If 5 kg of haematite contain 2.78 kg of iron then what is the percentage purity of haematite. It contains gangue?

Mass fraction of Fe in Fe₂O₃ (hematite) = (55.85×2 g/mol) / [(55.85×2 + 16.00×3) g/mol] = 111.7/159.7

Mass of Fe in the sample = 2.78 kg
Mass of Fe₂O₃ in the sample = (2.78 kg) ÷ (111.7/159.7) = (2.78 kg) × (159.7/111.7) = 3.97 kg

Percentage purity of hematite = (3.97/5) × 100(%) = 79.4(%)