1064
J. H.
Rolston, J. den Hartog, and J. P. Butler
The Deuterium Isotope Separation Factor between Hydrogen and Liquid Water? J. H. Rolston,. J. den Hartog, and J.
P. Butler
Atomic Energy of Canada Limited, Chalk River Nuclear Laboratories, Chalk River, Ontario. Canada KOJ IJO
(Received July 26, 1975)
Publication costs assisted by Atomic Energy of Canada Limited
The overall deuterium isotope separation factor between hydrogen and liquid water, a , has been measured directly for the first time between 280 and 370 K. The data are in good agreement with values of a calculated from literature data on the equilibrium constant for isotopic exchange between hydrogen and water vapor, K1, and the liquid-vapor separation factor, av. The temperature dependence of a over the range 273-473 K based upon these new experimental results and existing literature data is given by the equation In a = -0.2143 (368.9IT) (27 870/T2). Measurements on av given in the literature have been surveyed and the results are summarized over the same temperature range by the equation In (YV = 0.0592 - (80.3/T) (25 490/T2).
+
+
+
Introduction A precise knowledge of the equilibrium distribution of deuterium between hydrogen and liquid water is required for the economic evaluation of heavy water production processes involving exchange of isotopes between hydrogen and liquid water. This distribution has not previously been measured directly but has been calculated from gas phase exchange data and the isotopic fractionation between vapor and liquid water. At low deuterium levels the isotope distribution in the gas phase is given by the equilibrium constant, K1, for the exchange reaction
+
+
H ~ O ( V ) HD HDO(V) H2 (1) Early determinations of K1, involving equilibration over a variety of noble and base metal catalysts, show considerable scatter but in general support the values calculated from statistical mechanics.l Examination of the data on K1 reported by Kirshenbaum’ together with those of Cerrai et a1.2and Suess3shows there are very few data available below 323 K; a fact which has been noted by Weston4 and by Wolfsberg.5 Furthermore, below 373 K, the agreement with theory is rather poor and both authors have suggested that refined measurements of K1 should be attempted in the low temperature range. Such a study would appear opportune in view of the recent advances in the theoretical calculation of isotope exchange equilibrium constants which have followed from the rediscovery6of Go, an isotope and quantum number-dependent term in the expression for the vibrational energy of a molecule in its rotational ground state. With this modification, most of the controversy concerning corrections for anharmonicity effects appears to have been r e ~ o l v e dPreviously .~ Bottinga8 reported an anharmonicity correctionto K1 as large as -16.1% at 298 K while Wolfsberg5has shown that the corrections are only - 10.8%of the value calculated under the usual harmonic approximation. Furthermore, Wolfsberg has demonstrated that these corrections are partially off-set by the incorporation of Go into the partition functions and lead to revised theoretical values of K1 numerically identical with those calculated 32 years ago and reported by Kirshenbaum et a1.l More recently, isotope partition function ratios for selected simple molecules have been evaluated from molecular potential function^.^ These functions are independent of the + A.E.C.L.4412. The Journal of Physical Chemistry, Voi. SO,No. 10, 1976
isotopic mass within the Born-Oppenheimer (BO) approximation and together with equilibrium geometries evaluated from spectroscopic studies provide an alternative approach to the evaluation of isotopic equilibrium constants. This method is gaining general acceptance as it does not rely directly on the measured values of vibrational frequenciesin the determination of the partition functions. In the next paper Bardo and WolfsberglO have calculated values of K1 by this procedure and have compared their results with the experimental data presented here. The theoretical curve of the equilibrium constant as a function of temperature agrees with the experimental curve within 0.5% in the temperature range 273-473 K. The general paucity of low temperature data on K1 and the less than satisfactory agreement between theory and experiment reduced our confidence in being able to predict the value of the equilibrium constant, K2, for the gas-liquid exchange reaction H20(1) HD + HDO(1) H2 (2) over an extended range of temperature. At low deuterium levels K2 can be calculated by multiplying K1 by the separation factor for isotopic distillation, av. The more straightforward approach, reported below, is to measure Kz directly and to avoid the additional work and uncertainties in measuring K1 and av separately.
