# Freezing Point - Depression In Freezing Point

In this section, we will learn about the depression in the freezing point of a solvent when mixed with a solute. As we know, the vapor pressure of any liquid decreases with the decrease in its temperature. When the temperature of pure water kept at 25°C is decreased, it starts to freeze eventually after attaining the temperature of 0°C, as at this temperature the vapor pressure of the water sample becomes equal to the vapor pressure of the ice under those conditions.

Freezing point: The freezing point of a substance is defined as the temperature at which the vapor pressure of the liquid becomes equal to the vapor pressure in its solid state at those conditions as at the freezing point; the solid phase of a substance attains a state of dynamic equilibrium with the liquid phase.

As per the Raoult’s law, the vapor pressure of a pure solvent decreases with the addition of a solute. As the vapor pressure of a non-volatile solvent is zero, so the overall vapor pressure of the solution is lesser than that of the pure solvent.

Vapour pressure vs temperature

In the graph shown above, we can see the change in vapor pressure of a pure solvent and a solution with the increase in temperature. Here, we can see that the two samples, the solvent, and the solution, will attain the condition of freezing when their vapor pressure becomes equal to that of the frozen sample of the pure solvent. We can see here, the pure solvent attains this condition at a temperature equal to Tf° whereas, for the solution to attain this pressure, the temperature of the sample needs to be decreased further by a small amount equal to ΔTf, such that,

Here the value ΔTf is the depression in freezing point. The value of ΔTf for a solution depends upon the number of molecules of the non-volatile solute. It has been shown experimentally that the depression in freezing point is directly proportional to the molal concentration of the solute in a solution.

freezing point vs molal concentration

Where, kb is the freezing point depression constant or the cryoscopic constant and m is the molality of the solution that is equal to the number of moles of solute dissolved in 1 kg of solvent.