While freezing ice from salt water, does the salt dissolve in the ice or is it separated out?

Question

I know that salt decreases the freezing point of water. We have freezing point (in Celsius), $\mathrm{T_f=-K_f\cdot m}$ (molality of salt). But, is it true that all of the solution doesn't freeze at the same temperature? (i.e. either parts of the ice form at temperature less than $0^\circ C$ but greater than $T_f$ or the process of freezing gets completed at a temperature less than $T_f$)

My question arises from the second part of the following question in my homework:

Two hypotheses came to my mind:

1. the molality of salt in the frozen part at temperature $T < 0$ is always such that the freezing point of that part is $T$

2. the molality of salt in the unfrozen part at temperature $T <T_f$ is always such that the freezing point of that part is $T$

Upon repeated trial and error, I found that the second hypothesis worked out to give the correct answer of $15g$ when I also assumed that no salt is being frozen with the ice. This was in accordance to the fact that icebergs in oceans (of salt water) are always composed of fresh water.

But, this led to another question. Like salt sugar is also a non volatile solute. How are ice lollies sweet when sugar can't be frozen into ice?

I would like to know at which part of my deduction am I going wrong.

Answer 1

Your process occurs under fractional crystallization, which is a separations process. Assuming that freezing takes place relatively "slowly" (e.g., under conditions where "flash" freezing doesn't occur), ice crystals will form in the salt water solution at a temperature below 0 C, and no salt will be incorporated in those ice crystals. As freezing proceeds, this obviously leads to higher salt concentrations in the remaining water, so the freezing temperature will drop as freezing proceeds.