Question

Consider an amphoteric hydroxide, M(OH)2(s), where M is a generic metal. Ksp=7x10-16 Kf=0.07

Estimate the solubility of M(OH)2 in a solution buffered at pH = 7.0, 10.0, and 14.0.

Answer 1

To estimate the solubility of the amphoteric hydroxide $M(OH)_{2}$ at the provided pH= 7,10 and 14, we just have to determine the solubility of the generic metal $M^{2+}$ (say the solubility of $M^{2+}$= S) from the solubility equilibrium,

$M(OH)_{2} _{(s)} \rightleftharpoons M^{2+}_{(aq)} + 2OH^{-}_{(aq)}$

$\therefore K_{sp}=[M^{2+}].[OH^{-}]^{2}=7\times 10^{-16}$... (1)

Now from the individual pH data given, we can determine the $[OH^{-}]$ for each from the equation $pH+pOH=14$.

Now, at pH=7

apt P POH =子 Pultrg K +be EoHe]om e to eT C- - (6 2 x10-2 O O7M

pHtpoH 10 +po14 pot 0 Using taker e Kap-0Loue 子X10 子×10~6 0-4)2 )=S x 10 at H P 14poH 4 Using, kentefom 2 Ksp [M2.oue xto- H20) 2

hence the solubility of the metal hydroxide at-

• pH =7 , $S=0.07 (M)$
• pH=10 ,$S=7\times 10^{-8} (M)$
• pH=14 ,. $S=7\times 10^{-16} (M)$ .