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.

Options

A. 5
B. 9
C. `11.5`
D. `2.5`

Answer

B

Explanation

`{:(M(OH)_(2),hArr,M^(2+),+,2OH^(-)),(,,s,,2s):}`
`K_(sp)=(s) (2s)^(2)=4s^(3)`
`s^(3)=(K_(sp))/(4)=(5xx10^(-16))/(4)=1.25xx10^(-16)`
`=125xx10^(-18)`
`:. S=5xx10^(-6)M, i.e., [OH^(-)]2xx5xx10^(-6)M`
`=10^(-5)M`
pOH = 5.0
pH=14-5 = 9