My teacher gave the following diagram in the class notes. He said that when a solution containing a non-volative solute (for e.g. a solution of $\ce{NaCl}$ in water) is freezed, then there will be some depression in freezing point and some part of the solution will freeze and some part won't freeze due to the presence of the non-volatile solute. My teacher said that the non-volatile solute which is trapped in the solid solvent will gradually move into the solution which has not freezed and make it more and more concentrated until finally we get a pure solid solvent on one side and a highly concentrated solution containing the non-volatile solute on the other side. But why does the non-volatile solute go into the part of the solution which has not freezed? I mean it is trapped in the solid solvent, right? So, why does it go into the liquid part? In the diagram $\ce{NaCl}$ is moving from frozen water to liquid water and eventually all of the $\ce{NaCl}$ from the frozen water will go into the liquid part. But why does this happen? What is the reason behind this? Please explain. I am so confused. Please help (In the diagram the arrows show the movement of the $\ce{NaCl}$).

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1The solute stays in solution, the lattice of the solid does not accommodate it. – Karsten May 07 '21 at 03:08
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It is hard to follow quite what is going on. If the NaCl/water/ice is frozen it is at a lower temperature than the liquid water, so some, if not all this frozen mush will melt and the whole become a NaCl solution. – porphyrin May 07 '21 at 07:26
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there is a phase diagram in this answer. https://chemistry.stackexchange.com/questions/116302/where-does-the-energy-come-from-to-lower-the-temperature-of-a-brine-solution/116316#116316 What happens depends where you are on this plot. – porphyrin May 07 '21 at 07:53
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I invite you to use the first comment by Karsten Theis for an easy to grasp sense of the story. – Alchimista May 07 '21 at 09:00