Answer:
The solubility of [tex]BaSO_4[/tex] is more than [tex]Al(OH)_3[/tex] as the solubility of [tex]BaSO_4[/tex] is [tex]1.048\times 10^-^5[/tex] and that of [tex]Al(OH)_3[/tex] is [tex]10^-^8[/tex]. The solubility of [tex]Al(OH)_3[/tex] will decrease in presence of [tex]0.10M[/tex] [tex]NaOH[/tex] due to the common ion effect. And the solubility of [tex]Al(OH)_3[/tex] in presence of a common ion effect will be [tex]2.7\times 10^-^2^8[/tex].
Explanation:
Let Solubility [tex]BaSO_4[/tex] of be "S"
Then,
[tex]BaSO_4\rightarrow Ba^+^2+SO4^-^2\\[/tex]
S S
Ksp of BaSO₄⇒[tex][Ba^+^2][SO4^-^2][/tex] (1)
By substituting the value of Ksp of [tex]BaSO_4[/tex] in equation (1) we get;
[tex]1.1\times 10^-^1^0=[S][S][/tex]
[tex]S^2=1.1\times 10^-^1^0[/tex]
[tex]S=1.048\times 10^-^5[/tex] (2)
Let Solubility of [tex]Al(OH)_3[/tex] be "S'"
Then,
[tex]Al(OH)_3\rightarrow Al^+^3+3OH^-^1[/tex]
S' 3S'
Ksp of Al(OH)₃⇒[tex][Al^+^3[3OH^-^1][/tex]
[tex]2.7\times 10^-^3^1=[S'][3S']^3[/tex]
[tex]S'=10^-8[/tex] (3)
From equations (2) and (3) we can see that the solubility of [tex]BaSO_4[/tex] is more than [tex]Al(OH)_3[/tex].
The solubility of [tex]Al(OH)_3[/tex] will decrease in presence of 0.10M NaOH due to the common ion effect.
Let's understand this by the reaction.
[tex]NaOH\rightarrow Na^++OH^-[/tex]
[tex]0.10M[/tex] [tex]0.10M[/tex] [tex]0.10M[/tex]
Total solubility of [tex][OH^-]\rightarrow{[OH^- from Al(OH)_3]+0.10}[/tex]
Now,
[tex]Ksp=2.7\times 10^-^3^1=[S'][[OH⁻ from Al(OH)₃]+0.10]^3[/tex]
We know that [tex][OH^-] < < < < 0.10[/tex]
So, we can neglect it.
Then,
[tex]2.7\times 10^-^3^1=S'[0.10]^3[/tex]
[tex]S'=2.7\times 10^-^2^8[/tex]
Hence, the solubility of [tex]BaSO_4[/tex] is more than [tex]Al(OH)_3[/tex] as the solubility of [tex]BaSO_4[/tex] is [tex]1.048\times 10^-^5[/tex] and that of [tex]Al(OH)_3[/tex] is [tex]10^-^8[/tex]. The solubility of [tex]Al(OH)_3[/tex] will decrease in presence of [tex]0.10M[/tex] [tex]NaOH[/tex] due to the common ion effect. And the solubility of [tex]Al(OH)_3[/tex] in presence of a common ion effect will be [tex]2.7\times 10^-^2^8[/tex].