The solubility product of magnesium hydroxide at `25 ^(@)C is .1.8 xx 10 ^(-11).` Calculate the solubility of magnesium hydroxide.

Explanation

The solubility equilibrium of `Mg (OH ) _(2) : Mg (OH ) _(2) ` (s, sat. sol.) `hArr Mg ^(2+) (aq) + 2 OH ^(-) (aq)`
If `S mol L ^(-1)` is the solubility of `Mg (OH) _(2) ` rthen `[Mg ^(2+)] = S mol L ^(-1) and [OH^(-)] = 2 S mol L ^(-1)`
`K _(sp ) = [ Mg ^(2+) ][OH^(-) ] ^(2) implies K _(sp ) = S (22S) ^(2) implies K _(sp ) = 4S ^(3)`
`4S ^(3) = 1 . 8 xx 10 ^(-11) implies S = 1. 65 xx 10 ^(-4) mol L ^(-1) `
`therefore` Solubility of `Mg (OH) _(2) = 1. 65 xx 19 ^(-4) mol L ^(-1) = 1. 65 xx 10 ^(-4) mol L ^(-1) xx 58 g mol ^(-1) = 0.00957 g L ^(-1)`