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Difficulty: MediumSolubility Curves and Temperature Effects

A saturated solution of potassium chloride, KCl\text{KCl} (molar mass = 74.5 g mol−174.5\text{ g mol}^{-1}), has a solubility of 4.0 mol dm−34.0\text{ mol dm}^{-3} at 80∘C80^\circ\text{C} and 1.5 mol dm−31.5\text{ mol dm}^{-3} at 20∘C20^\circ\text{C}. If 600 cm3600\text{ cm}^3 of this saturated solution at 80∘C80^\circ\text{C} is cooled to 20∘C20^\circ\text{C}, what mass of KCl\text{KCl} will crystallize out of the solution?

  1. 111.75 g111.75\text{ g}Answer
  2. B
    67.05 g67.05\text{ g}
  3. C
    178.80 g178.80\text{ g}
  4. D
    1.50 g1.50\text{ g}

Answer

The mass of KCl\text{KCl} that crystallizes out of the solution is 111.75 g111.75\text{ g}.
The correct answer is 111.75 g111.75\text{ g}. Cooling 0.60 dm30.60\text{ dm}^3 of saturated solution from 80∘C80^\circ\text{C} to 20∘C20^\circ\text{C} reduces the solubility by 2.5 mol dm−32.5\text{ mol dm}^{-3}, causing 1.50 mol1.50\text{ mol} of KCl\text{KCl} to precipitate. Multiplying 1.50 mol1.50\text{ mol} by the molar mass (74.5 g mol−174.5\text{ g mol}^{-1}) yields 111.75 g111.75\text{ g}.

Step-by-Step Solution

1
Convert the volume of the solution from cm3\text{cm}^3 to dm3\text{dm}^3.
V=600 cm31000=0.60 dm3V = \frac{600\text{ cm}^3}{1000} = 0.60\text{ dm}^3
Concentration is given in mol dm−3\text{mol dm}^{-3}, so volume must be in dm3\text{dm}^3.
2
Calculate the difference in solubility between 80∘C80^\circ\text{C} and 20∘C20^\circ\text{C}.
ΔC=4.0 mol dm−3−1.5 mol dm−3=2.5 mol dm−3\Delta C = 4.0\text{ mol dm}^{-3} - 1.5\text{ mol dm}^{-3} = 2.5\text{ mol dm}^{-3}
This represents the number of moles of solute precipitated per dm3\text{dm}^3 of solution upon cooling.
3
Calculate the number of moles crystallized in 0.60 dm30.60\text{ dm}^3 of solution.
n=2.5 mol dm−3×0.60 dm3=1.50 moln = 2.5\text{ mol dm}^{-3} \times 0.60\text{ dm}^3 = 1.50\text{ mol}
Scaling the molar amount precipitated to the specified solution volume.
4
Convert moles of crystallized salt to mass in grams.
\text{Mass} = 1.50\text{ mol} \times 74.5\text{ g mol}^{-1} = 111.75\text{ g}
Using the relation mass=moles×molar mass\text{mass} = \text{moles} \times \text{molar mass}.

Key Concept

Crystallization from Saturated Solutions on Cooling
Estimated Time:1m 30s
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Topics

Solubility Curves and Temperature Effects

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