Final answer:
Solution b, containing 0.50 mol of KCl and 0.50 mol of MgCl₂ (both strong electrolytes), will have a lower freezing point than solution a with 1.0 mol of urea and 2.0 mol of ethylene glycol (both nonelectrolytes), due to the greater number of solute particles resulting from the dissociation of the electrolytes.
Step-by-step explanation:
The student has asked to identify which solution will have a lower freezing point: a solution containing 1.0 mol of urea and 2.0 mol of ethylene glycol (both nonelectrolytes) or a solution containing 0.50 mol of KCl and 0.50 mol of MgCl₂ (both strong electrolytes), each dissolved in 1.0 kg of water.
When considering freezing point depression, the colligative properties of solutions must be considered. The freezing point depression is a colligative property that depends on the number of solute particles in a solvent, not their identity. Thus, we determine the number of solute particles produced in each solution. Nonelectrolytes, like urea and ethylene glycol, do not dissociate into ions and therefore contribute a single particle per molecule to the solution.
On the other hand, strong electrolytes like KCl and MgCl₂ dissociate into ions when dissolved in water. KCl dissociates into two ions (K+ and Cl-), and MgCl₂ dissociates into three ions (Mg2+ and 2 Cl-), increasing the total number of particles in the solution. The more solute particles there are, the lower the freezing point of the solution will be. Therefore, solution b, containing 0.50 mol of KCl and 0.50 mol of MgCl₂, will have a lower freezing point than solution a, containing 1.0 mol of urea and 2.0 mol of ethylene glycol, because the ions from the electrolytes result in a higher total number of dissolved particles.