Freshly prepared aluminium and magnesium hydroxides are stirred vigorously in a buffer solution containing `0.25M` of ammonium chloride and `0.05M` of ammonium hydroxide. Calculate the concentration of aluminium and magesium ions in solution `(K_(b) NH_(4)OH = 1.8 xx 10^(-5), K_(sp) Mg(OH)_(2) = 6 xx 10^(-10), K_(sp) Al(OH)_(3) = 6 xx 10^(-32)`.

Explanation

pOH of buffer solution = `pK_(b) + log[NH_(4)^(+)]/[NH_(4)OH] = -log(1.8 xx 10^(-5))+log0.25/0.005 = 5.44`
`[OH^(-)] = 3.6 xx 10^(-6)M`
`[Al^(3+)] = K_(sp)/[OH^(-)]^(3) = 6xx10^(-32)/(3.6 xx 10^(-6)) = 1.28 xx 10^(-15)M`
`[Mg^(2+)] = K_(sp)/[OH^(-)]^(2) = 8.9 xx 10^(-12)/(3.6 xx 10^(-6))^(2) = 0.68 M`