Igniting `MnO_(2)` in air converts it quantitatively to `Mn_(3)O_(4)`. A sample of pyrolusite is of the following composition: `MnO_(2) = 80%`, `SiO_(2)` and other inert constituents = 15%, and rest bearing `H_(2) O`. The sample is ignited to constant weight. What is the percent of `Mn` in the ingnited sample?

Explanation

`undersetunderset("=261 g")(3(55+2xx16))(3MnO_(2))rarrundersetunderset("= 229 g")(3xx55+4xx16)(Mn_(3)O_(4))+O_(2)`
Suppose the amount of pyrolusite ignited = 100 g
`therefore" "MnO_(2)" present in it = 80 g"`
`SiO_(2)" and other inert contents = 15 g"`
`"Water "=100-(80+15)=5g`
`"Now, 261 g of "MnO_(2)" give "Mn_(3)O_(4)=229g`
`therefore" 80 g of "MnO_(2)" will give "Mn_(3)O_(4)=(229)/(261)xx80g=70.19g`
An on ignition, water is removed but `SiO_(2)` and other inert contents remain, therefore total mass of the residue after ignition `=70.19+15g=85.19g`
`underset(=229g)underset(3xx55+4xx16)(Mn_(3)O_(4))-=underset(=165g)underset(3xx55)(3Mn)`
`"229 g "Mn_(3)O_(4)" contain Mn"=165 g`
`therefore" "70.19 Mn_(3)O_(4)" contain Mn"=(165)/(229)xx70.19g=50.57g`
This is present in 85.19 g of the total residue
`therefore" "%" of Mn in the residue "=(50.57)/(85.19)xx100=59.36`