Three sparingly soluble salts that have same solubility products are given below :

I) A₂X II) AX III) AX₃

Their solubilities in a saturated solution will be such that

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II > III > I

II > I > III

III > I > II

III > II > I

answer is B.

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Detailed Solution

$\large {A_2}X(s) \rightleftharpoons \mathop {{A_2}X}\limits_{{S_1}} (aq) \to \mathop {2{A^ + }}\limits_{2{S_1}} (aq) + \mathop {{X^{ - 2}}}\limits_{{S_1}} \left( {aq} \right)$

$\large {K_{sp}} = {\left( {2{S_1}} \right)^2} \times {S_1} = 4S_1^3$

$\large AX(s) \rightleftharpoons \mathop {AX}\limits_{{S_2}} (aq) \to \mathop {{A^ + }}\limits_{{S_2}} (aq) + \mathop {{X^ - }}\limits_{{S_2}} {\text{(aq)}}$

$\large {K_{sp}} = S_2 \times {S_2} = S_2^2$

$\large A{X_3}(s) \rightleftharpoons \mathop {A{X_3}}\limits_{{S_3}} (aq) \to \mathop {{A^{ + 3}}}\limits_{{S_3}} (aq) + \mathop {3{X^ - }}\limits_{3{S_3}} (aq)$