direct isotope dilution analysis (DIDA), Chemistry

A solution contains an unknown amount of osmium at the µg/g level, or below. Chemically pure osmium (Os) may be separated from the solution, but the chemical yields are variable and low. The determination is done by direct isotope dilution analysis (DIDA). The isotopic abundances of 186Os and 190Os are 1.58 and 26.4%, respectively. 7.80 x 10-9 g of isotopically pure, stable 186Os is added to the unknown solution and mixed thoroughly, and then a small amount of pure Os is extracted from the mixture. With a mass spectrometer, the 190Os/186Os mass ratio in the extracted sample is found to be 7.40. Calculate the amount of Os originally present in the unknown solution.
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