+
+
Experimental Section (1) Apparatus. The equilibration cell used was fabricated from a 50-ml round-bottom flask as shown in Figure 1. The solid glass barrel of the Young valve (J.Young Co. Ltd., Acton, England) was lengthened by a 4 cm length of glass rod which served to compress a silicone rubber tip against a 13-pm diameter hole in.the wall of the reaction flask. The “pinhole” leak was created by sealing a 13-pm diameter tungsten wire in the glass wall, grinding the outside surface flat and removing the metal by applying a discharge from a Tesla coil through the wire to a ground. The length of the leak was kept to the thickness of the wall and thus minimized the dead space available during sampling., A stainless steel bellows was used to connect the Young valve to a series of spirally wound vapor traps which were kept partially immersed in liquid N2. (2) Procedure. A novel catalyst suitable for equilibrating hydrogen with liquid water was prepared by impregnating a
I
1065
Deuterium Isotope Separation Factor
so that given the mass 2 peak height, Pht(2),the H3+ correcGLUSS WOOL
%
S S BELLOWS
WBTER VPPOUR TRM
M O D I F I E D YOUNG
S I L I C O N E RUBBER
'\a 5 0 ML PYREX BULB
"PINHOLE" LEUK
\
MUGNET
Figure 1. Schematic drawing of hydrogen-liquid water isotope equilibration cell.
3-mm thick porous Teflon sheetll with an acetone solution of chloroplatinic acid, evaporating the solvent, and reducing the acidic deposits at 473 K under hydrogen.12 The impregnated sheet was cut into 3-mm cubes,weighed, and loaded into the equilibration flask. The flask and catalyst were rinsed with a stock solution of deuterium enriched water (atom ratio, D/H = 19 564 X and evacuated to dryness. A fresh 5-ml sample of deuterium enriched water was transferred to the flask and degassed by three freeze-pump-thaw cycles, using liquid nitrogen. The degassed water and catalyst were frozen and the flask was pressurized with 0.1450 MPa of purified hydrogen (DIH = 9681 X The flask was placed in a thermostatted bath controlled to f0.005 K and cell temperatures were measured with a calibrated thermometer to fO.O1 K. The solution and floating catalyst cubes were continuously agitated by a magnetic stirrer mounted below the cell. After allowing time for temperature equilibration, gas samples for mass spectrometric analysis were taken from the exchange cell a t intervals of 30 min. (3) Mass Spectrometry. The hydrogen samples were analyzed on a Consolidated Electronics Corp. spectrometer Model CEC 21-614. To ensure reliable and reproducible results the inlet gas pressure was carefully controlled and provision was made for analysis of standard samples under conditions nearly identical with those prevailing at the time of the equilibration experiments.The spectrometer was operated with high input sensitivity (low input pressures). During each analysis masses 2 and 3 were scanned consecutivelyand both peak heights were measured 2.0 min after introduction of the sample, by linear extrapolation of the peak heights. A correction curve for H3+ was constructed by measuring a hydrogen sample with a low deuterium concentration (D/H = 10 x 10-9 over an extended range of inlet pressures and filament currents. These data were fitted to an equation of the form A3 = A.Pht(2) B.Pht(2)' (3)
+
tion to the mass 3 peak, &, could be accurately calculated. For inlet pressures of 0.6 Pa the hydrogen background and H3+ correction were less than 0.5 and 1% of the mass 2 and mass 3 peak heights, respectively, when measured against a hydrogen sample with an atom ratio D/H = 5000 X (4) Standards. Hydrogen standards of varying deuterium contents were prepared by total decomposition of deuterium enriched water over uranium metal at 873 K. These were used to establish the sensitivity factor, f , of the spectrometer for the Hz and HD species and to show that this ratio was independent of the deuterium concentration over the range expected for samples from the reaction cell. Analysis of each hydrogen sample taken from the exchange cell was followed by an analysis of a hydrogen standard attached above the spiral trap so as to avert errors due to drifting of the spectrometer sensitivity with time. ( 5 ) Calculations. The determination of the separation factor between two chemical species such as hydrogen and water generally requires simultaneous analysis of both qomponents under conditions which do not disturb the isotopic equilibrium. This procedure can be simplified when there is a large molar excess of one component relative to the other so that the deuterium content of the major component is not substantially altered.13 In the present instance the use of an excess of liquid water ensures this condition. Liquid water was transferred from a reservoir of known isotopic content and frozen in the cell before hydrogen was added. Thus initially the reactor cell contained no water vapor or dissolved hydrogen. Provided the quantities of hydrogen and water vapor removed from the cell in the course of the experiments are negligible, a deuterium balance between the phases can be applied. Hence the deuterium atom fraction of the liquid at equilibrium, F L ~can , be evaluated from
