First slide
Solubility product(KSP)
Question

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

Moderate
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)

\large {K_{sp}} = {\left( {3{S_3}} \right)^3} \times {S_3} = 27S_3^4

Given, \large 4S_1^3=S_2^2=27S_3^4

S3 > S1 > S2

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