Expanded uncertainty associated with determination of isotope enrichment factors: Comparison of two point calculation and Rayleigh-plot
Abstract
The enrichment factor (ε) is a common way to express Isotope Effects (IEs) associated with a phenomenon.
Many studies determine ε using a Rayleigh-plot, which needs multiple data points. More recent articles describe
an alternative method using the Rayleigh equation that allows the determination of ε using only one
experimental point, but this method is often subject to controversy. However, a calculation method using
two points (one experimental point and one at t0) should lead to the same results because the calculation is
derived from the Rayleigh equation. But, it is frequently asked “what is the valid domain of use of this two point
calculation?” The primary aim of the present work is a systematic comparison of results obtained with these two
methodologies and the determination of the conditions required for the valid calculation of ε. In order to
evaluate the efficiency of the two approaches, the expanded uncertainty (U) associated with determining ε has
been calculated using experimental data from three published articles. The second objective of the present work
is to describe how to determine the expanded uncertainty (U) associated with determining ε. Comparative
methodologies using both Rayleigh-plot and two point calculation are detailed and it is clearly demonstrated
that calculation of ε using a single data point can give the same result as a Rayleigh-plot provided one strict
condition is respected: that the experimental value is measured at a small fraction of unreacted substrate (f <
30%). This study will help stable isotope users to present their results in a more rigorous expression: ε ± U and
therefore to define better the significance of an experimental results prior interpretation.
Origin : Files produced by the author(s)
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