A mineral haematite `(Fe_(2)O_(3))` contains unwanted material called gangue in addition to `Fe_(2)O_(3)`. If 5 kg of the ore contains 2.78 kg of iron, what is the percentage purity of `Fe_(2)O_(3)` ?

Answer

0.7943

Explanation

Step I. Mass of pure `Fe_(2)O_(3)` in haematite
`underset(bar(112+48(=160g)" "2xx56=(112g)))(Fe_(2)O_(3)=2Fe)`
112 g of iron are present in `Fe_(2)O_(3) = 160 g`
2.78 kg (2780 g) of iron are present in `Fe_(2)O_(3)=(160)/(11)xx2780=3971.4g=3.9714g`
Step II. Percentage purity of haematite mineral
`= ("Mass of "Fe_(2)O_(3))/("Mass of mineral")=(3.9714)/(5.0)xx100=79.43%`.