Question 13.4: Applying Solubility Data in Fractional Crystallization A sol...

(a) Using Figure 13-8, we estimate that the solubility of NH_4Cl at 20 °C is 37 g NH_4Cl/100  g  H_2O. The quantity of NH_4Cl in the saturated solution at 20 °C is

200.0  g  H_2O \times \frac{37  g  NH_4Cl}{100  g  H_2O} = 74  g  NH_4Cl

The mass of NH_4Cl recrystallized is 95 – 74 = 21 g NH_4Cl.

(b) The yield of NH_4Cl in (a) is rather poor−21 g out of 95 g, or 22%. We can do better: (1) The solution at 60 °C, although concentrated, is not saturated. Using Figure 13-8, we estimate that a saturated solution at 60 °C has 55 g NH_4Cl/100  g  H_2O. Thus, the 95 g NH_4Cl requires less than 200.0 g H_2O to make a saturated solution. At 20 °C, a smaller quantity of saturated solution would contain less NH_4Cl than in (a), and the yield of recrystallized NH_4Cl would be greater. (2) Instead of cooling the solution to 20 °C, we might cool it to 0 °C. Here the solubility of NH_4Cl is less than at 20 °C, and more solid would recrystallize. (3) Still another possibility is to start with a solution at a temperature higher than 60 °C, say closer to 100 °C. The mass of water needed for the saturated solution would be less than at 60 °C. Note that options (1) and (3) both require changing the conditions by using a different amount of water from that originally specified.

Assess
The amount of dissolved salt can be increased by increasing the volume of solvent or by increasing the temperature. Keep in mind that fractional crystallization works best when the quantities of impurities are small and the solubility curve of the desired solute rises steeply with temperature.