The solution water curve is shifted below the curve for pure water because the RT ln x solution water term is less than zero. When the ice curve intersects with a liquid curve, the chemical potentials are equal and the phases are in equilibrium. The intersections correspond to freezing points. On the graph, T 0 is the freezing point of the pure water. The lower chemical potential of solution water shifts the point of intersection to the left, so the freezing point of the solution is lower than the freezing point of the pure solvent.
T is the freezing point of the solution.
Similar arguments can be used to explain why boiling points of solutions are higher than those of the pure solvent. Assume the solution is ideal. If we can assume that the solution is very dilute, the equation becomes much simpler. That would suggest that equal concentrations of ions or molecules cause equal freezing point depressions, regardless of what the solute is. Experimental results agree with this prediction, so long as the concentrations are low.