The `K_(sp)` value of two sparingly soluble salts `Ni(OH)_2` and AgCN are `2.0xx10^(-15)` and `6.0xx10^(-17)` respectively. What salt is more soluble ?

Explanation

`AgCN hArr Ag^(+)+CN^-`
Suppose the solubility of AgCN is x mol `L^(-1)` so that
`[Ag^+]=x, [CN^-]=x`
`K_(sp)=[Ag^+][CN^-]`
`=x xx x =x^2`
or `x=(K_(sp))^(1//2) =(6.0xx10^(-17))^(1//2)`
`=7.75xx10^(-9)`
`Ni(OH)_2 hArr Ni^(2+) + 2OH^-`
Let solubility of `Ni(OH)_2` is y mol `L^(-1)` so that
`[Ni^(2+)]=y, [OH^-]=2y`
`K_(sp)=[NI^(2+)][OH^-]^2`
`=y xx (2y)^2 =4y^3`
`therefore y=(K_(sp)/4)^(1//3)`
`=((2.0xx10^(-15))/4)^(1//3)`
`=(0.5xx10^(-15))^(1//3)`
or `y=7.93xx10^(-5)`
`Ni(OH)_2` is more soluble than AgCN.