Question

The scientist van’t Hoff introduced a factor (i) to account for the extent of association or dissociation of solutes. It is mathematically expressed as:

i = `"normal molecular mass"/"experimental molecular mass"`

In case of association, i < 1 and in case of dissociation i > 1.

1. In the calculation of molecular mass of K₄[Fe(CN)₆] by using a colligative property, what will be the value of van’t Hoff factor if the solute is 25% dissociated?
2. Find the value of van’t Hoff factor for a dilute aqueous solution of benzoic acid in water when it is completely associated to form a dimer.

Answer 1

i. The dissociation equation is:

\[\ce{K4[Fe(CN)6] <=> 4K+ + [Fe(CN)6]^{4-}}\]

This means that one molecule of K₄[Fe(CN)₆] dissociates into 5 particles (4K⁺ and 1 [Fe(CN)₆]⁴⁻).

Degree of dissociation (α) = 25% = 0.25

Van’t Hoff factor (i) is calculated as:

i = 1 + α(n − 1)

Where,

n = total number of particles after dissociation (5)

α = 0.25

Initial undissociated solute = 1

i = 1 + (0.25 × (5 − 1))

= 1 + (0.25 × 4)

= 1 + 1

= 2

Thus, the Van’t Hoff factor for K₄[Fe(CN)₆] with 25% dissociation is 2.

ii. The effect of solute particles on colligative qualities is measured by the van’t Hoff factor (i). The van’t Hoffman factor is less than one for a solute that experiences association. The quantity of dissolved particles falls in the case of benzoic acid (C₆H₅COOH), which fully combines in solution to create dimers (C₆H5COOH)₂, resulting in a decrease in colliding characteristics. At this point, the benzoic acid association process is:

\[\ce{2C6H5COOH -> (C6H5COOH)2}\]

Before association, there are two benzoic acid particles. There is one dimer particle following the association.

i = `"number of particles after association"/"number of particles before association"`

= `1/2`

= 0.5

Therefore, when benzoic acid is fully linked to form a dimer, the Van’t Hoff factor for a diluted aqueous solution of the acid in water is 0.5.