Advertisement

Journal of Solution Chemistry

, Volume 8, Issue 9, pp 655–690 | Cite as

The solubility and isotopic fractionation of gases in dilute aqueous solution. I. Oxygen

  • Bruce B. Benson
  • Daniel KrauseJr.
  • Mark A. Peterson
Article

Abstract

A very precise and accurate new method is described for determination of the Henry coefficient k and the isotopic fractionation of gases dissolved in liquids. It yields fully corrected values for k at essentially infinite dilution. For oxygen the random error for k is less than 0.02%, which is an order of magnitude better than the best previous measurements on that or any other gas. Extensive tests and comparison with other work indicate that systematic errors probably are negligible and that the accuracy is determined by the precision of the measurements. In the virial correction factor (1+λPt), where Pt is the total pressure of the vapor phase, the coefficient λ for oxygen empirically is a linear decreasing function of the temperature over the range 0–60°C. The simple three-term power series in 1/T proposed by Benson and Krause,
$$\ln k = a_0 + a_1 /T + a_2 /T^2 $$
provides a much better form for the variation of k with temperature than any previous expression. With a0=3.71814, a1=5596.17, and a2=−1049668, the precision of fit to it of 37 data points for oxygen from 0–60°C is 0.018% (one standard deviation). The three-term series in 1/T also yields the best fit for the most accurate data on equilibrium constants for other types of systems, which suggests that the function may have broader applications. The oxygen results support the idea that when the function is rewritten as
$$\ln k = - (A_1 + A_2 ) + A_1 \left( {\frac{{T_1 }}{T}} \right) + A_2 \left( {\frac{{T_1 }}{T}} \right)^2 $$
it becomes a universal solubility equation in the sense that A2 is common to all gases, with T1 and A1 characteristic of the specific gas. Accurate values are presented for the partial molal thermodynamic function changes for the solution of oxygen in water between the usual standard states for the liquid and vapor phases. These include the change in heat capacity, which varies inversely with the square of the absolute temperature and for which the random error is 0.15%. Analysis of the high-temperature data of Stephan et al., in combination with our values from 0–60°C, shows that for oxygen the fourterm series in 1/T,
$$\ln k = - 4.1741 + 1.3104 \times 10^4 /T - 3.4170 \times 10^6 /T^2 + 2.4749 \times 10^8 /T^3 $$

where p=kx and p is the partial pressure in atmospheres of the gas, probably provides the best and easiest way presently available to calculate values for k in the range 100–288°C, but more precise measurements at elevated temperatures are needed. The new method permits direct mass spectrometric comparison of the isotopic ratio34O2/32O2 in the dissolved gas to that in the gas above the solution. The fractionation factor α=32k/34k varies from approximately 1.00085 (±0.00002) at 0°C to 1.00055 (±0.00002) at 60°C. Although the results provide the first quantitative determination of α vs. temperature for oxygen, it is not possible from these data to choose among several functions for the variation ofInα with temperature. If the isotopic fractionation is assumed to be due to a difference in the zero-point energy of the two species of oxygen molecules, the size of the solvent cage is calculated to be approximately 2.5 Å. The isotopic measurements indicate that substitution of a34O2 molecule for a32O2 molecule in solution involves a change in enthalpy with a relatively small change in entropy.

