Question

Solubility product of an electrolyte at a particular temperature is defined as the product of conc. of its ions in a saturated solution, each conc. raised to the power equal to the number of ions produced on dissociation of one molecule of the electrolyte.
$A_x{B}_y\rightleftharpoons x{A}^{+}+y{B}^{-}$
$K_{sp}={\left[A^{+}\right]}^x{\left[B^{-}\right]}^y$
Ionic product of the electrolyte $A_x{B}_y$ is also equal to ${\left[A^{+}\right]}^x{\left[B^{-}\right]}^y$ but it is applicable to all types of solutions, which may be saturated or unsaturated.
.Three sparingly soluble salts $M_{2}B,MB$ and $M{B}_3$ have the same solubility product. Their solubilities will be in the order

• A. $M{B}_3>M_{2}B>MB$
• B. $MB>M_{2}B>M{B}_3$
• C. $M{B}_3>MB>M_{2}B$
• D. $MB>M{B}_3>M_{2}B$

Answer 1

Answer: (B)

For $MB\rightleftharpoons M^{+}+B^{-},K_{sp}=s_1^2$ or $s_1=\sqrt{K_{sp}}$
For $M_{2}B\rightleftharpoons 2M^{+}+B^{2-};K_{sp}=4s_2^3$
or $s_2=\sqrt[3]{\frac{K_{sp}}{4}}$
For $M{B}_3\rightleftharpoons M^{3+}+3B^{-};K_{sp}=27s_3^4$
$=r{s}_3=\sqrt[4]{\frac{K_{sp}}{27}}$
Hence $s_1>s_2>s_3$