How is alumina separated from silica in the bauxite ore associated with silica? Give equations?

Explanation

Serpecks's process is used for the purification of white Bauxite i.e., Bauxite containing silica as impueity.
In this process bauxite is mixed with coke and heated to 2075K in a current of nitrogen. Silica is to silicon and eacapes as a vapour.
`SiO_(2)+2CrarrSiuarr+2COuarr`
`Al_(2)O_(3)+3C+N_(2)overset(2075K)rarr2AlN+3CO`
Aluminium nitride formed in the above step is hydroysed to form aluminium hydroxide.
`AlN+3H_(2)OrarrAl(OH)_(3)darrNH_(3)uarr`
`Al(OH)_(3)` PPt is washed dried and then ignited to from purified bauxite.
`2Al(OH)_(3)overset(1200^(@)C)rarrAl_(2)O_(3)+3H_(2)O`