Calculating Atomic Mass

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Background

The atomic mass of the elements is required to determine correct formulas of compounds - i.e. to encode the percent composition of the compound. Historically, this presented a problem. Chemists needed atomic masses to calculate formulas, but they needed a correct formulas to calculate atomic masses. Eventually, the problem was solved by finding alternative routes to some formulas. The historic calculation below assumes that the formula of a compound of an unidentified element, X, is known. The problem Illustrates how the atomic masses were calculated. Textbook Discussion: Section 5.6, page 116. See Also: Example IIIA, page 117 and Example IIIB, page 118.

Problem

A chemical compound under study is know to contain only the elements X and the element sulfur. Quantitative analysis shows that the compound is 27.9 percent X by mass. The atomic mass of sulfur is known to be 32.1 amu. Assuming that the formula of this compound is X₂S₅, what is the atomic mass of element X?