23. Marion, G.M., Farren, R.E.: Mineral solubilities in the Na–K–Mg–Ca–Cl–SO4–H2O system: a re-evaluation of the sulfate chemistry in the Spencer–M∅ller–Weare model. Geochim. Cosmochim. Acta 63, 1305–1318 (1999)

    Article  CAS  Google Scholar 

  24. Miller, D.G.: Certain transport properties of binary electrolyte solutions and their relation to the thermodynamics of irreversible processes. J. Phys. Chem. 64, 1598–1599 (1960)

    Article  CAS  Google Scholar 

  25. Miller, D.G.: Application of irreversible thermodynamics to electrolyte solutions. I. Determination of ionic transport coefficients lij for isothermal vector transport processes in binary electrolyte systems. J. Phys. Chem. 70, 2639–2659 (1966)

    Article  CAS  Google Scholar 

  26. Miller, D.G.: Explicit relations of velocity correlation coefficients to Onsager lij's, to experimental quantities, and to infinite dilution limiting laws for binary electrolyte solutions. J. Phys. Chem. 85, 1137–1146 (1981). The terms r12c/(103ρ2) and r22c/(103ρ2) should be in front of the left-hand square brackets of Eq. A1 and Eq. A2, respectively, and the term in front of the square bracket of Eq. A3 should be c02/(103ρ2)

  27. Zhong, E.C., Friedman, H.L.: Self-diffusion and distinct diffusion of ions in solution. J. Phys. Chem. 92, 1685–1692 (1988)

    Article  CAS  Google Scholar 

  28. Pitzer, K.S.: Ion interaction approach: theory and data correlation. In: Pitzer, K.S. (ed.) Activity coefficients in electrolyte solutions, 2nd edn. CRC Press, Boca Raton (1991)

    Google Scholar 

  29. Archer, D.G., Kirklin, D.R.: Enthalpies of solution of sodium chloride and potassium sulfate in water. Thermodynamic properties of the potassium sulfate + water system. J. Chem. Eng. Data 47, 33–46 (2002)

    Article  CAS  Google Scholar 

  30. Palmer, D.A., Archer, D.G., Rard, J.A.: Isopiestic determination of the osmotic and activity coefficients of K2SO4(aq) at the temperatures 298.15 and 323.15 K, and revision of the thermodynamic properties of the K2SO4 + H2O system. J. Chem. Eng. Data 47, 1425–1431 (2002)

    Article  CAS  Google Scholar 

  31. Rard, J.A., Clegg, S.L., Palmer, D.A.: Isopiestic determination of the osmotic coefficients of Na2SO4(aq) at 25 and 50 °C, and representation with ion interaction (Pitzer) and mole fraction thermodynamic models. J. Solution Chem. 29, 1–49 (2000)

    Article  CAS  Google Scholar 

  32. Palmer, D.A., Rard, J.A., Clegg, S.L.: Isopiestic determination of the osmotic and activity coefficients of Rb2SO4(aq) and Cs2SO4(aq) at T = (298.15 and 323.15) K, and representation with an extended ion-interaction (Pitzer) model. J. Chem. Thermodyn. 34, 63–102 (2002)

    Article  CAS  Google Scholar 

  33. Harned, H.S., Blake, C.A., Jr.: The diffusion coefficients of lithium and sodium sulfates in dilute aqueous solution at 25°. J. Am. Chem. Soc. 73, 2448–2450 (1951)

    Article  CAS  Google Scholar 

  34. Harned, H.S., Blake, C.A., Jr.: The diffusion coefficient of cesium sulfate in dilute aqueous solution at 25°. J. Am. Chem. Soc. 73, 5882–5883 (1951)

    Article  CAS  Google Scholar 

  35. Leaist, D.G., Goldik, J.: Diffusion and ion association in concentrated solutions of aqueous lithium, sodium, and potassium sulfates. J. Solution Chem. 30, 103–118 (2001)

    Article  CAS  Google Scholar 

  36. Miller, D.G., Albright, J.G.: Optical methods. In: Wakeham, W.A., Nagashima, A., Sengers, J.V. (eds.) Measurement of the transport properties of fluids; experimental thermodynamics, vol. III, pp. 272–294. Blackwell Scientific Publications, Oxford (1991) . (references on pp. 316–320)

    Google Scholar 

  37. Gosting, L.J., Kim, H., Loewenstein, M.A., Reinfelds, G., Revzin, A.: A versatile optical diffusiometer including a large optical bench of new design. Rev. Sci. Instrum. 44, 1602–1609 (1973)

    Article  Google Scholar 

  38. Trimble, H.M.: The solubility of potassium permanganate in solutions of potassium sulfate and of sodium sulfate. J. Am. Chem. Soc. 44, 451–460 (1922)

    Article  CAS  Google Scholar 

  39. Palitzsche, S.: Studies of surface tensions of solutions. I. The effect of salts upon the surface tension of aqueous Urethan solutions: the measurements. Z. Phys. Chem. (Leipzig) A138, 379–398 (1928)

    Google Scholar 

  40. Jones, G., Ray, W.A.: The surface tension of electrolytes as a function of the concentration. I. A differential method for measuring relative surface tension. J. Am. Chem. Soc. 59, 187–198 (1937)

    Article  CAS  Google Scholar 

  41. Wirth, H.E.: The partial molar volumes of potassium chloride, potassium bromide and potassium sulfate in sodium chloride solutions. J. Am. Chem. Soc. 59, 2549–2554 (1937)

