Thermodynamic Description of Isotope Effects

Thermodynamic energy terms (and equilibrium constants) may differ for isotopic species of an element. This effect is described in theoretical detail by Urey (1947), and applications to geochemistry are discussed by Broecker and Oversby (1971) and Faure (1977). In the case of the vapor/liquid equilibrium for water, the vapor is enriched relative to the liquid in the lighter isotopic species, relative to 

Small variations in isotopic composition are usually described by comparing the ratio of isotopes in the sample material to the ratio of isotopes in a reference material. The standard measure of isotopic composition is dX, defined in parts per thousand (per mil or %o) by  

The amount of the standard isotopic species and the tracer isotopic species are represented by X and X for the sample and the reference material. The reference substance is chosen arbitrarily, but is a substance that is homogeneous, available in reasonable amounts, and treatable by standard analytical techniques for measuring isotopes (generally mass spectrometry). For instance, a sample of ocean water known as Standard Mean Ocean Water (SMOW) is used as a reference for and 0. Calcium carbonate from the Pee Dee sedimentary formation in North Carolina, USA (PDB) is used for the carbon isotopes. 

If the sample has less of the tracer isotopic species than the reference material, 5 will be negative. Since many of the tracer species are heavier than the reference species ( C, C vs C or S vs S), this has led to use of the term light for substances having less of a tracer species than the standard species. 

As an example, the ratio of the equilibrium vapor pressures for water (pi) and water ( 2) depends on temperature and is expressed by the following equation (see Faure, 1977). The relationship of this expression to the van t Hoff equation can be seen  

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