## Raoult’s Law:

### Statement:

The partial vapour pressure of any volatile component of a solution is the product of vapour pressure of that pure component and the mole fraction of the component in the solution.

#### Explanation:

• Let us consider a solution containing two volatile components say A1 and A2, with mole fractions x1 and x2 respectively. Let  p10 and  p2be the vapour pressures of the pure components A1 and A2 respectively, then by Raoult’s law

p1 = p10 x1   and   p2 = p20 x2

• The total vapour pressure of the solutions of two volatile components is the sum of partial vapour pressures of the two components. • The solution which obeys Raoult’s law over the entire range of concentration is called an ideal solution. If a solution does not obey Raoul’s law are called non-ideal solutions.

### Raoult’s Law for a Solution of Non-Volatile Solute:

• Let us consider a solution containing two volatile component A1 and non-volatile component A2, with mole fractionsx1 and x1 respectively.
• Let p10 and  p2be the vapour pressures of the pure components A1 and A2 respectively. Now component A2 is non-volatile, hence it will not contribute to vapour pressure. Thus  p2= 0. We have • Thus vapour pressure of a solution of non-volatile solute is the product of vapour pressure p10 of pure solvent and mole fraction x1  of the solvent, which is Raoult’s law.
• The equation shows that vapour pressure of the solution p < p10 ,  i.e. there is lowering of the vapour pressure of the solution.
The lowering of vapour pressure is given by • In a solution containing several non-volatile solutes, the lowering of the vapour pressure depends on the sum of the mole fraction of different solutes.
Now, the relative lowering of vapour pressure is given by • This relation proves that the lowering of vapour pressure is colligative property because it depends on the concentration of non-volatile solute.

### Raoult’s Law as Special Case of Henry’s Law:

• By Raoult’s law, we have • By Henry’s law, we have • If we compare the two equations for Raoult’s law and Henry’s law, it can be seen that the partial pressure of the volatile component or gas is directly proportional to its mole fraction in solution. Only the proportionality constant KH differs from p10 . Thus, Raoult’s law becomes a special case of Henry’s law in which KH is equal to p10.

### Relation Between Molar Mass of Solute and Lowering of Vapour Pressure:

Let W2 g of the solute of molar mass M2 be dissolved in W1 g of the solvent of molar mass M1. The number of moles of solvent and solute are given by The mole fraction of solute is given by Now for dilute solutions n2 << n1. Hence n2 can be neglected. This is the relation between the molar mass of solute and lowering of vapour pressure.