+
F L ~ N =L F~ L ~ N L ~F H ~ N H F~ H ~ N H ~ - FveNve - F D ~ N D( ~4 ) in which F denotes the deuterium atom fraction and N the number of moles of each component. The superscripts i and e refer respectively to the initial charges to the cell and to the values at equilibrium and the subscripts L, V,H, and D refer to liquid water, water vapor, gaseous hydrogen, and dissolved hydrogen, respectively. Application of mass balances over the chemical species simplifies eq 4 to
+ + R ( F H -~ F H ~ )
F L =~ F L ' ( ~ S )
- SFve + & F H " (-~ CYD)
(5) where R denotes the mole ratio of the initially added hydrogen to liquid water at equilibrium and S is the mole ratio of vapor to liquid water a t equilibrium. The deuterium separation factor between dissolved and gaseous hydrogen, CYD,is given, at low concentrations, by the ratio FDe/FHe and Q is the equilibrium mole ratio of dissolved hydrogen to liquid at each temperature. Typically, Q is 1.5 X and CYDis not expected to exceed 1.1 at any temperature above 273 KT5 hence the last term in eq 5 is lo-% of the first term in the expression and can therefore be neglected. If it is further assumed that Fve/ F L can ~ be equated to q 7 - l where
then the equilibrium atom fraction of the liquid can be calculated from F L ' ( ~ S ) R ( F H~F H ~ ) F L ~ (7) 1 + Sav-1
+ +
The Journal of Physical Chemistry, Vol. 80, No. IO, 1976
J. H. Rolston, J. den Hartog, and J. P. Butler
1066
It should be noted that F L is~ essentially equal to FL' plus a small correction. The correction is about 0.2% because the molar ratios of hydrogen and water vapor to liquid water are gmall (typically 0.008 and 0.005, respectively) and the initial deuterium concentration of the hydrogen was not too different from the equilibrium values at each temperature. Thus an error in the fractionation factor between liquid water and water vapor or in the relative amounts of gas to liquid will have little effect on the calculated value of F L ~ . Results and Discussion At low deuterium concentrations the isotopic separation factor, a, between hydrogen and liquid water is defined in terms of the atom fractions of deuterium to protium in the liquid water, F L ~and , in the hydrogen gas, F H ~a t, equilibrium, by the equation F ~ e (1F H ~ ) (1 - F L ~ ) F H ~ The atom fraction of deuterium present in the liquid at equilibrium at each temperature was calculatedfrom eq 7. The results from two runs with initial deuterium contents of FL' = 19 964 X and 34 626 X are listed in Table I. These data are compared in Figure 2 with the product of vapor phase measurements of K1 made by Cerrai et aL2and Suess3and the vapor liquid separation factor, av (eq 10). With the exception of the two data points of Cerrai et al. at 332 and 337 K the agreement between the two independent methods of determining the overall separation factor (Y is excellent. On the strength of the more numerous data collected in the present study the two points mentioned above were excluded and the remaining data points were fitted by a weighted linear leastsquares regression for one dependent variable14to a=
In a = -0.2143
368.9 + 27 870 +T T2
in which T is the absolute temperature. Weights for the individual dependent variables, In ai, were set equal to ai2 divided by the variance of ai. The standard deviations of the ai were assumed to be constant a t 0.04 through the range of temperatures studied. Our measurements of the separation factor, a , depend primarily on the initial deuterium content of the liquid water, F L ~and , the deuterium content of the hydorgen gas at equilibrium, F H ~The . liquid was prepared by gravimetricdilutions of 99.80% D20 and its deuterium concentration has an estimated error of f0.1%. The deuterium atom fraction of the hydrogen gas depends primarily on the peak height ratio of mass 2 and 3, the sensitivity factor, f , and the accuracy of the hydrogen standards. An error of f0.5% is estimated for each of these determinations. Assuming all these errors to be random, the overall accuracy of a is estimated as f1.0%. This estimate of the error is reasonable since this is approximately equal to the standard deviation of f1.296 of the five values given in Table I at 333.9 K. The standard deviation in In a obtained from the residual variance in the weighted leastsquares fitting of eq 9 is 0.013 units which corresponds to a f1.3% error in a. As mentioned in the Introduction, it is possible to extract values of K1 from measurements of the overall separation factor, a, between hydrogen and liquid water if allowance is made for the vapor-liquid fractionation. The necessary fractionation factors, av, for temperatures up to 473 K were obtained from the data of Van Hook et al.l5 below 373 K and by the application of the relation, a = (PHzO/PDz0)0'524, sugThe Journal of Physical ChernMry, Vol. 80. No.
