Question

Two salts A₂X and MX have the same value of solubility product of 4.0 × 10⁻¹². The ratio of their molar solubilities i.e., `("S"("A"_2"X"))/("S"("MX")` = ______. (Round off to the Nearest Integer)

Options

• 20

• 30

• 40

• 50

Answer 1

Two salts A₂X and MX have the same value of solubility product of 4.0 × 10⁻¹². The ratio of their molar solubilities i.e., `("S"("A"_2"X"))/("S"("MX")` = 50.

Explanation:

\[\ce{AX2(s) <=> A^{2+}(aq) + 2X^-(aq)}\]

Let's solubility is x mol/L

[A²⁺] = x mol/L

[X⁻] = 2x mol/L

K_sp = [A²⁺].[X⁻]²

4 × 10⁻¹² = [x].[2x]²

4 × 10⁻¹² = 4x³

x = 10⁻⁴ = \[\ce{S_{AX_2}}\]

Like that solubility product for MX

\[\ce{MX_{(s)} <=> M^+_{ (aq)} + X^-_{( aq)}}\]

K_sp = [M⁺].[X⁻]

4 × 10⁻¹² = [x].[x]

4 × 10⁻¹² = x²

x = 2 × 10⁻⁶ = \[\ce{S_{MX}}\]

So, the ratio of their molar solubilities

= `("S"_("AX"_2))/("S"_"MX")`

= `10^-4/(2 xx 10^-6)`

= 50