The uncertainty of atomic mass fractions in a molecule

The mass fraction of a certain atom species in a molecule is needed for the calculation of the result of some chemical analyses. Common examples are gravimetric determinations (e.g., the sulfur concentration in a sample that can be obtained from the mass of precipitated barium sulfate). A similar problem is encountered when a reference solution of an ion is prepared by dissolution of a salt. This paper presents how the uncertainty of the mass fraction is calculated from the uncertainties of the atomic weights as published by IUPAC. The value is needed for the determination of the combined standard uncertainty of the analysis. Some calculated examples illustrate the mathematical considerations presented in the paper.