Calculate simultaneous solubility of AgCNS and AgBr in a solution of water. `(K_(SP)of AgBr = 5xx10^(-13) and K_(SP)of AgCNS = 1xx10^(-12))`

Explanation

Let solubility of AgCNS and AgBr in a solution be a and b mol `"litre"^(-1)` respectively .
`AgCNS (s) hArr Ag^(+) + CNS^(-)`
At equil [Ion] furnished on dissolution `(a+b)` a
`AgBr(s) hArr Ag^(+) +Br^(-)`
At equil [Ion] furnished on dissolution `(a+b)` b
` :. ` For AgCNS `K_(sp_(AgCNS)) = [Ag^(+)] [CNS^(-)] `
` 1 xx 10^(-12) = (a+b) (a) " " ` ...(1)
For AgBr `K_(sp_(AgBr)) = [Ag^(+)] [Br^(-)] `
`5 xx 10^(-13) = (a+b) (b)" "...(2)`
By Eqs.(1) and (2)
` :. " "a/b = (10^(12))/(5 xx10^(-13) ) = 2`
or a = 2b
By Eq . (1) ,`(a+a//2) (a) = 1xx10^(12)`
` a = 8.16 xx10^(-7) " mol litre "^(-1)`