`K_(sp)` of `AI(OH)_3` is `1xx10^(-15) M`. At what pH does `1.0xx10^(-3) M AI^(3+)` precipitate on the addition of buffer of `NH_4 CI` and `NH_4 OH` solution.

Explanation

`Al(OH)_(3) hArr Al^(3+) (aq)+3OH^(-) (aq)`
`K_(sp)=[Al^(3+)][OH^(-)]^(3)`
`Al(OH)_(3)` precipitates when
`[Al^(3+)][OH^(-)]^(3)`
`[Al^(3+)][OH^(-1)]^(3) gt K_(sp)`
`(1xx10^(-3))[OH^(-1)]^(3) gt 1xx10^(-15)`
`[OH^(-)]^(3) gt 1 xx10^(-12)`
`[OH^(-)] gt 1 xx 10^(-4)M`
`[OH^(-)]=1xx10^(-4)M`
`pOH=-log_(10)[OH^(-)]= -log(1xx10^(-4))=4`
`pH=14-4=10`
Thus, `Al(OH)_(3)` precipitates at a pH of 10