IO, 1976
TABLE I: Temperature Dependence of Isotope Separation Factor, a Deuterium atom fractions Temp, K
106F~e
106F1,~
Separation factor (a)
280.03 295.40 295.40 313.14 333.92 333.92 333.92 354.62 305.35 305.35 313.99 330.17 291.25 286.00 323.47 367.91
4 612 5 213 5 173 5 648 6 399 6 389 6 475 7 130 5 563 5 503 5 810 6 251 5 132 4 900 6 084 7 504
20 005 20 000 20 000 19 997 19 992 19 992 19 992 19 988 19 999 19 999 19 997 19 993 20 002 20 003 19 995 19 985
4.349 3.894 3.925 3.592 3.168 3.173 3.130 2.840 3.648 3.688 3.492 3.243 3.916 4.145 3.333 2.697
279.70 279.70 292.39 292.39 292.39 296.95 296.95 304.02 304.02 313.37 313.37 324.46 324.46 333.88 333.88 344.45 344.45 355.28 364.23 364.23 288.00 288.00
8 290 a 364 8 891 9 069 8 999 9 379 9 619 9 734 9 674 10 073 10 094 10 a99 10 894 11 453 11448 11938 11788 12 498 13 116 12-763 8 639 8 a34
34 641 34 641 34 633 34 633 34 633 34 630 34 630 34 626 34 626 34 620 34 620 34 614 34 614 34 609 34 609 34 604 34 604 34 598 34 593 34 593 34 637 34 637
4.293 4.251 3.999 3.920 3.951 3.789 3.693 3.649 3.672 3.524 3.517 3.255 3.255 3.094 3.094 2.967 3.005 2.832 2.696 2.772 4.117 4.026
--tl p?
0 !-
u
4 LL
z D 13
4 +
p:
4 k
m w
I 250
I
300
350
900
'450
1 500
TEMPERATURE ( K )
Figure 2. Dependence of hydrogen-liquid water separation factor (Y upon temperature: (0)data from run A; (0)data from run B; data of Cerrai et ai. ( 0 )and of Suess (+) multiplied by av from eq 10.
1067
Deuterium Isotope Separation Factor
gested by Van Hook,lGto the vapor pressure data above 373 K summarized by Wha1ley.l' The exponent is larger than . 0.500 predicted on the assumption of the rule of the geometric mean18formulated from the suggestion of Lewis and Cornish19 that the vapor pressure of a mixed isotope molecule such as HDO could be calculated as the square root of the product of the vapor pressures of the isotopically pure species. However, it is necessary to use the higher power dependence of the vapor pressure ratio to bring consistencybetween the data on vapor pressure isotope effects (VPIE)reported by Van Hook et al.15 and the direct measurements of Majoube20and Merlivat et a1.21 Similar deviations from the law of the mean are noted22 in the equilibrium constant for isotopic self-exchange in water. The combined data were fitted by a weighted least-squares regression to 80.3 + 25 490 In orv = 0.0592 - - T T2 The standard deviation in In av as estimated from the residual variance is 0.0003 units corresponding to 0.03% in av. However, the uncertainty in the magnitude of the exponent 0.524 required to bring consistency between the VPIE data of Van Hook et al. and the direct measurements of Majoube and Merlivat et al. raises the error in av to fO.l%. Values of the vapor-liquid separation factor av calculated from this equation over the temperature range 273-473 K differ by less than +0.1% from those calculated from the three appropriate equations recently published by Van Hook.23 The hydrogen-water vapor equilibrium constant, K1, is equal to alav, so that by combining eq 9 and 10, K1 as a function of temperature is given by In K1 = -0.2735
449 2
+T
+
2380 -
T2
Values of K1 at three temperatures calculated from eq 11are listed in Table 11. Also tabulated are theoretical values calculated by Wolfsberg5 and Bottinga8 under the harmonic approximation together with those calculated with the inclusion of Go.5 The value of K1 calculated by Bottinga a t 298 K is 18%larger than the experimental value obtained in this study. As discussed by Bardo and WolfsberglO in the accompanying paper this large discrepancy arises through the neglect of Go and to the direct use of spectroscopic data in the evaluation of the partition function ratios. Better agreement (1.9-2.5%) is shown between the experimental values and those calculated5 with the Go correction. This can be compared with agreement of better than 1%claimed22for the NH3-HD exchange. Values of K1 calculated by Bardo and Wolfsberglo in the next paper within the framework of the BO approximation likewise show a positive deviation from our experimental values. However, refinements of their theoretical procedures to account for the inexactness of the BO approximation give theoretical values of the equilibrium constant as a function of temperature which are in excellent agreement with our
TABLE 11: Comparison of Values of Kl with Theory Values of K1 Harmonic Temp, K
This work
Ref 8
Ref 5
Go coir ref 5
298 348 373
3.53 2.82 2.58
4.17
3.86 3.04
3.62 2.88 2.63
2.77
experimental least-squares curve obtained between 273 and 473 K. Over the entire temperature range the experimental values are only 0.5% lower than the theoretical values. Such agreement between experiment and theory for values of K1 in the low temperature range reported here supports the validity of our expression for calculating a to a nominal accuracy of 1%.
