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) = (5 xx 10^(-16))/(4) , s = 5 xx 10^(-6) = [OH^(-)]`
`-log [OH]^(-) = 5.30 = pOH`
`pH = 14 - 5.30 = 8.70 ~~ 9.00`.