J . Phys. Chem. 1984, 88, 823-825
823
Measurement of the Isotope Fractionation Associated with Diffusion of Carbon Dioxide in Aqueous Solution Marion H. O'Leary' Departments of Chemistry and Biochemistry, University of Wisconsin, Madison. Wisconsin 53706 (Received: May 5, 1983; In Final Form: July 25, 1983)
An isotope ratio method has been developed which permits measurement of the isotope fractionation associated with diffusion of solutes in solution. Diffusion is conducted in a diaphragm cell of the type usually used for tracer diffusion measurements. The difference in isotopic composition of the solute before and after the diffusion process is measured by means of an isotope ratio mass spectrometer. This difference is then used to calculate the ratio of diffusion coefficients for the two isotopic species. By this method the isotope fractionation associated with diffusion of C 0 2 dissolved in water has been found to be D(12C0,)/D(13C02) = 1.0007 & 0.0002 at 25 OC. The same series of experiments also produced a value of 1.001I for the ratio of solubilities of I2CO2and I3CO2in water at 30 "C, in excellent agreement with the published value.
Introduction The changes in chemical2and physicalH properties which result from isotopic substitution provide a subtle and sensitive probe of molecular dynamics. Because potential functions are invariant with isotopic substitution within the limitation of the Born-Oppenheimer approximation, many factors that are important but poorly known in comparisons of different molecules can be neglected in comparisons of different isotopic species of the same molecule. Current theories of liquids are inadequate to answer with certainty the question of whether a small isotope fractionation is to be expected during diffusion of isotopic solute species in the liquid state.' If such an effect exists, it must certainly be quite small. Existing measurements of isotope fractionation during tracer diffusion in the liquid state also fail to give an unambiguous answer to this question. The best measurements of diffusion coefficients by radiochemical techniques generally are capable of giving a precision of a few tenths of one percent. Unfortunately, this is the approximate magnitude which might be expected for an isotope effect on a tracer diffusion coefficient. Harris and Mills8 failed to find an isotope fractionation during the diffusion of benzene and benzened, in octamethylcyclotetrasiloxaneor for cyclohexane and cyclohexane-d,, in the same solvent. Freer and Sherwood9~lo have used 14C-3Hdouble labeling in a diaphragm cell and in gels to measure the isotope fractionation associated with diffusion of organic molecules in several solvents. Fractionations of up to 1% have been observed in some circumstances, but the overlap of the radioactive p spectra for I4C and 3H makes the method subject to significant uncertainty. Except in the case of the isotopes of hydrogen, isotopic differences in properties are small, seldom exceeding 1% for physical properties and 5% for chemical properties. Techniques for the measurement of isotopic differences in properties are generally not the same as those used for measurement of the properties themselves. The most sensitive method for determination of isotope fractionations in chemical and physical processes is generally the (1) Address correspondence to Department of Chemistry, University of Wisconsin, 1101 University Avenue, Madison, WI 53706. (2) Melander, L.; Saunders, W. H. 'Reaction Rates of Isotopic Molecules"; Wiley-Interscience: New York, 1980. (3) Rock, P. A. 'Isotopes and Chemical Principles"; American Chemical Society: Washington, DC, 1975. (4) Buckingham, A. D.; Urland, W. Chem. Reu. 1975, 75, 113. (5) Jansco, G.;Van Hook, A. Chem. Reu. 1974, 74, 689. (6) Bigeleisen, J.; Lee,M. W.; Mandel, F. Annu. Rev.Phys. Chem. 1973, 24, 407. (7) Mills, R.; Harris, K. R. Chem. SOC.Rev. 1976, 5, 215. (8) Harris, K. R.; Mills, R. J. Phys. Chem. 1977, 81, 2191. (9) Freer, R.;Shenvood, J. N. J . Chem. Soc., Faraday Trans. 1 1980, 76, 1030. (10) Freer. R Sherwood, J. N. J. Phys. Chem. 1981, 85, 102, 907.
