Negligible fractionation of Kr and Xe isotopes by molecular diffusion in water
Introduction
The inert noble gases and their isotopes have been established to trace physical processes in aquatic systems, e.g. the transport and exchange of solutes and fluids (Brennwald et al., 2013). Molecular diffusion in water is a key transport mechanism that plays an important role in aquatic systems and in particular in the sediments of lakes, rivers and oceans. Despite the great potential of noble gases and their isotopes to analyse diffusive transport in lacustrine sediments, the isotopic fractionation of noble gases diffusing through water has only be studied for He, Ne and Ar (Jähne et al., 1987; Tyroller et al., 2014). As a follow-up to our recent work on the diffusion of Ne and Ar isotopes in water (Tyroller et al., 2014), this paper assesses the possible fractionation of Kr and Xe isotopes by molecular diffusion in water. In general, the study used the same experimental set-up, analytical techniques, principles and equations as presented by Tyroller et al. (2014). The present study is motivated by the unexpected results of a computational simulation (Bourg and Sposito, 2008) and the aforementioned experimental study (Tyroller et al., 2014), both of which challenged the commonly held assumption that molecular diffusion in water results in a fractionation of noble gas isotope ratios according to the square root relation, that is also refereed to as Graham's Law (Graham, 1833). This relation is derived from the kinetic theory of gases (Moore, 1999) and can be written as (e.g. Richter et al., 2006): where and are the diffusion coefficients of the diffusing gases i and j, with their molecular mass and , respectively, and .
However, our previous study (Tyroller et al., 2014) found a different fractionation behaviour of Ne isotopes during molecular diffusion in water. Ar isotopes do fractionate as predicted by the square root relation, in contrast to Ne isotope fractionation, which was found to be much lower and which agreed to a reasonable extent with the results from molecular dynamics calculations (Bourg and Sposito, 2008). These molecular dynamics calculations simulate the diffusion of different noble gases and their isotopes in water on an atomic scale by applying a combination of chemical theories and classical, non-quantum–mechanical theories.
In order to explain the different behaviour of Ne and Ar isotope fractionation and to understand the fractionation behaviour of other noble gas isotopes as a results of molecular diffusion in water, this study aims to complete the experimental dataset on noble gases by assessing the fractionation behaviour of Kr and Xe. The fractionation of Kr (82Kr, 83Kr, 84Kr, 86Kr) and Xe (129Xe, 132Xe, 134Xe, 136Xe) isotopes was determined by directly measuring the relative differences of fluxes of isotopes through a diffusion column containing immobilised water. In addition, the elemental diffusion coefficients of Kr and Xe were determined with the same set-up in order to confirm the correct operation of the experiment.
Section snippets
Experimental setup
The method used to determine the possible fractionation of Kr and Xe isotopes closely follows the method described in our earlier work measuring the fractionation of Ne and Ar isotopes undergoing molecular diffusion in water (Jähne et al., 1987; Tyroller et al., 2014). In general, the same experimental set-up, analytical techniques, principles and equations were used, with the exception of a modification in sample processing which is discussed below in some detail.
The key constituent of the
Results
Fig. 3 shows the observed and the theoretical breakthrough curves of the test gas diffusing through the water cell (see Section 2.2) normalised to the steady state concentration of Kr and Xe. The observed and the fitted breakthrough curves agree with each other. As a by-product of the measurements, the elemental diffusion coefficients of Kr and Xe were estimated.
Table 2 summarises the results of the different replicate gas dilution experiments and analyses to determine the relative isotopic
Discussion
The good agreement of the observed and the fitted breakthrough curves of Kr and Xe (see Fig. 3) suggests that our diffusion experiment performed well. Furthermore, the calculated elemental diffusion coefficients for Kr and Xe agree with some of the previous results to a reasonable extent (see Table 3).
Our experimental data (Table 2) make the case that Kr and Xe isotopes do not significantly fractionate during molecular diffusion through liquid water. In addition our results reject the
Conclusions
We empirically quantified the elemental diffusion coefficients of Kr and Xe isotopes in water as well as the respective isotope fractionation in response to molecular diffusion in water. The estimated elemental diffusion coefficients of Kr ( m2 s−1) and Xe ( m2 s−1) in water agree reasonably well with preceding studies. This suggests that our diffusion experiment using a diffusive layer of immobilised water performed well.
Kr and Xe isotopes were found to only
Acknowledgments
This work was financed by the Swiss National Science Foundation (SNF-project 200020-132155). We thank two anonymous reviewers for helping to improve the manuscript with their constructive criticism. Special thanks go to Nadia Vogel for her introduction to the magnet sector field noble gas mass spectrometer built in-house at the noble gas laboratory at ETH Zürich.
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