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NEET CHEMISTRYEasy

What is the molarity of the saturated solution if the solubility product for a salt of type AB is 4×1084 \times 10^{-8}?

A

2×104 mol/L2 \times 10^{-4} \text{ mol/L}

B

16×1016 mol/L16 \times 10^{-16} \text{ mol/L}

C

2×1016 mol/L2 \times 10^{-16} \text{ mol/L}

D

4×104 mol/L4 \times 10^{-4} \text{ mol/L}

Step-by-Step Solution

For a salt of type AB\text{AB}, the dissociation equilibrium in its saturated solution is: AB(s)A+(aq)+B(aq)\text{AB}(s) \rightleftharpoons \text{A}^+(aq) + \text{B}^-(aq)

If SS is the molar solubility (molarity of the saturated solution), then the equilibrium concentrations of the ions are: [A+]=S[\text{A}^+] = S [B]=S[\text{B}^-] = S

The solubility product constant (KspK_{sp}) is given by the product of the ion concentrations: Ksp=[A+][B]=S×S=S2K_{sp} = [\text{A}^+][\text{B}^-] = S \times S = S^2

Given that Ksp=4×108K_{sp} = 4 \times 10^{-8}: S2=4×108S^2 = 4 \times 10^{-8} S=4×108=2×104 mol/LS = \sqrt{4 \times 10^{-8}} = 2 \times 10^{-4} \text{ mol/L}

Therefore, the molarity of the saturated solution is 2×104 mol/L2 \times 10^{-4} \text{ mol/L}.

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