Freezing point depression represents the variation in the freezing temperature of a pure solvent from that of the solvent in solution. In the equation ΔT=Kf m i, where i is the van’t Hoff factor, Kf represents the molal freezing point depression constant, also called the cryoscopic constant.
The change in the freezing temperature of pure solvent from that of its solution is calculated by using two constants. These are multiplied by the molality of the solution in moles per kilogram. In the relevant equation, ΔT represents the change in freezing temperature of the pure solvent from that of the solution, and m represents the molal concentration of the solution.
This concept is easily demonstrable by working an example. Take a solution of 1.6g of naphthalene dissolved in 20g of benzene. The freezing point of pure benzene is 5.5 degrees Celsius and that of the mixture is 2.8 degrees Celsius. It is therefore possible to calculate the Kf of the solution as follows:
ΔT is 5.5 - 2.8 = 2.7 degrees Celsius.
Moles of Naphthalene in solution = (1.6) (1/128) = 0.0125.
Therefore, the molality of the solution is 0.0125 mol / 0.02 kg = 0.625 m.
Per the equation, 2.7= (Kf) (0.625m); therefore, Kf= (2.7)/(0.625).
In this example, the molal freezing point depression constant for the solution equals 4.3 degrees Celsius/m.