__Dissociation :__

Inorganic acids, bases and salts in aqueous solutions undergo dissociation, that is, the molecules break down into positively and negatively charged ions. In such cases, the number of effective particles increases and, therefore, osmotic pressure, elevation of boiling point and depression of freezing point are much higher than those calculated on the basis of an undissociated single molecule.

__Degree of Dissociation__

Degree of dissociation means the fraction of the total number of molecules which dissociates in the solution, that is, breaks into simpler molecules or ions.

Consider one mole of an univalent electrolyte like potassium chloride dissolved in a given volume of water. Let α be its degree of dissociation.

Then the number of moles of KCI left undissociated will be 1 – α

At the same time, α moles of K^{+} ions and α moles of Cl^{–} ions will be produced, as shown below.

KCl <—> K^{+} + Cl ^{–}

1-α α α

Thus, the total number of moles after dissociation = 1 – α + α + α = 1 + α

Hence, Since, as already, mentioned, osmotic pressure, vapour pressure lowering, boiling point elevation or freezing point depressions vary inversely as the molecular weight of the solute, it follows that

$\large i = \frac{Normal \; molar \; mass}{observed \; molar \; mass} = \frac{1+\alpha}{1}$

i = 1 + α = 1 + (2-1)α

In general, i = 1 + (n-1) α , Where, n = number of particles ( ions) formed after dissociation

From the above formula, it is clear that i > 1

Knowing, the observed molar mass and the Van’t Hoff factor, i, the degree of dissociation, α can be easily calculated.

Now, if we include Van’t Hoff factor in the formulae for colligative properties we obtain the normal results.

1. Relative lowering of vapour pressure,

$\large \frac{P_1^o – P_1}{P_1^o} = i X_2 = i \frac{n}{n + N}$

2. osmotic pressure, π = iCRT

3. Elevation in boiling point, ΔT = i. 1000 × K_{b} × molality

4. Depression in freezing point, = i 1000 × K_{f} × molality

**Note:** The value of i is taken as one when solute is non electrolyte.