# At the freezing point, why is the vapor pressure of the liquid phase equal to the vapor pressure of the solid phase?

At the freezing point of a substance, the solid phase is in dynamic equilibrium with the liquid phase. My textbook defines the freezing point of a substance as: "the temperature at which the vapor pressure of the substance in its liquid phase is equal to its vapor pressure in the solid phase". Why is this so? How does the vapor phase even come into the picture during freezing? Shouldn't it be all about the solid and the liquid?

My book also states that when we add a non volatile solute to a liquid solvent, "the solution will freeze at the temperature when its vapor pressure is equal to the vapor pressure of the pure solid solvent". This doesn't make sense to me as well. Assuming the first statement is true, shouldn't the second statement read, "...is equal to the vapor pressure of the solid solution"? Are the two statements somehow related to each other?And why are they true?

• Vapor per se does not really come into the picture, except maybe in some specific setup. It is that we mention vapor pressure as a measure of activity of the substance. Commented Dec 29, 2016 at 8:02
• I find the first statement to be a bit of a stretch. It is a certain feature of any substance that the vapour pressure of solid and liquid are equal at the freezing point. The inverse statement is only true because in equillibrium, water does not exist below 0 °C, and neither does ice above. Might even turn out false if you look at a supercooled liquid.
– Karl
Commented Dec 29, 2016 at 11:40
• And the second statement is overstretched so far it turns wrong. The actual freezing is a process that is strongly kinetically hindered, to state that it will happen at a certain temperature only from thermodynamic reasoning is nonsense. Ah, and the point is that you will not get a solid solution but nearly pure frozen solvent.
– Karl
Commented Dec 29, 2016 at 11:55
• The vapour pressure comes in because via Raoult's law the activities (or free energy /mole) are equal in the crystal and liquid at the freezing point. In a solution on cooling the solvent separates out as a crystal while the solute remains in solution being insoluble in the crystallised solvent. When at a temperature T the solution is in equilibrium with crystal T is the freezing point and the chemical potentials of the two phases (crystal/solution) are equal. Commented Dec 29, 2016 at 14:36