MY and $\mathrm{N}{\mathrm{Y}}_3$ , two nearly insoluble salts, have the same ${\mathrm{K}}_{\mathrm{s}\mathrm{p}}$ values of $6.2\times {10}^{-13}$ at room temperature. Which statement would be true in regard to MY and $\mathrm{N}{\mathrm{Y}}_3$ ?

• A

  The molar solubilities of MY and $\mathrm{N}{\mathrm{Y}}_3$ in water are identical.
• Correct answer
  B

  The molar solubility of MY in water is less than that of $\mathrm{N}{\mathrm{Y}}_3$ .
• C

  The salts MY and $\mathrm{N}{\mathrm{Y}}_3$ are more soluble in 0.5 M KY than in pure water.
• D

  The addition of the salt of KY to solution of MY and $\mathrm{N}{\mathrm{Y}}_3$ will have no effect on their solubilities.

Solution

MY insoluble salt $K_{sp}=s^2$



$N{Y}_3$ salt $K_{sp}=s{\left(3s\right)}^3$

$=27s^4$

$S={\left(\frac{k_{sp}}{27}\right)}^{\frac{1}{n}}$

$S_{N{Y}_3}$ $={\left(\frac{K_{sp}}{27}\right)}^{\frac{1}{4}}$ $={\left(\frac{6.2\times {10}^{-13}}{27}\right)}^{\frac{1}{4}}$

$\therefore {\mathrm{S}}_{\left(\mathrm{M}\mathrm{Y}\right)}=\sqrt{6.2\times {10}^{-13}}=7.8\times {10}^{-7}$

Solubility values

$\therefore {\mathrm{S}}_{\left(\mathrm{M}\mathrm{Y}\right)}<{\mathrm{S}}_{\left(\mathrm{N}{\mathrm{Y}}_3\right)}$

Hence, the correct answer is option: 'B'.