Chemical and Ionic Equilibrium - Result Question 127
####70. Freshly precipitated aluminium and magnesium hydroxides are stirred vigorously in a buffer solution containing $0.25 mol / L^{-}$of $NH _4 Cl$ and $0.05 M$ of ammonium hydroxide. Calculate the concentration of aluminium and magnesium ions in solution.
$$ \begin{aligned} K _b\left[NH _4 OH\right] & =1.8 \times 10^{-5} \ K _{\text {sp }}\left[Mg(OH) _2\right] & =8.9 \times 10^{-12} \ K _{\text {sp }}\left[Al(OH) _3\right] & =6 \times 10^{-32} \end{aligned} $$
(1989, 3M)
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Solution:
- $pOH$ of buffer solution $=p K _b+\log \frac{\left[NH _4^{+}\right]}{\left[NH _4 OH\right]}$
$$ \begin{aligned} & =-\log \left(1.8 \times 10^{-5}\right)+\log \frac{0.25}{0.05}=5.44 \ {\left[OH^{-}\right] } & =3.6 \times 10^{-6} M \ {\left[Al^{3+}\right] } & =\frac{K _{\text {sp }}}{\left[OH^{-}\right]^{3}}=\frac{6 \times 10^{-32}}{\left(3.6 \times 10^{-6}\right)^{3}}=1.28 \times 10^{-15} M \ {\left[Mg^{2+}\right] } & =\frac{K _{\text {sp }}}{\left[OH^{-}\right]^{2}}=\frac{8.9 \times 10^{-12}}{\left(3.6 \times 10^{-6}\right)^{2}}=0.68 M \end{aligned} $$
