Sir,Can you please explain how The Lowering Of Freezing Point occurs in a solution,in terms of the vapour pressures of the solution and of the solid solvent and also with respect to the chemical potential of the system ?

 let's consider what happens to the vapor pressure of the solvent when we add a solute to form a solution!~ We'll define P^o as the vapor pressure of the pure liquid the solvent and P as the vapor pressure of the solvent after a solute has been added!~

P^o = vapor pressure of the pure liquid, or solvent!~

P = vapor pressure of the solvent in a solution!~

When the temperature of a liquid is below its boiling point, we can assume that the only molecules that can escape from the liquid to form a gas are those that lie near the surface of the liquid!~

When a solute is added to the solvent, some of the solute molecules occupy the space near the surface of the liquid, as shown in the figure below!~ When a solute is dissolved in a solvent, the number of solvent molecules near the surface decreases, and the vapor pressure of the solvent decreases!~

This has no effect on the rate at which solvent molecules in the gas phase condense to form a liquid!~ But it decreases the rate at which the solvent molecules in the liquid can escape into the gas phase!~ As a result, the vapor pressure of the solvent escaping from a solution should be smaller than the vapor pressure of the pure solvent!~

Between 1887 and 1888, Francois-Marie Raoult showed that the vapor pressure of a solution is equal to the mole fraction of the solvent times the vapor pressure of the pure liquid!~

This equation, which is known as Raoult's law, is easy to understand!~ When the solvent is pure, and the mole fraction of the solvent is equal to 1, P is equal to P^o!~ As the mole fraction of the solvent becomes smaller, the vapor pressure of the solvent escaping from the solution also becomes smaller!~

Let's assume, for the moment, that the solvent is the only component of the solution that is volatile enough to have a measurable vapor pressure!~ If this is true, the vapor pressure of the solution will be equal to the vapor pressure of the solvent escaping from the solution!~ Raoult's law suggests that the difference between the vapor pressure of the pure solvent and the solution increases as the mole fraction of the solvent decreases!~

The change in the vapor pressure that occurs when a solute is added to a solvent is therefore a colligative property!~ If it depends on the mole fraction of the solute, then it must depend on the ratio of the number of particles of solute to solvent in the solution but not the identity of the solute!~

Raoult's law :

Which states that the addition of solute to a liquid lessens the tendency for the liquid to become a solid or a gas, i.e., reduces the freezing point and the vapor pressure vapor pressure, pressure exerted by a vapor that is in equilibrium with its liquid. A liquid standing in a sealed beaker is actually a dynamic system: some molecules of the liquid are evaporating to form vapor and some molecules of vapor are condensing to form liquid.

(solution is the homogeneous mixture of two or more substances. The dissolving medium is called the solvent , and the dissolved material is called the solute. A solution is distinct from a colloid or a suspension .

 For example, the addition of salt to water causes the water to freeze below its normal freezing point (0°C;) and to boil above its normal boiling point (100°C;). Qualitatively, depression of the freezing point and reduction of the vapor pressure are due to a lowering of the concentration of water molecules, since the more solute is added, the less the percentage of water molecules in the solution as a whole and therefore the less their tendency to form into a crystal solid or to escape as a gas. Quantitatively, Raoult's law states that the solvent's vapor pressure in solution is equal to its mole mole, in chemistry, a quantity of particles of any type equal to Avogadro's number, or 6.02×10²³ particles. One gram-molecular weight of any molecular substance contains exactly one mole of molecules.

 fraction times its vapor pressure as a pure liquid, from which it follows that the freezing point depression and boiling point elevation are directly proportional to the molality of the solute, although the constants of proportion are different in each case. This mathematical relation, however, is accurate only for dilute solutions. The fact that an appropriate solute can both lower the freezing point and raise the boiling point of a pure liquid is the basis for year-round antifreeze for automobile cooling systems. In the winter the antifreeze lowers the freezing point of the water, preventing it from freezing at its normal freezing point; in the summer it guards against boilover by raising the boiling point of the water