The solubility product constant `K_(sp)` of `Mg(OH)_(2)` is `9.0 xx 10^(-12)`. If a solution is 0.010 M with respect to `Mg^(2+)` ion, what is the maximum hydroxide ion concentration which could be present without causing the precipitation of `Mg(OH)_(2)`

Options

A. `1.5 xx 10^(-7)`M
B. `3.0 xx 10^(-7)` M
C. `1.5 xx 10^(-5)` M
D. `3.0 xx 10^(-5)` M

Answer

D

Explanation

`underset (K_(sp))(Mg(OH)_(2))hArr underset (S)(Mg^(++))+ underset((2S)^(2))(2OH^(-))`
`K_(sp)= S xx 4S^(2)`
`(K_(sp))/(Sxx4) =S^(2) = (9xx10^(-12))/(0.010xx4) = 2.25 xx10^(-10)`
`S = sqrt(2.25 xx10^(-10))=1.5 xx10^(-5)`m/L