Kinetic isotope effect effects, while "k"/"k" ~ 1.15-1.3 are typical for β secondary kinetic isotope effect. For reactants containing several isotopically-substituted β-hydrogen atoms, the observed isotope effect is often the result of several H/D's at the β position acting in concert. In these cases, the effect of each isotopically-labeled atom is multiplicative, and cases where "k"/"k" > 2 are not uncommon. The following simple expressions relating deuterium and tritium kinetic isotope effects, which are also known as the Swain equation (or the Swain-Schaad-Stivers equations), can be derived from the general expression given above using some simplifications: i.e., In deriving these expressions, the reasonable
Hydrogen isotope biogeochemistry constants would allow extrapolation to original isotopic compositions. While this solution holds promise, there is too much disagreement in the literature for robust calibrations. Vapor isotope effects occur for protium, deuterium, and tritium, because each isotope has different thermodynamic properties in the liquid and gaseous phases. For water molecules, the condensed phase is more enriched while the vapor is more depleted. For example, rain condensing from a cloud will be heavier than the vapor starting point. Generally, the large variations in deuterium concentrations of water are from the fractionations between liquid, vapor, and solid reservoirs. In contrast to the fractionation