# Depression of Freezing Point by a Non-Volatile Solute

At the freezing point of pure solvent the rates at which its molecules stick together to form a solid and leave it to return to a liquid are equal.

When a solute is present fewer solvent molecules in solution are in contact with surface of the solid because solute particles get in their way. Therefore, solvent molecules adhere to the surface more slowly.
However the rate at which molecules leave the solid which is pure solvent is unchanged. Therefore even at the melting point of pure solvent there is net flow of molecules away from the solid and solid melts. Only if temperature is lowered will that flow be stopped and the equilibrium restored.

Freezing point is the temperature at which solid and liquid states of a substance have the same vapour pressure. It is observed that the freezing point of the solution (Tf) containing non volatile solute is always less than the freezing point of the pure solvent (Tf°) .

Thus, Tf° – Tf = ΔTf

It can be seen that

ΔTf ∝ molality

that, is freezing point depression of a dilute solution is directly proportional to the number of moles of the solute dissolved in a given amount of the solvent and is independent of the nature of solute or ΔTf = Kfm

Kf : molal freezing point depression constant of the solvent or cryoscopic constant

m : molality of the solution

Molal freezing point depression constant of the solvent or cryoscopic constant, is defined as the depression in freezing point which may theoretically be produced by dissolving 1 mole of any solute in 1000g of the solvent.

or , $\large \Delta T_f = \frac{1000 \times K_f \times w}{m_1 \times W}$

where m1 = molecular weight of solute and w and W are weights of solute and solvent

By the use of phase diagram we can show why the normal boiling point of water is raised by addition of a non volatile solute while the freezing point is lowered