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Difficulty: MediumSolubility, Solubility Curves, and Solubility Product (Ksp)

The solubility of a sparingly soluble salt MX2MX_2 (molar mass =200 g mol−1= 200\text{ g mol}^{-1}) in water at 25∘C25^\circ\text{C} is 0.20 g dm−30.20\text{ g dm}^{-3}. What is the solubility product (KspK_{sp}) of MX2MX_2 at this temperature?

  1. A
    1.0×10−9 mol3 dm−91.0 \times 10^{-9}\text{ mol}^3\text{ dm}^{-9}
  2. 4.0×10−9 mol3 dm−94.0 \times 10^{-9}\text{ mol}^3\text{ dm}^{-9}Answer
  3. C
    2.0×10−9 mol3 dm−92.0 \times 10^{-9}\text{ mol}^3\text{ dm}^{-9}
  4. D
    3.2×10−2 mol3 dm−93.2 \times 10^{-2}\text{ mol}^3\text{ dm}^{-9}

Answer

The solubility product (KspK_{sp}) of MX2MX_2 at 25∘C25^\circ\text{C} is 4.0×10−9 mol3 dm−94.0 \times 10^{-9}\text{ mol}^3\text{ dm}^{-9}.
To find the solubility product (KspK_{sp}), first convert the solubility from g dm−3\text{g dm}^{-3} to molar solubility (ss) in mol dm−3\text{mol dm}^{-3} by dividing by the molar mass: s=0.20200=1.0×10−3 mol dm−3s = \frac{0.20}{200} = 1.0 \times 10^{-3}\text{ mol dm}^{-3}. The dissociation equation MX2(s)⇌M2+(aq)+2X−(aq)MX_2(s) \rightleftharpoons M^{2+}(aq) + 2X^-(aq) yields [M2+]=s[M^{2+}] = s and [X−]=2s[X^-] = 2s. Substituting these into the solubility product expression gives Ksp=[M2+][X−]2=4s3=4×(1.0×10−3)3=4.0×10−9 mol3 dm−9K_{sp} = [M^{2+}][X^-]^2 = 4s^3 = 4 \times (1.0 \times 10^{-3})^3 = 4.0 \times 10^{-9}\text{ mol}^3\text{ dm}^{-9}.

Step-by-Step Solution

1
Convert solubility from g dm−3\text{g dm}^{-3} to molar solubility (ss) in mol dm−3\text{mol dm}^{-3}
s=Solubility in g dm−3Molar Mass=0.20 g dm−3200 g mol−1=1.0×10−3 mol dm−3s = \frac{\text{Solubility in g dm}^{-3}}{\text{Molar Mass}} = \frac{0.20\text{ g dm}^{-3}}{200\text{ g mol}^{-1}} = 1.0 \times 10^{-3}\text{ mol dm}^{-3}
Solubility product calculations require concentration units in mol dm−3\text{mol dm}^{-3}.
2
Write the ionic dissociation equation and express equilibrium concentrations
MX2(s)⇌M2+(aq)+2X−(aq)MX_2(s) \rightleftharpoons M^{2+}(aq) + 2X^-(aq)
[M2+]=s=1.0×10−3 mol dm−3[M^{2+}] = s = 1.0 \times 10^{-3}\text{ mol dm}^{-3}
[X−]=2s=2.0×10−3 mol dm−3[X^-] = 2s = 2.0 \times 10^{-3}\text{ mol dm}^{-3}
Each mole of MX2MX_2 yields 1 mole of M2+M^{2+} and 2 moles of X−X^- upon dissolution.
3
Write the KspK_{sp} expression and calculate the numerical value
Ksp=[M2+][X−]2=(s)(2s)2=4s3=4×(1.0×10−3)3=4.0×10−9 mol3 dm−9K_{sp} = [M^{2+}][X^-]^2 = (s)(2s)^2 = 4s^3 = 4 \times (1.0 \times 10^{-3})^3 = 4.0 \times 10^{-9}\text{ mol}^3\text{ dm}^{-9}
Substitute the molar equilibrium concentrations into the equilibrium constant expression.

Key Concept

Relationship between Molar Solubility and Solubility Product (KspK_{sp})
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Topics

Solubility, Solubility Curves, and Solubility Product (Ksp)

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