Negligible fractionation of Kr and Xe isotopes by molecular diffusion in water

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Highlights

  • Kinetic gas theory is not suitable to predict isotopic fractionation of Kr and Xe diffusing through water.

  • Quantum–mechanical interactions might determine Kr and Xe isotope diffusion in water.

  • Kr and Xe data complete our current understanding of noble gas diffusion in aquatic systems.

Abstract

Molecular diffusion is a key transport process for noble gases in water. Such diffusive transport is often thought to cause a mass-dependent fractionation of noble gas isotopes that is inversely proportional to the square root of the ratio of their atomic mass, referred to as the square root relation. Previous studies, challenged the commonly held assumption that the square root relation adequately describes the behaviour of noble gas isotopes diffusing through water. However, the effect of diffusion on noble gas isotopes has only been determined experimentally for He, Ne and Ar to date, whereas the extent of fractionation of Kr and Xe has not been measured. In the present study the fractionation of Kr and Xe isotopes diffusing through water immobilised by adding agar was quantified through measuring the respective isotope ratio after diffusing through the immobilised water. No fractionation of Kr and Xe isotopes was observed, even using high-precision noble gas analytics. These results complement our current understanding on isotopic fractionation of noble gases diffusing through water. Therefore this complete data set builds a robust basis to describe molecular diffusion of noble gases in water in a physical sound manner which is fundamental to assess the physical aspects of gas dynamics in aquatic systems.

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):DiDj=(MjMi)β where Di and Dj are the diffusion coefficients of the diffusing gases i and j, with their molecular mass Mi and Mj, respectively, and β=0.5.

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 (DKr=1.9±0.2×109 m2 s−1) and Xe (DXe=1.7±0.2×109 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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