The freezing point of a pure liquid is fixed. If a non-volatile solute is dissolved in a liquid the freezing point of the solution is lowered. The freezing point is that temperature at which the solvent has the same vapour pressure in two phases liquid solution and solid solvent. Since the solvent vapour pressure in solution is depressed, its vapour pressure will become equal to that of the solid solvent at a lower temperature

`Delta T_f = T_f^o -T_f`

It is found that depression in freezing point is directly proportional to the number of moles of the solute in given amount of the solvent(`m`).

Hence., `DeltaT_f prop m`

`DeltaT_f = K_f m`

Where `m`= molality of solution

`K_f = ` molal depression constant

When molarity (`m`) of the solution is one, then

`Delta T_f = K_f`

Hence molal depression constant or molal cryoscopic constant may be defined as the depression in freezing point when one mole of non-volatile solute is dissolved per kilogram (`1000` gm) of solvent and molar depression constant is defined as the depression in freezing point when one mole of non-volatile solute is dissolved per litre (`1000` ml) of solvent. The molecular mass of the non-volatile solute may be calculated by the use of following mathematical equation

`M_B = (K_f xx W_B xx 1000)/(W_A xx Delta T_f)`

Where `W_A =` mass of solvent, `W_B =` mass of solute,

`M_A =` Molar mass of solvent, `M_B =` Molar mass of solute.

`text(Determination of)` `K_f` `text(of solvent)` : `K_f` is characteristic of a particular solvent and can be calculated from the thermodynamical relationship.

`K_f = (RT_f^2)/(1000L_f)............................(3)`

where `T_f` is the freezing point of solvent in absolute scale and `L_f`, the latent heat of fusion in calories per gram of the solvent. For water,

`K_f = (0.002 xx (273)^2)/80 = 1.86 K-kg/text(mole)`

If energy is taken in joule then use `R= 8.314 JK^(-1) text(mole)^(-1)`
Energy is taken in calorie then use `R = 2 cal K^(-1) text(mole)^(-1)`

`text(Antifreeze solutions)` : Water is used in radiators of vehicles as cooling liquid. If the vehicle is to be used at high altitudes where temperature is sub-zero, water would freeze in radiators. To avoid this problem, a solution of ethylene glycol in water is used in radiators which will lower the freezing point lower than zero.