1.

The solubility of Mg`(OH)_(2)` is `8.352xx10^(-3)` g/litre at `290^(@)` C. Find out its `K_(sp)` at this temperature.

Answer» `Mg(OH)_(2)` ionizes completely in the solution as : `Mg(OH)_(2)rarrMg^(2+)+2OH^(-)`
`:. [Mg^(2+)]=[Mg(OH)_(2)] and [OH^(-)] = 2xx [ Mg (OH)_(2)]`
But Molar mass of Mg`(OH)_(2) = 58 g "mol"^(-1)`
`:. [Mg(OH)_(2)]=("Strength in g / litre")/("Molar mass") = (8.352xx10^(-3))/(58) = 1.44 xx 10^(-4)` moles/litre
`:. [Mg^(2+)]=1.44xx10^(-4)` moles/litre and `[OH^(-)] = 2xx1.44xx10^(-4)=2.88xx10^(-4)` moles/litre
`:. K_(sp) ` for `Mg(OH)_(2)=[Mg^(2+)][OH^(-)]^(2)=(1.44xx10^(-4))xx(2.88xx10^(-4))^(2)=1.194xx10^(-11)`


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