Calculation of Equilibrium Constants for Isotopic Exchange Reactions

Bigeleisen, Jacob; Mayer, Maria Goeppert

doi:10.1063/1.1746492

Cited by 1,710 publications

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“…Stable isotope fractionation is driven by equilibrium and/or kinetic processes. For the former, the magnitude of the effect is proportional to 1/T 2 (Urey, 1947;Bigeleisen and Mayer, 1947), so that lower temperature environments yield the greatest isotope fractionations, whereas fractionation magnitudes can become vanishingly small at mantle temperatures. In the case of thallium and other heavy elements such as Hg, isotope fractionation that would otherwise be predicted to be very limited given the small relative mass difference between each isotope, is enhanced by nuclear volume effects (e.g., Schauble, 2007).…”

Section: Accepted M Manuscriptmentioning

confidence: 99%

Thallium elemental behavior and stable isotope fractionation during magmatic processes

et al. 2017

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Please cite this article as: Prytulak, J., Brett, A., Webb, M., Plank, T., Rehkämper, M., Savage, P.S., Woodhead, J., Thallium elemental behavior and stable isotope fractionation during magmatic processes, Chemical Geology (2016), doi: 10.1016/j.chemgeo. 2016.11.007 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT AbstractStable thallium (Tl) isotopes are an extremely sensitive tracer for the addition of small amounts of sediments or materials altered at low temperatures to the source(s) of mantle-derived melts. The ability of Tl to trace such materials is due to the large concentration contrast between the mantle (Tl < 2ng/g) and possible exotic inputs (Tl ~100ng/g to >g/g), which also often display fractionated Tl isotope compositions.However, the magnitude of Tl isotope fractionation induced by igneous processes alone has not been systematically assessed. Here, two suites of co-genetic magmas, spanning a large range of differentiation, from Hekla, Iceland, and Anatahan, in the Mariana arc, are used to assess the behavior of thallium and its stable isotope variations during magmatic processes. Thallium behaves as a near-perfectly incompatible lithophile element throughout magmatic evolution, mirroring elements such as Rb, Cs, and K. Lavas from Hekla have restricted Cs/Tl ratios and stable Tl isotope compositions, which overlap with mantle estimates. Lavas from subductionrelated Anatahan volcano also have a restricted range in Tl isotope composition, which overlaps with Hekla and MORB, demonstrating that fractional crystallisation and partial melting does not fractionate stable Tl isotopes. Subduction environments display variable Cs/Tl, indicating that the subduction process commonly fractionates these two elements. The immunity of thallium stable isotopes to fractionation by magmatic processes coupled with its extreme sensitivity for tracing pelagic sediments, FeMn crusts and low temperature altered oceanic crust highlight its value in elucidating the nature of mantle sources of both oceanic basalts and arc lavas.Critically, meaningful interpretation of thallium isotope compositions need not be restricted to primitive lavas.

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Section: Accepted M Manuscriptmentioning

confidence: 99%

Thallium elemental behavior and stable isotope fractionation during magmatic processes

et al. 2017

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“…The following outline of isotopic fractionation for single-atom isotopic substitution in equilibrium chemical reactions is based on Bigeleisen and Mayer (1947) and is included to show the basis for predictions that the fractionation ratio for 14 C/ 12 C and 13 C/ 12 C is ~1.9. It should be noted that extrapolating from this value to complex processes such as photosynthesis is difficult.…”

Section: Appendix A: Isotopic Fractionation In Chemical Equilibria Anmentioning

confidence: 99%

“…Since this result has important implications for 14 C calculations, a derivation based on work by Bigeleisen and Mayer (1947) is included here in Appendix A. Detailed reaction calculations for a variety of chemical equilibria have typically produced values for b in the range of 1.85-1.9 (Stern and Vogel 1971;Hartshorn and Shiner 1972), though calculations by Saliege and Fontes (1984) suggest b ~2.05 for reactions involving CO 2 .…”

Section: Introductionmentioning

confidence: 99%

Are the Fractionation Corrections Correct: Are the Isotopic Shifts for ¹⁴C/¹²C Ratios in Physical Processes and Chemical Reactions Really Twice Those for ¹³C/¹²C?

