The reason why the freezing point depression of a solvent depends on the concentration, it is because the solute occupies space between the solvent molecules.
The freezing point depression of a solvent does depend on the concentration of the solute because the solute occupies space between the solvent molecules, thus reducing the number of molecules that can interact.
When a solute is dissolved in a solvent, it takes up space between the solvent molecules. This reduces the number of molecules that can interact, and thus lowers the freezing point of the solvent. The more concentrated the solution, the greater the effect on the freezing point.
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