Final answer:
The student's question pertains to the degree of dissociation of water when KNO₃ is dissolved, lowering the freezing point. The calculation involves using the freezing point depression constant and the van't Hoff factor, assuming full dissociation of KNO₃. However, the exact degree of dissociation of water is not provided and is not needed for the calculation.
Step-by-step explanation:
The student is asking about the degree of dissociation of water when 1 mol of KNO₃ is dissolved in it, decreasing the freezing point by 3.01°C. The colligative properties of solutions, which include freezing point depression, are used to understand this phenomenon. The van't Hoff factor (i) plays a critical role here as it accounts for the number of particles into which a compound dissociates in solution. For KNO₃, which fully dissociates into K⁺ and NO₃⁻, the factor i would be 2 (1 mol of KNO₃ yields 1 mol of K⁺ + 1 mol of NO₃⁻). Knowing the freezing point depression constant (Kf) for water and the change in freezing point (ΔTf), we can calculate the molal concentration of the solution (Μ) using ΔTf = Kf × m × i.
Given that Kf for water is 1.86°C/m, and the freezing point depression observed is 3.01°C, the calculation would look like this:
ΔTf = Kf × m × i
3.01 = 1.86 × m × 2
m = 3.01 / (1.86 × 2) = 0.8102 m
However, because the degree of dissociation is not given in the question nor required for this calculation, the initial assumption that KNO₃ fully dissociates (degree of dissociation = 100%) is used. Thus, the degree of dissociation of water is not directly determined from the information given.