Southon¹

2011

Radiocarbon

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ABSTRACT. Conventional radiocarbon calculations correct for isotopic fractionation using an assumed value of 2.0 for the fractionation of 14 C relative to 13 C. In other words, isotopic discrimination in physical and chemical processes is assumed to cause relative shifts in 14 C/ 12 C ratios that are exactly double those of 13 C/ 12 C. This paper analyzes a 1984 experiment that produced a value for the fractionation ratio in photosynthesis of 2.3, which is used to this day by some researchers in the fields of hydrology and speleothem geochemistry. While the value of 2.3 is almost certainly incorrect, theoretical work suggests that the true value may indeed deviate from 2.0, which would have significant implications for 14 C calculations.

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“…The general formula of (s/s')f of a species is expressed, under the Born-Oppenheimer and harmonic oscillator approxima-tions, as< 2 ) ,…”

Section: Theory Of Isotope Effects and Objectives Of The Present mentioning

confidence: 99%

Calculations of Reduced Partition Function Ratios of Monomeric and Dimeric Boric Acids and Borates by theab initioMolecular Orbital Theory

2000

Journal of Nuclear Science and Technology

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With the final goal to elucidate boron isotope fractionation observed experimentally, molecular orbital calculations were performed on boric acid and borate monomers and dimers. The geometries of B(OH)3 and B(OH) 4 were first optimized and their vibrational frequencies were calculated at their optimized structures. The estimated 11 B-to-10 B isotopic reduced partition function ratios (RPFRs) of B( OH)3 and B( OH) 4 and the calculated equilibrium constant of the boron isotope exchange reaction between the two boron species revealed that a more advanced molecular orbital theory with a higher level basis set did not necessarily yield better results. It was concluded that HF /6-31G( d) calculations were most appropriate for the present purpose. The RPFRs of the dimers, H4B20s, HsB20 6 and H5B20~-, estimated from the RPFRs of the monomers by the use of additivity of the logarithm of RPFRs agreed with those calculated using the frequencies of the dimers within a margin of 1%. This error corresponded to the error of 5% on ln(RPFR). The equilibrium constant of boron isotope exchange reaction between two boron species among the monomer and dimers at 25°C varied from 1.0207 to 1.0360, indicating the importance of accurate estimation of the RPFRs of polyboric acids and polyborates in real systems.

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Calculation of Equilibrium Constants for Isotopic Exchange Reactions

Cited by 1,710 publications

References 5 publications

Thallium elemental behavior and stable isotope fractionation during magmatic processes

Thallium elemental behavior and stable isotope fractionation during magmatic processes

Are the Fractionation Corrections Correct: Are the Isotopic Shifts for ¹⁴C/¹²C Ratios in Physical Processes and Chemical Reactions Really Twice Those for ¹³C/¹²C?

Calculations of Reduced Partition Function Ratios of Monomeric and Dimeric Boric Acids and Borates by theab initioMolecular Orbital Theory

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Calculation of Equilibrium Constants for Isotopic Exchange Reactions

Cited by 1,710 publications

References 5 publications

Thallium elemental behavior and stable isotope fractionation during magmatic processes

Thallium elemental behavior and stable isotope fractionation during magmatic processes

Are the Fractionation Corrections Correct: Are the Isotopic Shifts for 14C/12C Ratios in Physical Processes and Chemical Reactions Really Twice Those for 13C/12C?

Calculations of Reduced Partition Function Ratios of Monomeric and Dimeric Boric Acids and Borates by theab initioMolecular Orbital Theory

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Are the Fractionation Corrections Correct: Are the Isotopic Shifts for ¹⁴C/¹²C Ratios in Physical Processes and Chemical Reactions Really Twice Those for ¹³C/¹²C?