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Question

Solubility product constant (Ksp) of salts of types MX,MX2 and MX3 at temperature T are 4.0×108,3.2×1014 and 2.7×1015 respectively. Solubilities (mol dm3) of the salts at temperature 'T' are in the order :

A
MX>MX2>M3X
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B
M3X>MX2>MX
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C
MX2>M3X>MX
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D
MX>M3X>MX2
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Solution

The correct option is D MX>M3X>MX2
Let 's' be the solubilityMX(s)M+(aq)+X(aq)
Then solubility product Ksp=[M+][X] s s

Ksp=s2
or s=Ksp
s=4×108=2×104

Similarly, for MX2
MX2(s)M2+(aq)+2X(aq) s 2s

Ksp=[M2+][X]2
Ksp=s×(2s)2=4s3
or s=[Ksp4]13
s=[3.2×10144]13=[324×1015]13
s=[8×1015]13
s=2×105

and for MX3
MX3(s)M3+(aq)+3X(aq) s 3s

Ksp=[M3+][X]3
Ksp=s×3s3=27s4
or s=[Ksp27]14
s=[2.7×101527]14
s=[1016]14
s=104
Thus the solubilities are in the order MX>MX3>MX2
i.e the correct answer is (d).

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