Carbon dioxide is together with water vapour, methane and nitrous oxide one of the major contributors to the atmospheric greenhouse gas concentration. The atmospheric concentration of carbon dioxide is heavily and continuously increasing since the beginning of the industrialization, and its contribution to the global warming is commonly accepted. Due to the roll of carbon dioxide in the global carbon cycle and its global warming potential the isotopic composition of carbon dioxide is of great interest since it is an important analytical tool. This tool helps to understand the global carbon flux and to discriminate between anthropogenic and natural sources and thus it also helps to verify and control emission regulations and in the end to reduce the emission. The isotopic composition of carbon dioxide is measured with the highest achievable accuracy by mass spectrometry. With mass spectrometers only the measured ion intensity ratios are directly available. These measured ion intensity ratios differ from the actual isotope ratios and correction is needed. This difference is commonly known as mass bias, which is a collective term for all the effects that lead to this difference. Unfortunately, mass bias cannot be avoided completely, it can only be reduced. As mass bias is inevitable, it is common praxis to use a certified isotopic reference material. By comparing the certified isotope ratios with the measured ratios, mass bias correction factors (K-factors) can be determined. With these correction factors also the measured intensity ratios of the unknown sample can be corrected, provided both the reference and the sample were measured in the same sequence and under the same conditions. In the case of the isotopic variations of carbon dioxide, this reference is NBS19, which is used to report relative differences between a virtual calcite (called VPDB) and the sample. These differences are reported on the international VPDB d scale. There are two major problems with this scale. The first problem is that the absolute isotope ratios of NBS19 (and hence VPDB) are not known in a way that they are traceable to the base unit mole. This is the reason for the usage of the relative differences. The lack of traceability to the mole can lead to comparability issues between different laboratories and makes the whole reference scale vulnerable to drifts of the defining material, NBS19. The second major problem is, that NBS19 is out of stock and cannot be ordered any more, this endangers the whole scale and makes it difficult to continue the scale without increasing uncertainties by introducing a new reference material. For these reasons the knowledge of absolute isotope ratios of carbon dioxide is urgently needed, since then the above mentioned problems would be solved. VII In this cumulative thesis it is presented for the first time how K-factors can be calculated analytically for systems with more than three isotopes. In addition to the calculation of the Kfactors it is presented how the uncertainties associated with the Kfactors can be calculated, in order to consider their contribution to the uncertainty associated with the absolute isotope ratios and render the traceability-chain to the mole unbroken. The knowledge gained about the calculation of the K-factors for atomic systems served as the base for the adaption of the approach to molecular systems. In the fourth section of this thesis, it is shown how the gravimetric mixture approach must be adapted for carbon dioxide, since a statistical isotope distribution must be considered. A new mathematical approach is presented which considers the statistical distribution and allows to calculate the correct K-factors. This approach has also been generalized so that in future it can be applied also to other isotopologue systems. A buoyancy correction scheme for masses of gases in closed gas vessels was developed for this study and is also presented. F

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