Question

What is the ratio of moles of Mg(OH)₂ and Al(OH)₃ present in 1 litre saturated aqueous solution of Mg(OH)₂ and Al(OH)₃ (Given K_sp of Mg(OH)₂ = 4 × 10^–12 and K_sp of Al(OH)₃ is 1 × 10^–33).

Report your answer after multiplying by 10^–17.     

Answer 1

Mg(OH) ₂  \(\leftrightharpoons\)  Mg²⁺   + 2OH^–

                           x          2x + 3y

Al(OH)₃  \(\leftrightharpoons\)  Al³⁺   +   3OH^–

                         y          3y + 2x

Since K_sp of Mg(OH)₂ > K_sp of Al(OH)₃

∴  x >> y             ∴ 2x + 3y \(\simeq\) 2x

4 × 10^–12 = [Mg²⁺][OH^–]²

= x × (2x)²

∴ x = 10^–4

Similarly 1 × 10^–33 = [Al³⁺][OH^–]³

1 × 10^–33 = y × (2x)³

∴ \(y = \frac{{{{10}^{-21}}}}{8}\)

Thus \(\frac{x}{y}\)= 8 × 10¹⁷

∴ Ans. = 8 × 10⁺¹⁷ × 10^–17 = 8