Isotope dilution equation application

It should be mentioned that the same kind of equations hold if stable isotopes are applied for labelling of the elements or compounds to be determined by isotope dilution analysis. In this application, isotope ratios are taking the place of specific activities and they are preferably measured by mass spectrometry. 

A special and very useful application of the isotope-dilution method is in the determination of optical purity of resolved or partially racemic optical enantiomers. Berson and Ben-Efraim (1959) derived the following equations ... 

Isotope dilution This relatively new calibration method is occasionally used in specialized forensic applications. The method affords exceptional accuracy and precision, but is limited by the availability of suitable standards. Although the use of deuterated internal standards is sometimes equated with isotope dilution, the techniques are not the same. Isotope-dilution calibration is based on the addition of standards that contained enriched levels of stable isotopes of common elements such as C. The enriched standard, referred to as the spike, is added to the sample and allowed to reach equilibrium. The sample is then analyzed via mass spectrometry. Because the spike is chemically identical to the target analyte, the matrix correction is as good as that achieved with standard-addition calibration. However, until enriched stable isotope analogs of forensic analytes are available and affordable, isotope dilution will not be widely applied in forensic chemistry. 

Calibration using the double-spike method is an ingenious application of isotope dilution in mass spectrometry. Admixing the measurand and the spike (calibrant) results in a mixture, the isotopic composition of which is governed by the conservation of matter. Two sets of equations can be established one that describes the conservation of matter during the mixing, and the other that expresses the relationship between the measured and true isotope amount ratios, that is, the discrimination law ... 

---