Key words

Gas solubility isotopic fractionation oxygen water temperature dependence Henry coefficient thermodynamic functions 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. E. Markham and K. A. Kobe,Chem. Rev. 28, 519 (1941).Google Scholar
  2. 2.
    R. Battino and H. L. Clever,Chem. Rev. 66, 395 (1966).Google Scholar
  3. 3.
    E. Wilhelm, R. Battino, and R. J. Wilcock,Chem. Rev. 77 219 (1977).Google Scholar
  4. 4.
    Water, A Comprehensive Treatise, Four Volumes, F. Franks, ed. (Plenum Press, New York, 1972).Google Scholar
  5. 5.
    L. W. Winkler,Ber. Dtsch. Chem. Ges. 22, 1764 (1889).Google Scholar
  6. 6.
    L. W. Winkler,Ber. Dtsch. Chem. Ges. 24, 3602 (1891).Google Scholar
  7. 7.
    C. J. J. Fox,Trans. Faraday Soc. 5, 68 (1909).Google Scholar
  8. 8.
    Handbook of Chemistry and Physics, 39th edn. (Chemical Rubber Publishing Co., Cleveland, Ohio, 1957).Google Scholar
  9. 9.
    G. B. Whipple and M. C. Whipple,J. Am. Chem. Soc. 33, 362 (1911).Google Scholar
  10. 10.
    G. A. Truesdale, A. L. Downing, and G. F. Lowden,J. Appl. Chem. 5, 53 (1955).Google Scholar
  11. 11.
    T. J. Morrison and F. Billett,J. Chem. Soc., 3819 (1952).Google Scholar
  12. 12.
    H. Steen,Limnol. Oceanogr. 3, 423 (1958).Google Scholar
  13. 13.
    J. C. Morris, W. Stumm, and H. A. Galal,Proc. Am. Soc. Civ. Eng., J. Sanit. Eng. Div. 87, SA1, 81 (1961).Google Scholar
  14. 14.
    H. L. Elmore and T. W. Hayes,Proc. Am. Soc. Civ. Eng., J. Sanit. Eng. Div. 86, SA4, 41 (1960).Google Scholar
  15. 15.
    B. B. Benson and P. D. M. Parker,J. Phys. Chem. 65, 1480 (1961).Google Scholar
  16. 16.
    C. E. Klots and B. B. Benson,J. Mar. Res. 21, 48 (1963).Google Scholar
  17. 17.
    H. A. C. Montgomery, N. S. Thom, and A. Cockburn,J. Appl. Chem. 14, 280 (1964).Google Scholar
  18. 18.
    E. Douglas,J. Phys. Chem. 68, 169 (1964).Google Scholar
  19. 19.
    K. Grasshoff,Kiel. Meersforsch. 20, 143 (1964).Google Scholar
  20. 20.
    J. H. Carpenter,Limnol. Oceanogr. 11, 264 (1966).Google Scholar
  21. 21.
    E. J. Green and D. E. Carritt,J. Mar. Res. 25, 140 (1967).Google Scholar
  22. 22.
    C. N. Murray and J. P. Riley,Deep-Sea Res. 16, 311 (1969).Google Scholar
  23. 23.
    E. C. W. Clarke and D. N. Glew,Trans. Faraday Soc. 62, 539 (1966).Google Scholar
  24. 24.
    S. Valentiner,Z. Phys. 42, 253 (1927).Google Scholar
  25. 25.
    R. F. Weiss,Deep-Sea Res. 17, 721 (1970).Google Scholar
  26. 26.
    C. N. Murray, J. P. Riley, and T. R. S. Wilson,Deep-Sea Res. 16, 297 (1969).Google Scholar
  27. 27.
    C. N. Murray and J. P. Riley,Deep-Sea Res. 17, 203 (1970).Google Scholar
  28. 28.
    B. B. Benson and D. Krause, Jr.,J. Chem. Phys. 64, 689 (1976).Google Scholar
  29. 29.
    D. M. Himmelblau,J. Phys. Chem. 63, 1803 (1959);J. Chem. Eng. Data 5, 10 (1960).Google Scholar
  30. 30.
    C. E. Klots and B. B. Benson,J. Chem. Phys. 38, 890 (1963).Google Scholar
  31. 31.
    J. Polgar, Unpublished B.A. Thesis, Amherst College (1965).Google Scholar
  32. 32.
    R. F. Weiss,Science 168, 247 (1969).Google Scholar
  33. 33.
    P. Kroopnick and H. Craig,Science 175, 54 (1972).Google Scholar
  34. 34.
    J. Muccitelli and W.-Y. Wen,J. Solution Chem. 7, 257 (1978).Google Scholar
  35. 35.
    T. E. Crozier and S. Yamamoto,J. Chem. Eng. Data 19, 242 (1974).Google Scholar
  36. 36.
    P. H. Bigg,Br. J. Appl. Phys. 15, 1111 (1964).Google Scholar
  37. 37.
    J. M. H. L. Sengers, M. Klein, and J. S. Gallagher, inAmerican Institute of Physics Handbook, 3rd edn., D. E. Gray, coordinating editor; M. W. Zemansky, Section 4 editor (McGraw-Hill Book Co., New York, 1972).Google Scholar
  38. 38.
    D. L. Hammond, C. A. Adams, and P. Schmidt,Trans. Instrum. Soc. Am. 4, 349 (1965).Google Scholar
  39. 39.
    B. B. Benson and D. Krause, Jr.,Rev. Sci. Instrum. 45, 1499 (1974).Google Scholar
  40. 40.
    A. O. Nier,Rev. Sci. Instrum. 18, 398 (1947).Google Scholar
  41. 41.
    C. R. McKinney, J. M. McCrea, S. Epstein, H. A. Allen, and H. C. Urey,Rev. Sci. Instrum. 21, 724 (1950).Google Scholar
  42. 42.
    K. B. Wiberg,Computer Programming for Chemists, (Benjamin, New York, 1965).2 Google Scholar
  43. 43.
    F. S. Feates and D. J. G. Ives,J. Chem. Soc., 2798 (1954).Google Scholar
  44. 44.
    D. J. G. Ives and P. D. Marsden,J. Chem. Soc., 649 (1965).Google Scholar
  45. 45.
    R. A. Pierotti,J. Phys. Chem. 69, 281 (1965).Google Scholar
  46. 46.
    E. F. Stephan, N. S. Hatfield, R. S. Peoples, and H. A. H. Pray, USAEC BMI-1067 (1956).Google Scholar
  47. 47.
    J. Bigeleisen,J. Chem. Phys. 34, 1485 (1961).Google Scholar
  48. 48.
    R. D. Bardo and M. Wolfsberg,J. Phys. Chem. 80, 1068 (1976).Google Scholar
  49. 49.
    J. H. Rolston, J. den Hartog, and J. P. Butler,J. Phys. Chem. 80, 1064 (1976).Google Scholar
  50. 50.
    W. A. Van Hook and J. T. Phillips,J. Phys. Chem. 70, 1515 (1966).Google Scholar
  51. 51.
    E. J. Green, Ph.D. Thesis, Massachusetts Institute of Technology (1965).Google Scholar
  52. 52.
    J. P. Jacobsen,Middelelser fra Kommisionen for Havundersogelser, Serie Hydrografi, Bind 1, No. 8, Copenhagen.Google Scholar
  53. 53.
    W. E. Adeney and H. G. Becker,Philos. Mag. 38, 317 (1919).Google Scholar
  54. 54.
    T. Carlson,J. Chim. Phys. 9, 228 (1911).Google Scholar

Copyright information

© Plenum Publishing Corporation 1979

Authors and Affiliations

  • Bruce B. Benson
    • 1
  • Daniel KrauseJr.
    • 1
  • Mark A. Peterson
    • 1
  1. 1.Department of PhysicsAmherst CollegeAmherst

Personalised recommendations