    Article  CAS  Google Scholar 

  42. Pearce, J.N., Eckstrom, H.C.: Vapor pressures and partial molal volumes of aqueous solutions of the alkali sulfates. J. Am. Chem. Soc. 59, 2861–2869 (1937)

    Google Scholar 

  43. Jones, G., Colvin, J.H.: The viscosity of solutions as a function of the concentration. VII. Silver nitrate, potassium sulfate and potassium chromate. J. Am. Chem. Soc. 62, 338–340 (1940)

    Article  CAS  Google Scholar 

  44. Kaminsky, M.: Experimental study of the concentration and temperature dependence of the viscosity of aqueous strong electrolytes. III. KCl, K2SO4, MgCl2, BeSO4, and MgSO4 solutions. Z. Phys. Chem. N. F. 12, 206–231 (1957)

    Article  CAS  Google Scholar 

  45. Dunn, L.A.: Apparent molar volumes of electrolytes. Part 1—some 1–2, 2–2, 3–1 electrolytes in aqueous solution at 25 °C. Trans. Faraday Soc. 62, 2348–2354 (1966)

    Article  CAS  Google Scholar 

  46. Millero, F.J., Ward, G.K., Chetirkin, P.V.: Relative sound velocities of sea salts at 25 °C. J. Acoust. Soc. Am. 61, 1492–1498 (1977)

    Article  CAS  Google Scholar 

  47. Hovey, J.K., Hepler, L.G., Tremaine, P.R.: Apparent molar heat capacities and volumes of aqueous HClO4, HNO3, (CH3)4NOH and K2SO4 at 298 15 K. Thermochim. Acta 126, 245–253 (1988)

    Article  CAS  Google Scholar 

  48. Mydlarz, J., Jones, A.G.: Potassium sulfate water–alcohols systems. J. Chem. Eng. Data 35, 214–216 (1990)

    Article  CAS  Google Scholar 

  49. Dedick, E.A., Hershey, J.P., Sotolongo, S., Stade, D.J., Millero, F.J.: The PVT properties of concentrated aqueous electrolytes IX. The volume properties of KCl and K2SO4 and their mixtures with NaCl and Na2SO4 as a function of temperature. J. Solution Chem. 19, 353–374 (1990)

    Article  CAS  Google Scholar 

  50. Creeth, J.M.: Studies of free diffusion in liquids with the Rayleigh method. I. The determination of differential diffusion coefficients in concentration-dependent systems of two components. J. Am. Chem. Soc. 77, 6428–6440 (1955)

    Article  CAS  Google Scholar 

  51. Albright, J.G., Miller, D.G.: Mutual diffusion coefficients at 25° in the system silver nitrate–water. J. Phys. Chem. 76, 1853–1857 (1972)

    Article  CAS  Google Scholar 

  52. Albright, J.G., Miller, D.G.: Analysis of Gouy interference patterns from binary free-diffusion systems when the diffusion coefficient and refractive index have C1/2 and C3/2 terms, respectively. J. Phys. Chem. 84, 1400–1413 (1980)

    Article  CAS  Google Scholar 

  53. Rard, J.A.: Mutual diffusion coefficients of aqueous Na2SO4 at C = 0.02989 mol·dm–3 and 298.15 K by using Rayleigh interferometry with free diffusion boundary conditions: experimental test of the effect of the C3/2 concentration dependence of refractive index at low concentration. J. Solution Chem. 50, 886–893 (2021)

    Article  CAS  Google Scholar 

  54. Robinson, R.A., Stokes, R.H.: Electrolyte solutions (revised), 2nd edn. Butterworths, London (1965)

    Google Scholar 

  55. Eysseltová, J., Bouaziz, R.: IUPAC-NIST solubility data series. 93. Potassium sulfate in water. J. Phys. Chem. Ref. Data 41, 013103-1-013103–48 (2012)

    Article  Google Scholar 

  56. Rard, J.A., Miller, D.G.: Mutual diffusion coefficients of SrCl2–H2O and CsCl–H2O at 25 °C from Rayleigh interferometry. J. Chem. Soc., Faraday Trans. 78, 887–896 (1982); errata: 79, 1049 (1983)

  57. Rard, J.A., Miller, D.G.: Mutual diffusion coefficients of aqueous MnCl2 and CdCl2, and osmotic coefficients at 25 °C. J. Solution Chem. 14, 271–299 (1985)

    Article  CAS  Google Scholar 

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Acknowledgements

This work was performed under the auspices of the U.S. Department of Energy (DOE) by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. Support from the Chemistry and Biochemistry Department of Texas Christian University for J.G.A. and O.A. is gratefully acknowledged. The work of J.A.R. and D.G.M. was performed in part under the auspices of the Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences of the U. S. Department of Energy by University of California, Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48. Lawrence Livermore National Laboratory is now managed by Lawrence Livermore National Security LLC rather than the University of California. We thank Dr. Donald A. Palmer for supplying us with the Aldrich “Gold Label” K2SO4(s)

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Rard, J.A., Miller, D.G., Albright, J.G. et al. Mutual Diffusion Coefficients and Refractive Index Increments of K2SO4(aq) at 298.15 K from Rayleigh Interferometry. J Solution Chem 50, 1315–1334 (2021). https://doi.org/10.1007/s10953-021-01118-y

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