**Colligative properties – a relative lowering of vapor pressure**

As per the definition, those solution’s properties which is dependent on solute molecules’ number, regardless of their behavior, w.r.t to total molecules’s number having its presence in the solution are defined as the **colligative properties**.

For the solution, freezing point’s depression, relative vapor pressure’s lowering, boiling point elevation, and the osmotic pressure are known as the colligative properties which finds a tremendous apllication in your routine life.

**Relative Lowering of Vapour Pressure**

Vapor pressure refers to pressure applied by the vapors on the liquid under equilibrium conditions at some give temperature. At present, we have taken the example of the pure liquid, the liquid’s surface is occupied by liquid’s molecules.

Let us assume a solute which is non-volatile in nature now it’s added in this pure liquid.

Since the molecules present in the solute are of non-volatile nature, therefore the vapor formed above solution is having molecules of solvent only which is a pure liquid. After the addition of solute, solution’s vapour pressure is seen at lower level in comparison to pure liquid at the given temperature.

This relative reduction in the pressure of vapor is because of the fact that after addition of solvent (pure liquid), the surface of liquid is now having molecules of pure liquid and solute, both.

Solvent molecules’ number escapes into vapor state and it gets reduced and as the result is – the pressure is applied by the vapour phase is reduced too. This is called the relative lowering of vapour pressure. This reduction in the pressure of vapor is dependent on non-volatile solutes’ amount which is added to the solution regardless of its behavior and therefore, it’s one of the “colligative properties”.

Moreover, for the given solvent-solute mass ratio, whole of the colligative properties are propotional inversely to the molar mass of solute.

Measuring colligative properties of a non-ionized solute for the dilute solution like glucose or urea in water or any other solvent can result in determining the relative molar mass for both polymers and small molecules which can’t be studied by any other means. As an alternate option, for ionized solutes, the separation percentage can result into calculation of dissociation percentage which occurs.

Mostly the Colligative properties are studied in relation to dilute solutions. The solutions whose nature might generally be approximated like of the ideal solution.

**The Mathematical Representation**

Now you’ll understand and see that how this vapor pressure’s lowering is mathematically determined:

Now presume a binary solution having solvent’s mole fraction as x1 and x2 of solute.

P1 = solvent’s vapor pressure

P2 = solvent’s vapor pressure in pure form

As per Raoult’s Law:

**p1=x1p2…………………………..(1)**

The reduction in vapour pressure of the solvent (∆p1) is given by:

**=> ∆p1=p2-p1**

**=> ∆p1=p2-p21** **[using equation (1)]**

**=> ∆p1=p2 (1-x1)**

Since we have assumed the solution to be binary solution, **x2=1-x1**

**=> ∆p1=p2x2**

**=> x2= ∆p1/p2**

The above-mentioned equation provides you “the relative lowering in vapour pressure” that is equal to solute’s mole fraction.