From the formula, the mole amount of iron in the magnetite sample is three times the mole amount of iron(II,III) oxide. This amount is the mass of magnetite divided by its molar weight.
n[Fe] = 3 m[Fe3O4]/w[Fe3O4]
The amount of iron in the converted assay is twice the amount of iron(III) oxide. That amount is again the mass of assay divided by its molecular weight.
n[Fe] = 2 m[Fe2O3]/w[Fe2O3]
All of the magnetite was converted, so the amount of iron must remain the same. It is conserved. So we can equate them.
3 m[Fe3O4]/w[Fe3O4] = 2 m[Fe2O3]/w[Fe2O3]
We are given three of these terms and wish to find the fourth. Rearranging gives the mass of magnetite in the sample.
m[Fe3O4] = (2/3) m[Fe2O3] w[Fe3O4] / w[Fe2O3]
Evaluating:
m[Fe3O4] = (2/3)*(26g)*(231.5333)/(159.6887)
An ore contains Fe3O4 and no other iron.The iron in a 39.5-gram sample of the ore is all converted by a series of chemical reactions to Fe2O3. The mass of Fe2O3 is measured to be 26.7 g. What was the mass of Fe3O4 in the sample of ore?
Answer in units of g.
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