A pure sample of an anhydrous sulfate has the empirical formula M (SO )

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Problem

A pure sample of an anhydrous sulfate has the empirical formula M2_2(SO4_4)3_3. Quantitative elemental analysis shows that the compound is 27.9\,% by mass element M. Assume sulfate behaves as a discrete polyatomic ion in the lattice. (a) Derive an algebraic expression that relates the mass percent of element M to its atomic mass MatomicM_{\text{atomic}} for the formula M2_2(SO4_4)3_3. (b) Using the experimental mass percent, calculate the atomic mass of M. (c) Identify the element M and state its common oxidation state in the compound. (d) Provide a detailed explanation, based on electron configuration and periodic trends, for why the oxidation state obtained in part (c) is favored for this element when it forms a sulfate.

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