0022-3654/84/2088-0823$01 S O / O
isotope ratio method, in which the ratio of amounts of two isotopic species is monitored during the course of the reaction or process by means of an isotope ratio mass spectrometer. Such ratio methods have higher precision than direct methods which rely on separate measurements for different isotopic species. Measurements of isotopic ratios for isotopes of carbon, oxygen, nitrogen, and a variety of other elements can be made routinely with precision sufficient that under most circumstances the isotope ratio measurement contributes negligibly to the overall uncertainty in the fractionation measurement. Such methods are capable of measuring isotopic differences of 0.1% or less. The stable-isotope ratio method has not previously been applied to determination of isotopic fractionation during diffusion in the liquid phase. As noted above, an analogous radiochemical method has given seemingly contradictory results. We report here the details of the measurement of isotope fractionations in diffusion by the ratio method and the application of this method to diffusion of dissolved C 0 2 in water. Experimental Section Diaphragm Cell. Diffusion studies were carried out in a Stokes-type diaphragm cell of the usual design." All measurements were carried out at 25.00 f 0.02 OC. The cell had previously been calibrated by use of KC1. The nominal volume of each compartment was 50 mL. The diaphragm cell was filled with water that had been degassed by boiling and was then equilibrated to 25 OC. A sample of water was purged for 1 h at 30 "C with C 0 2 by using a fritted glass sparger, after which the solution was sealed and equilibrated at 25 OC. After both cell and C 0 2 solution were at 25 OC, about three-fourths of the contents of the top compartment of the diaphragm cell was removed, and nitrogen pressure was used to fill the top of the diaphragm cell with the C 0 2 solution. Following this procedure the C 0 2concentration in the top compartment was near 0.02 M. The cell was then closed and sealed. Simultaneously, a sample of the C02-saturated water used to fill the top compartment was taken for later isotopic analysis. Diffusion was allowed to proceed for 16-22 h (about 20% transfer), after which the top of the cell was opened and a sample of its contents was quickly taken. The top of the cell was then resealed, the cell was inverted, the bottom of the cell was opened, and sample was taken from the bottom compartment. Sampling Procedure. Elaborate precautions were taken in handling aqueous C 0 2 solutions in order to eliminate any isotopic changes resulting from losses of C 0 2 during transfers. Transfer and sampling procedures were designed to minimize contact with the atmosphere and thus to minimize possibilities for loss. The following procedure was used for removing samples of CO, so(1 l ) Mills, R.;Woolf, L. A. "The Diaphragm Cell"; Australian National University Press: Canberra, 1968.
0 1984 American Chemical Society
024
The Journal of Physical Chemistry, Vol. 88, No. 4, 1984
lutions for isotopic analysis: A 250-mL round-bottom flask equipped with a stopcock and a standard taper joint was evacuated. The flask was attached to the cell compartment, and the vacuum was used to draw 20-30 mL of the cell contents quickly into the flask. This flask was then attached to a vacuum line operated at below lo-' torr. The gaseous contents of the flask were pumped consecutively through a dry ice trap and a liquid-nitrogen trap. The CO, thus collected was distilled repeatedly to remove traces of water and was then subjected to an isotope ratio measurement. Control experiments conducted with CO, samples of known isotopic composition demonstrated that this procedure results in no fractionation of carbon isotopes. Mass Spectrometry. Isotope ratios were measured on a Micromass 602 dual-inlet isotope ratio mass spectrometer. Isotope ratios for both m / e 45/44 and m l e 46/44 were measured for each sample. The 46/44 ratio was found to be constant for all samples within f l % . The 46/44 ratios were used to correct the 45/44 ratios for the presence of I7Oin the 45 peak by the usual The standard used was the tank COz which was used for the diffusion measurements. This material had k e n calibrated against local standards and was found to have an isotopic composition S(13C) = -27.57% compared to the usual PDB standard.', Isotope ratios are reported as 6(13C) values defined by ~ ( 1 3 ~=)
103
[
Rsple
- Rstd
Rstd
]
OLeary coefficients of very high precision is ultimately desired, an uncertainty of up to 10% in this term is acceptable, as uncertainties in the denominator and numerator will largely compensate each other. Having calculated a value for the denominator term, we can use this value together with material balance conditions (involving the known volumes of the two cell compartments and the diaphragm) to calculate relative values for To,T, and B. These values are then used in the numerator, together with the three measured ratios. The ability to measure an accurate ratio of diffusion coefficients in an experiment such as this depends on the total range of R values compared to the uncertainty in the measurement of R; the smaller the range of R's, the more difficult it is to obtain an accurate diffusion coefficient ratio. Early in the diffusion process, RT = Ro, and RB is very different from them. As diffusion progresses, RT diverges from Ro, and ultimately R , and RB approach each other (becoming exactly equal when equilibrium is reached). The maximum difference of R values occurs near the beginning of the diffusion experiment. Thus, it is advantageous to stop the diffusion process at 5-20% transfer, rather than going to the 30% transfer that is more common in ordinary diaphragm cell experiments. However, this early stop creates a problem. The numerator of the left side of eq 5 can be rewritten as
where R is the calculated isotope ratio 13C02/12C02.
