W. ALEXANDER VANHOOK
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Vapor Pressures of the Isotopic Waters and Ices
by W. Alexander Van Hook Chemistry Department, University of Tennessee, Krwzville, Tennessee 9701 6
(Received September 16, 1067)
A detailed application of the theory of isotope effects in condensed systems is made to the various D, T, 017, and 0 1 8 vapor pressure isotope effects (VPIE) for liquid and solid water between 230 and 400°K. Force fields for the liquid and solid are developed which quantitatively correlate the VPIE’s for the 18 different isotopic isomers of water over this temperature range. The general precision of the agreement between calculated and observed results (where available) is excellent. Some limitations on the calculation are pointed out. Finally, nonideality in HzO, HDO, and DzO solutions is discussed.
Introduction The vapor pressure isotope effects (VPIE) displayed by the isotopic waters and ices are a matter of considerable interest from both a theoretical and a practical point of view. I n the present paper our interest lies in making a straightforward application of the theory of isotope effects in condensed systems’ to water. The results should prove to be of somewhat broader application, however, in view of the considerable geochemical interest in the natural isotopic fractionation processes of water2 as well as because of the interest in isotopic separation by distillation technique^.^ The general interest in this problem then and the success of our cell model calculations of the H-D vapor pressure isotope effects for several hydrocarbon systems4 led us to apply the model to the very complicated condensed phases of water. Most of the data on the VPIE’s of the isotopic waters and ices which are available in the literature are plotted as the points in Figure 1. The lines are calculated and discussed below. The isotope effects are normal for all species below about 450°K. At or around that temperature they undergo a crossover and become inverse. Our own calculations are limited to temperatures below 130” (PH,o 3 atm) because at higher temperatures the corrections for gas imperfection, etc., become large. Around 130” the VPIE is only about 2% for DOD; this increases an order of magnitude to 20% at the melting point and in ice all the way to 40% at -35”. The magnitude of the low-temperature effects and the temperature coefficients of the effects are truly large. This is, of course, a consequence of the hydrogen bonding in the condensed phases. The data in Figure 1 include (for the ices) that of Jones5 on TzO, of Kiss, Jaltly, and Illy6 and Matsuo, Kuniyoshi, and Miyake7 on D20, and of Merlivat and Niefs on HDO, and (for the waters) that of Jones5 on TzO and DzO, of Popov and Tazetdinove on TzO, of Combs, Googin, and Smithlo on DzO and of Smith and Fitch,” Avinur and Nir,12 and Zel’vinski, Shalygin, Tatrainskii, and Nikolaev13 on HOT, of Merlivat, Botter, and Nief14 on HDO, of Kiss, Jakly, and Illy,“
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The Journal of Physical Chemistry
and Whalleyls (smoothed from earlier workers) on D20, of Dostrovsky and R a v W on Hz0l8, and of Szapiro and Steckel” on H2018and HzO17.
The Model The theory of the vapor pressure isotope effect has been formulated by Bigeleisen.’ The result may be expressed in general terms as
1
-(PfY’ RT
- P V ) + {(BOP + 1/2COP2) (Bop
+ ‘ / Z C P ) ~-] G ( u , u’)
(1) I n this equation P f / P is the VPIE (the prime by con(1) J. Bigeleisen, J. Chem. Phys., 34, 1485 (1961). (2) See for example: E. Roth, J . Chim. Phys., 60, 339 (1963); R. Weston, Geochim. Cosmochim. Acta, 8 , 281 (1955). (3) See for example: T. F. Johns in “Separation of Isotopes,” H. London, Ed., George Newnes, Ltd., London, 1961, pp 41-94; R. Casini, Proc. Intern. Symp. Isotope Separation, Amsterdam, 1967, 368 (1958). (4) (a) W. A. Van Hook, J . Chem. Phys., 44, 234 (1966); 46, 1907 (1966); J . Phys. Chem., 71, 3271 (1967); (b) M. J. Stern, W. A . Van Hook, and M. Wolfsberg, J. Chem. Phys., 39, 3179 (1963). (5) W.M. Jones, LADC 6905 (1964). (6) I. Kiss, G . Jakly, and H. Illy, Acta Chim. Acad. Sci. Hung., 47, 379 (1966). (7) S. Matsuo, H. Kuniyoshi, and Y . Miyake, Science, 145, 1454 (1964). (8) L. ,Merlivat and G. Neif, Tellus, 19, 122 (1967). (9) M. M.Popov and F. I. Tasetdinov, At. Energ. (U.S.S.R.), 8,420 (1960). (10) R. L. Combs, J. M . Googin, and H. A. Smith, J . Phgs. Chem., 58, 1000 (1954). (11) H.A. Smith and K. R. Fitch, ibid.,67, 920 (1963). (12) P. Avinur and A. Nir, Nature, 188, 652 (1960). (13) Y. A. Zel’venski, V. A. Shalygin, V. S. Tatarinskii, and D. A. Nikolaev, At. Energ. (U.S.S.R.), 18, 56 (1965). (14) L. Merlivat, R. Botter, and G. Neif, J . Chim. Phys., 60, 56 (1963). (15) E. Whalley, “Proceedings of the Joint Conference on the Thermodynamic and Transport Properties of Fluids, 1957,”Institute of Mechanical Engineering, London, 1958,pp 15-26. (16) I. Dostrovsky and A. Raviv, Proc. Intern. S y m p . Isotope Separation, Amsterdam, 1967, 336 (1958). (17) S. Szapiro and F. Steckel, Trans. Faraday Soc., 63, 883 (1967).
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VAPORPRESSURES OF THE ISOTOPIC WATERSAND ICES
Figure 1. Vapor pressure isotope effects of isotopic waters and ices. On the left, waters; on the right, ices. The lines are calculated: waters, see Tables I and VI (column I); ices: solid, see Tables I and V; dotted, see text. The points are experimental: Ices: TOT, f , Jones;b DOD, A, Kiss, Jakly, and 1lly;B 0, Mahuo, Kuniyoshi, and Miyake;? HOD, 0, Merlivat and Nief.* Waters: TOT, 0, Jones;6 0 , Papov and Tazetdinov;e DOD, 0, Jones;b 0,Combs, Googin, and Smith;Io X, Kiss, Jakly, and Illy;8 0, Whalley;16 HOT, A, Smith and Fitch;LL 0, Avinur and Nir;'? X, Zel'vinski, Shalygin, Tatarinskii, and Nikolaev;l* HOD, 0, Merlivat, Botter, and Nief;" H,Ol*, 9, Dostrovsky and Raviv;IS A, Seapiro and Steckel;" N2O1', A, Szapiro and Steckel.17
vention refers to the lighter isotope), and (s/s')fc and (s/s')fg are the reduced partition functions for the condensed and gaseous phases introduced by Bigeleisen and Mayer.18 The last three terms correct for the isotope effect on molar volume of the condensed phase, for the effect of gas imperfection, and for nonclassical rotation in the gas phase. This last term may be neglected at the high temperatures (T 3 23OOK) of our calculation. We shall see that the other two terms are also negligibly small over the temperature range of the calculation. They are needed in the general formulation because the vapor pressures of the two (sepa-
rated) isomers are being compared a t the same temperature but at different pressures and molar volumes. The correction for the molar volume isotope effect is easily evaluated, at least for DzO, from the data cited in the review by Whalley.'5 The correction is completely negligible (
