Unit 8: Crystallisation & Solubility Curves

Solved Examples:

1. Why is a minimum amount of hot solvent used in recrystallisation?
   Solution: Using the minimum amount of solvent ensures that the solution is saturated or nearly saturated. This maximizes the yield of crystals that will form when the solution cools, as a larger amount of the solute will come out of the solution.
2. During purification, how are soluble impurities removed?
   Solution: Soluble impurities are removed because they remain dissolved in the cold solvent (the mother liquor) after the desired, less soluble compound has crystallized out. When the crystals are collected by filtration, the soluble impurities are washed away with the filtrate.
3. Why are the collected crystals washed with cold solvent, not hot solvent?
   Solution: They are washed with cold solvent to rinse away any remaining soluble impurities. If hot solvent were used, a significant portion of the pure crystals would redissolve, leading to a lower yield.

Solved Examples:

(Use the solubility curve graph above for the following examples)

1. What is the solubility of potassium nitrate ($KNO_3$) at 50 °C?
   Solution: Find 50 °C on the x-axis. Move up to the $KNO_3$ curve, then move left to the y-axis. The solubility is approximately 85 g / 100 g H₂O.
2. A solution contains 30 g of KCl dissolved in 100 g of water at 70 °C. Is the solution saturated or unsaturated?
   Solution: At 70 °C, the solubility of KCl is approximately 48 g / 100 g H₂O. Since the solution only contains 30 g, it is unsaturated.
3. A saturated solution of $KNO_3$ in 100 g of water is cooled from 60 °C to 20 °C. How much solid $KNO_3$ will crystallize out?
   Solution:
   - Solubility at 60 °C ≈ 108 g.
   - Solubility at 20 °C ≈ 32 g.
   - Mass crystallized = (Solubility at 60 °C) - (Solubility at 20 °C) = 108 g - 32 g = 76 g.
4. At what temperature does NaCl have the same solubility as KNO₃?
   Solution: Find the point where the curves for NaCl and KNO₃ intersect. This occurs at approximately 22 °C.
5. How much water is needed to dissolve 200 g of sugar ($C_{12}H_{22}O_{11}$) at 90 °C? (Assume sugar curve is similar to $KNO_3$ for this example, solubility at 90°C is ~200g/100g water)
   Solution: The solubility at 90 °C is approximately 200 g per 100 g of water. Therefore, 100 g of water is needed.
6. Which substance on the graph becomes less soluble as temperature increases?
   Solution: Cerium(III) sulfate, $Ce_2(SO_4)_3$. Its curve slopes downwards, which is unusual for a salt.
7. What is the maximum mass of NaCl that can be dissolved in 200 g of water at 100 °C?
   Solution: At 100 °C, the solubility of NaCl is 40 g per 100 g of water. In 200 g of water, you can dissolve twice that amount: $40 \times 2 = 80$ g of NaCl.