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 xA ^{+}+ yB ^{-} $
$K _{ sp }=\left[ A ^{+}\right]^{ x }\left[ B ^{-}\right]^{ y }$
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 $MB _{3}$ have the same solubility product. Their solubilities will be in the order

• A. $MB _{3}> M _{2} B > MB$
• B. $MB > M _{2} B > MB _{3}$
• C. $MB _{3}> MB > M _{2} B$
• D. $MB > MB _{3}> M _{2} B$

Answer 1

Answer: (B)

For $MB \rightleftharpoons M ^{+}+ B ^{-}, K _{ sp }= s _{1}^{2}$ or $s _{1}=\sqrt{ K _{ sp }}$
For $M _{2} B \rightleftharpoons 2 M ^{+}+ B ^{2-} ; K _{ sp }=4 s _{2}^{3}$
or $s _{2}=\sqrt[3]{\frac{ K _{ sp }}{4}}$
For $MB _{3} \rightleftharpoons M ^{3+}+3 B ^{-} ; K _{ sp }=27 s _{3}^{4}$
$=r s_{3}=\sqrt[4]{\frac{K_{s p}}{27}}$
Hence $s _{1}> s _{2}> s _{3}$