A 0.2 g sample of pyrolusite is analyzed for manganese content as follows. Add 50.0 mL of a 0.10 M solution of ferrous ammonium sulfate to reduce the MnO2 to Mn2+. After reduction is complete, the excess ferrous ion is titrated in acid solution with 0.0200 M KMno4, requiring 15.0 mL. Calculate the percent manganese in the sample as Mn3O4 (only part or none of the manganese may exist in this form, but we can make the calculations on the assumption that it does)