-= /3Dt
If the diffusion is stopped early, then the first ratio in this term is large and the second is quite small because TITo >> BITo. Since the first ratio contains R T / R orather than RB/Ro,the accuracy of the fractionation so calculated is likely to be poor. Thus, it is preferable to recast eq 5 into a form which relies less heavily on the comparison of RT with Ro. With use of a material balance condition on the R values, it is possible to eliminate R , from eq 5 and obtain
1 0' = PD't T ' - B'
where X = 1 i- vD/2vT (VDis the volume of the diaphragm, and VT is the volume of the top compartment of the diaphragm cell) and Q = T o / ( T- B ) . This is the best form of the equation for calculating the isotopic fractionation in diffusion. The value of the cell constant and the value of the diffusion coefficient for the species of interest are required for use in this equation. The best value of the diffusion coefficient for C 0 2 is cm-2 s-'.I3 considered to be 1.9 X
Theory The present conditions closely approximate the usual conditions for tracer diffusion. For a diaphragm cell in which only the top compartment initially contains the solute species, the diffusion coefficient is given by" TO T-B where To is the concentration in the top compartment at the beginning of the experiment, T is the concentration in the top compartment at time t, B is the concentration in the bottom compartment at time t, /3 is the cell constant, and D is the diffusion coefficient. When a second isotopic form of the same substance is present, its behavior can be described by a second equation of the same type, in which the primes indicate the heavier isotopic species: In
In
In the present situation, both isotopic species are at sufficiently low concentrations that the usual tracer diffusion conditions apply and their diffusion behaviors do not influence one another. We can then take the ratio of these two equations
(3) and this equation is true at any time. In an experiment of this type, the isotope ratios, R, which are measured are defined by Ro = To'/ To R , = T'/T RB = B'/B These measured ratios can be substituted in eq 3 to give
(4)
The denominator in eq 5 is obtained from the known diffusion coefficient of the species in question. Although a ratio of diffusion (12) Craig, H. Geochim. Cosmochim. Acta 1957, 12, 133.
Results Water was saturated with C 0 2 by purging with CO, from a tank for 1 h. Samples of this solution were taken, and the C 0 2 was purified for isotopic analysis. The ratio of solubilities of I2CO2 and I3CO2at 30 "C was calculated by comparison of the isotopic composition of the tank CO, with that of the dissolved CO,. The ratio of solubilities, S/S',was found to be 1.001 1 0.0001, in good agreement with the previously determined value of 1.00105 f 0.00004.14 The fact that the ratio is larger than unity indicates that I2CO2is slightly more soluble in water than is I3CO2. Data used to calculate the isotope fractionation in C 0 2diffusion, together with the calculated isotope fractionations, are summarized
*
(13) Duda, J. L.; Vrentas, J. S.AIChE J . 1968, 14, 286. Unves, A. A.; Himmelblau, D. M. J . Chem. Eng. Dura 1964, 9, 428. Davidson, J. F.; Cullen, E. J. Trans. Insf. Chem. Eng. 1957, 35, 51. Lohse, M.; Alper, E.; Quicker, G.; Deckwer, W.-D. AIChE J . 1981, 27, 626. Thomas, W. J.; Adams, M. J. Trans. Faraday SOC.1965, 61, 668. Clarke, J. K. A. Ind. Eng. Chem. Fundam. 1964, 3, 239. Scriven, L. E. Ph.D. Thesis, University of Delaware, Newark, 1956. Tang, Y. P.; Himmelblau, D. M. Chem. Eng. Sci. 1965, 20, 7. Vivian, J. E.; King, C. J. AIChE J . 1964, 10, 220. Woods, D. R. Ph.D Thesis, University of Wisconsin, Madison, 1961. Rhem, T. R.; Moll, A. J.; Babb, A. L. AIChE J . 1963, 9, 760. Ferrell, R.; Himmelblau, D. M. J . Chem. Eng. Dura 1967, 12, 1 1 1. (14) Vogel, J. C.; Grootes, P. M.; Mook, W. G . 2. Phys. 1970,230, 225.
