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Question

Consider a sparingly soluble salt (AB) with concentration C1 and highly soluble salt (AX) with concentration C2. Then which of the following relation holds true?
(Assume Ksp(AB)<<103)

A
Ksp=sC1
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B
Ksp=sC2
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C
s=KspC1
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D
s=KspC2
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Solution

The correct option is D s=KspC2
Consider sparingly soluble salt (AB) with concentration C1 and highly soluble salt (AX) with concentration C2
AX(aq)A+(aq)+X(aq)
C2
C2+s C2
AB(s)A+(aq)+B(aq)
C1
C1s s+C2 s

Solubility of AB is s because out of C1, s moles has dissociated only into ions.

Here A+ is the common ion in above reactions.

Ksp=[A+][B]
Ksp=(s+C2)(s)
Since AX is highly soluble ,
s+C2C2 because of the sparingly soluble salt where Ksp<<103
Ksp=(C2)(s)
s=KspC2


Theory:
Solubility in presence of common ion:
Consider an aqueous solution of PbCrO4(s)

The equilibrium between the undissolved solid and the ions in a saturated solution can be represented by the equation:
PbCrO4(s)Pb2+(aq)+CrO24

PbCrO4 is sparingly soluble salt in an aqueous solution. If in the solution, K2CrO4 is added. The common ion formed is CrO24.
The backward reaction is favoured when [CrO24] increases, and thus the solubility is further reduced.

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