The solubility product of a sparingly soluble metal hydroxide `[M(OH)_(2)]` is `5xx10^(-16) mol^(3)dm^(-9)` at 298 K. Find the pH of its saturated aqueous solution.

Answer

9

Explanation

`{:(M(OH)_(2)hArr,M^(2+)+,2OH^(-)),(,S,2S):}`
`:' K_(SP)=[S][2S]^(2)=4S^(3)`
`:. S=3sqrt((K_(SP))/(4))=3sqrt((5xx10^(-16))/(4))=5xx10^(-6)`
`=[OH^(-)]`
`-log[OH^(-)]=5.30=pOH`
`:. pH=14-5.30~~9`