Isotope Fractionation of Carbon Dioxide TABLE I : Determination of the Ratio of Diffusion Coefficients for ' T O , and '2C0, in H,O a t 25 "C
expt time, no, min
6 ('3C) valuesa
start
top
bottom
9 1218 -28.57 -28.59 -28.99 10 I 1 2 0 -28.69 -28.19 -29.13 11 1 0 0 8 -28.74 - 2 8 . 7 8 -29.43 12 1320 -28.73 -28.49 -29.29 1 3 1 2 7 8 -28.18 -28.28 -29.01 a 6("C)
D(12C0,)/D(13C0,) 1.00052 1.00054 1.00082 1.00072 1.00105 mean 1.00073 t 0.00022
values are reported relative to standard PDB.
in Table I. The best value of the diffusion coefficient ratio is D/D'= 1.0007 f 0.0002, with 12C02having the higher diffusion coefficient. Not shown in Table I are a number of earlier determinations of the fractionation which are of lower precision but which are in good agreement with the values shown in Table I.
Discussion Previous work has not answered with certainty the question of whether or not an isotope fractionation occurs during diffusion of tracer species in solution. The present work demonstrates that the ratio of diffusion coefficients for 12C02and I3CO2in water at 25 OC is 1.0007. This value is significantly different from unity but significantly smaller than the value predicted by most theoretical treatments (see below). It is clear from this value why previous measurements7-10 have not given consistent values for the isotopic fractionation associated with tracer diffusion-the isotopic difference is simply too small to be determined reliably by radiotracer methods. The isotope ratio method is probably the method of choice for measuring isotope fractionation during tracer diffusion in solution. The ratio method extends our ability to measure these isotopic differences by at least an order of magnitude. However, the ratio method will not be applicable to all situations. The necessary isotopic analyses can only be carried out on simple, volatile molecules such as C o t , CO, N2, H2, and CH3C1. Study of the diffusion of, for example, benzene by this method would necessitate conversion to a volatile form (probably C 0 2 for study of carbon isotopes or H2 for study of hydrogen isotopes) prior to isotopic analysis. Interestingly, the isotope fractionation accompanying C02 diffusion in water (1.0007) is smaller than the equilibrium fractionation accompanying the dissolution of C 0 2 in water (1.0011; this work and ref 14) and is slightly larger than the equilibrium fractionation between liquid C 0 2 and gaseous C 0 2 (1.0003 at 0 OC15). Comparison with Theory. For diffusion in the gas phase, theoretical treatments give an unambiguous answer as to the expected isotopic difference in diffusion coefficients. The Chapman-Enskog theory predicts that, for tracer diffusion, the ratio of isotopic diffusion coefficients will be equal to the square root of the ratio of reduced masses.16 For C 0 2 diffusing in air, this gives a value D I D f = 1.0044. Theoretical treatments of diffusion in the liquid phase give a less unambiguous a n ~ w e r .The ~ present study comes under the category of species of differing mass diffusing at low concentration in a reasonably uniform solvent. If the Chapman-Enskog treatment were valid, then we would predict a ratio of diffusion coefficients near DID' = 1.003; however, this treatment does not seem to be applicable to diffusion in the liquid phase.7 The isotopic difference measured in this study is almost an order of magnitude smaller than this prediction. (15) Grootes, P. M.; Mook, W. G.; Vogel, J. C. Z . Phys. 1969,221, 257. (16) Mason, E. A.; Marrero, T. R. Adu. At. Mol. Phys. 1970, 6, 155.