Acknowledgment. We wish to thank the following CRNL staff for assistance in this study: M. Hammerli and W. J. Olmstead for the preparation of hydrogen standards of known isotopic abundance and J. G. Wesanko for fabrication of the exchange cell. In addition we wish to express our thanks to Professor Wolfsberg for communicating to us his interest in this study prior to publication. References and Notes I. Kirshenbaum, H. C. Urey, and G. M. Murphy, Ed., "Physical Properties and Analysis of Heavy Water", McGraw-Hili, New York, N.Y., 1951 p 46. E. Cerrai, C. Marchetti, R. Renzoni, L. Roseo, M. Silvestri, and S. Villani, Chem. Eng. Prog. Ser., 50, No. 11, 271 (1954). H. E. Suess, Z.Naturforsch. A, 4, 328 (1949). R. E. Weston, Jr., J. Chem. Phys., 42, 2635 (1965). M. Wolfsberg, J. Chem. Phys., 50, 1484 (1969). M. Wolfsberg, Adv. Chem. Ser., No. 89, 185 (1969). J. Bigeleisen, M. W. Lee, and F. Mandel, Ann. Rev. Phys. Chern., 24, 407 (1973). Y. Bottinga, J. Phys. Chem., 72, 4338 (1968). J. Bron, C. F. Chang, and M. Wolfsberg, Z.Naturforsch. A, 28, 129 (1973). R. D. Bardo and M. Wolfsberg, J. phys. Chem., following paper in this issue. Original sample obtained from Cadillac Plastics, similar material is presently available from Fluoro Plastics Inc.. Phlladelphia, Pa. J. H. Rolston, W. H. Stevens, J. P. Butler, and J. den Hartog, Canadian Patent No. 941 134 (1974). J. Ravoire, P. Grandcollot, and G. Dirian, J. Chim. Phys., 60, 130 (1963). D. M. Himmeiblau, "Process Analysis by Statistical Methods", Wiley, New York, N.Y., 1970, p 114. J. Pupezln, G. Jakli, G. Jansco, and W. A. Van Hook, J. Phys. Chem., 76, 743 (1972). W. A. Van Hook, J. Phys. Chem., 76, 3040 (1972). E. Whaliey, Proc. Jt. Conf. Thermodyn. Transp. Prop. fluids, 1957, 15, (1958). J. Bigelseisen, J. Chem. Phys., 23, 2264 (1955). G. N. Lewis and R. E. Cornish, J. Am. Chem. SOC.,55,2616 (1933). M. Majoube, J. Chirn. Phys., Physiochim. Biol., 68, 1423 (1971). L. Merlivat, R. Botter, and G. Nief, J. Chim. Phys., 60, 56 (1963). J. W. Pyper and L. D. Christensen, J. Chem. Phys., 62, 2596 (1975). G. Jansco and W. A. Van Hook, Chem. Rev., 74,689 (1974). E. A. Symons and E. Buncel, Can. J. Chem., 51, 1673 (1973). A value of o 1 = ~ 1.02 can be calculated b applying the mean law to the solubility of H2 and D2 in water at 298 K?:
The Journal of Physical Chemistry, Vol. 80, No. IO, 1976
