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Question

# Consider two sparingly soluble salts AB and AC. If AB has solubility as x mol Lâˆ’1 in presence of AC , and AC has solubility as y mol Lâˆ’1 in presence of AB. Which of the following relations are correct?

A
Ksp1Ksp2=xy
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B
xy=Ksp1+Ksp2
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C
x+y=Ksp1+Ksp2
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D
Ksp2Ksp1=xy
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Solution

## The correct option is C x+y=√Ksp1+Ksp2Simultaneous solubility: Sparingly soluble salt 1: AB having x mol L−1 solubility in the presence of AC Sparingly soluble salt 2: AC having y mol L−1 solubility in the presence of AB AB(s)⇌ A+(aq)+B−(aq) with Ksp1 Equilibrium:C1−x x+y x AC(s)⇌ A+(aq)+C−(aq) with Ksp2 Equilibrium:C2−y y+x y From the above reactions the Ksp values are Ksp1=(x)(x+y) −(1) Ksp2=(y)(x+y) −(2) Dividing both the equations Ksp1Ksp2=xy Adding both the equations Ksp1+Ksp2=(x+y)2 x+y=√Ksp1+Ksp2 ∴ Option A and option C are correct.

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