The Journal of Physical Chemistry, Vol. 88, No. 4, 1984 825 FriedmanI7 has analyzed the present type of system in terms of linear-response theory. His analysis indicates that there should be a negligible mass dependence in the diffusion of isotopic solute molecules. As there are approximations in his theory, one can say that it is roughly in accord with the results of the present study. Recently, Bearman and Jolly (unpublished; see also ref 18) have made iterative molecular dynamics calculations using LennardJones potentials with uniform spherical particles of the size of argon. Diffusion coefficients have been calculated for mixtures of varying masses and compositions. The calculated isotope fractionation in such a system depends not only on the isotopic mass difference but on the ratio of the mass of the tracer to the mass of the solvent as well. Although the extrapolation from argon as solvent to water as solvent is a long one, this approach is worth considering. Analogous calculation of isotopic fractionation for COz (mass 44 or 45) diffusing in water (mass 18) gives an isotope fractionation D I D f = 1.0016, which is slightly larger than the observed value of 1.0007, Increasing the mass of water as a way of accounting for the self-association of water improves the agreement: the use of 50 for the mass of water gives 1.0012; the use of 100 for the mass of water gives 1.0010. Implications for Plant Physiology. Plants fractionate carbon isotopes during the photosynthetic assimilation of CO2.I9 Although chemical processes clearly play a role in determining this isotope fractionation, gas-phase diffusion is also an important contributor.20 Although a possible role for liquid-phase diffusion has been s~ggested,'~Jthere has until now been no information concerning the magnitude of the isotope fractionation that is associated with liquid-phase diffusion. The isotope fractionation which is observed during photosynthetic assimilation of COz in plants is 10-30 times larger than the fractionation associated with liquid-phase diffusion of C 0 2 . The present results show that even if liquid-phase diffusion of CO, were slow, it would not give rise to a large fractionation of carbon isotopes. However, in such a case the diffusion step could partially mitigate the expression of isotope fractionations from other steps. Different organs within a single plant sometimes show different isotopic composition^.'^ For example, potato tubers are about 2% more positive than leaves.22 In Juniperus monosperma, wood is about 2% more positive than leaves.23 The possibility has been consideredz3that this isotopic difference might arise because of isotopic differences in diffusion rates of glucose or other metabolites. The present results make that possibility unlikely. The isotope fractionation associated with diffusion of C 0 2 in solution is only 0.7%0,and the fractionation occurring during the diffusion of glucose or other heavier molecules would be negligible.
Acknowledgment. I am grateful to Dr. R. Mills and the staff of the Diffusion Research Unit, Research School of Physical Sciences, Australian National University, Canberra, for hospitality, support, and advice during these studies. Isotope-ratio measurements were made by Zarko Roczandik of the Department of Environmental Biology, Research School of Biological Sciences, The Australian National University, Canberra. Financial support was provided by the John Simon Guggenheim Foundation, the University of Wisconsin Graduate School, and the Australian National University. Registry No. I3C, 14762-74-4; carbon dioxide, 124-38-9. ~~
~
~~
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(17) Friedman, H . L. in "Molecular Motions in Liquids"; Lascombe, J., Ed., Reidel: Dordrecht, Holland, 1974; p 87. (18) Jolly, D. L.; Bearman, R. J. Mol.Phys. 1980, 41, 137. (19) O'Leary, M. H. Phytochemistry 1981, 20, 553. (20) OLeary, M. H.; Osmond, C. B. Plmr Physiol. 1980, 66, 931. (21) Vogel, J. C. Sitzungsber. Heidelb. Akad. Wiss., Math.-Natunviss. Kl. 1980, 3, 111. (22) Troughton, J. H . "Proceedings of the International Congress on Radiocarbon"; The Royal Society of New Zealand: Wellington, 1972; p 420. (23) Leavitt, S. W.; Long, A. Nature (London) 1982, 298, 742.
