Stoichiometry (n). The symbol, n, represents the stoichiometry of the reaction, specifically the number of atoms of a given element (e.g., carbon) in a molecule involved in the reaction
Isotopic abundance (δ). A measure of isotopic abundance, δ, is usually reported as the difference in parts per thousand, or permil (‰), from an international
standard. The δ can be negative or positive, depending on whether the sample is enriched or depleted in the heavy isotope
relative to the standard. In the case of carbon, for example, the difference is calculated as: .
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in which Rsmpl is the 13C/12C ratio of the sample and Rstd is the 13C/12C ratio in the standard. Thus, δ is linearly proportional to the isotopic ratio in the sample. Standards are available from
the International Atomic Energy Authority and a standard for each isotope is used to determine the zero point of an abundance
scale for that isotope. Standards include average seawater for H and O, calcium carbonate for C, air for N, and a meteorite
for S. When the sample is depleted in the heavy isotope relative to the standard, δ is negative. When the sample is enriched,
it has a positive value. If it has the same isotopic abundance, then δ = 0 (11).
Magnitude of the isotopic effect (ε). The ε value is a measure of the magnitude of an isotope effect. Its value depends on details of the reaction and on the
relative mass difference between isotopes. Effects are largest for D versus H and smaller for heavier elements. In general, the values of ε are specific to individual positions within the molecules
involved. They are largest at the reaction site, much smaller at neighboring positions, and usually not measurable elsewhere.
Like δ, ε relates to the isotopic difference between two materials (e.g., reactant and product) and is usually expressed in permil. For kinetic isotope effects in the system used in this article,
ε = –10‰, which means that a reaction site bearing the heavy isotope reacts 10 parts per thousand (or 1%) more slowly than
a site bearing a light isotope. For equilibrium isotope effects, εA/B = 15‰ would mean that, at equilibrium, A was enriched in the heavy isotope by 15 parts per thousand relative to B. In this
instance, A and B refer to specific atomic positions that can be related by a chemical equilibrium.
Variable related to the fractional conversion of reactants to products (f). The f is a measure of the reaction's progress. It is the most important variable governing fractionations caused by isotope effects.
Its value ranges from 1 to 0 and depends on factors such as temperature, pressure, or the availability of reactants. In equilibria
(A ⇔ B), f indicates the position of the equilibrium, with f
B = 1 indicating a complete conversion to B and, at any position, f
A + f
B = 1. In irreversible reactions, f
X indicates the portion of reactant X which remains unconsumed, with f
X → 0 as the reaction proceeds to completion.
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