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Define Van’t Hoff factor. How is it related to the degree of dissociation?

Last updated date: 23rd Apr 2024
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Hint: Van’t Hoff factor is defined as the ratio of the observed or practical colligative property to the theoretical colligative property. The degree of dissociation is the proportion in which the solute gets dissociated in the solution. We can derive the relation between the degree of dissociation and Van’t Hoff factor by considering the theoretical dissociation and practical dissociation of electrolyte in the solution.

Complete step by step answer:
Colligative properties: The properties of the solution depend only on the proportion or concentration of the solute and not on the type of solute. Colligative properties include osmotic pressure, elevation in boiling point, depression in freezing point, degree of dissociation, etc.
Scientists have observed that if polar or ionic solutes are dissolved in polar solvents, they get dissociated and increase the number of particles in the solution. Due to this, the molar mass calculated comes out to be less than the theoretical molar mass, which is known as abnormal molar mass.
Similarly, certain solutes when dissolved in solution react with each other and get associated. Due to this the molar mass comes out as greater than the actual molar mass.
Now, if the concentration of a polar solute is very high in a solution, it gets difficult to find the actual molar mass of the solute. Hence, the abnormal molar mass is calculated and then from it the actual molar mass is calculated using the Van’t Hoff factor $i$ .
Van’t Hoff factor $i$ : The ratio of the actual colligative properties to the theoretical colligative properties.
OR The ratio of the actual or theoretical molar mass to the abnormal or experimental molar mass.
OR The ratio of the total ions after dissociation or association to the total ions before the dissociation or association.
The value of Van’t Hoff factor is greater than one for dissociation, smaller than one for association, and equal to one for the non-electrolyte solute.
Now, as we know that the solute or electrolyte never dissociates or associates completely when dissolved in a solvent, but only up to a fraction known as the degree of dissociation which is expressed by the symbol $\alpha $ .
To obtain the relation between Van’t Hoff factor and degree of dissociation, consider an electrolyte that gives the following reaction
${{A}_{n}}\rightleftharpoons nA$
Let the degree of dissociation be $\alpha $ at the equilibrium condition which can be expressed as,

Initial $1$$0$
Final$1-\alpha $$n\alpha $

Hence, from this the Van’t Hoff factor is defined as the ratio of total particles after dissociation to the total particles before dissociation
$\therefore i=\dfrac{1-\alpha +n\alpha }{1}$
$\therefore i=1-\alpha (1-n)$
Making degree of dissociation the subject of equation,
$\therefore \alpha (1-n)=1-i$
$\therefore \alpha =\dfrac{i-1}{n-1}$ , where $n$ is the total number of ions of the electrolyte possible
This is the relation between the Van't Hoff factor and the Degree of dissociation.

We can understand from the above explanation that weak electrolytes only dissociate to a degree $\alpha $ when dissolved in a solution. Similarly, when two weak electrolytes that can react with each other are mixed in a solution, they only associate up to a degree of $\alpha $ . This is called a degree of association which is defined as the proportion in which solute associates in a solution. The degree of association is expressed as
$\alpha =\dfrac{1-i}{1-\dfrac{1}{n}}$
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