Explain depression in freezing point. Show that it is a colligative property.

Explanation

Depression in freezing point. The freezing point is the temperature at which the solid and liquid states of the substances have the same vapour pressure.
Since the addition of a non-volatile solute to the pure solvent lowers its vapour pressure, so the freezing point of a solution is expected to be less than that of the pure solvent. This is known as depression in freezing point. This has been represented graphically in Fig. The curves BC and DE represent the vapour pressure of the pure solvent and the solution respectively. The curve AB represents the vapour pressure of the solvent at different temperatures. At point B, the liquid solvent and the solid solvent meet, hence it corresponds to the freezing point of the pure liquid `(Delta T_(f)^(@))`. Since the vapour pressure of a solution is always less than that of the pure solvent, the vapour pressure curve for the solution runs parallel

but below the pure solvent curve. The vapour pressure curve for the solution meets the solid solvent curve at D which corresponds to the freezing point of the solution `T_f`. It is evident that `T_f` is less than `T_(f)^(@)` , indicating that there is depression in the freezing point of a solvent. Therefore, depression in freezing point,
`Delta T_f = T_(f)^(0)-T_(f).`
It has been experimentally found that depression in freezing point of a solution is proportional to the concentration of solute, i.e.
`Delta t_f prop m `
`or delta T_f = K_f m`
where `K_f` is the molal depression constant. It is also called molal cryoscopic constant.