Dissociation of Solute Molecules

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A number of electrolytes dissociate in solution to give two or more particles (ions). Therefore, the number of solute particles, in solution of such substances is more than the expected value. Accordingly, such solutions exhibit higher values of colligative properties.

Since the colligative properties are inversely related to molecular masses, therefore, molecular masses of such substances are calculated from colligative properties will be less than their normal values.

For e.g., KCl dissociates to K⁺ and Cl^- ions when dissolved in water. So the number of solute particles in its solution would be double the number of particles if no dissociation had taken place. Hence, it is expected to have molecular mass equal to half of its normal molecular mass i.e., 74.5/2 = 37.25. However, the molecular mass of 40.3 was found by studies of depression in freezing point. The difference in the two values is due to strong attractive forces present in the oppositely charged ions of the strong electrolyte in solution.

Vant Hoff's Factor

Vant Hoff introduced a factor 'i' called Vant Hoff factor to express the extend of association or disassociation of solute i is related to normal and observed molecular masses of the solute as,

In case of association, observed molecular mass is more than the normal. The factor i has value less than one. But in the case of dissociation the Vant Hoff factor is more than one because the observed molecular mass has a lesser value than the normal molecular mass. In case there is no dissociation or association the value of i becomes equal to one. Since the colligative property is inversely proportional to the molecular masses. The Vant Hoff 's factor may be written as

If no association or dissociation of solute particles takes place in the solution, then

The introduction of Vant Hoff's factor modifies the equations for the colligative properties as follows.

Using the value of 'i' (Vant Hoff 's factor) the degree of dissociation of a strong electrolyte and the degree of association can be calculated.

Degree of dissociation (a)

It is the fraction of the total number of molecules, which dissociate into simpler ions i.e.,

If a molecule of an electrolyte when dissolved in a solvent dissociates to give n ions and a is the degree of dissociation. Now if we start with 1 mole of the solute in solution, at equilibrium, there will be (1-a) moles of undissociated molecules and na moles of the ions. Then total number of particles of solute in the solution is

= 1- a + na = 1+(n-1) a

Van't Hoff factor

i = Vant Hoff 's factor

n = Number of ions provided by one formula unit.

Example: n = 2 for NaCl, n = 3 for BaCl₂

Degree of association (a)

It is the fraction of the total number of molecules, which associate forming bigger molecules i.e.,

Now for a solute A if n simple molecules associate to form a associated molecule A_n

and if a is the degree of association and we start with 1 mole of solute A, then at equilibrium

Number of moles of A = 1 - a

Number of moles of A_n = a/n

\ Total number of moles of particles in the solution is

Then,

where n is the number of molecules which associate form the larger molecule.

Example: n for acetic acid and benzoic acid = 2.