Hint: The Van’t Hoff factor is defined as the ratio of the observed or actual colligative property to the expected theoretical colligative property. The degree of dissociation refers to the fraction of solute that dissociates in the solution. We can establish a relationship between the degree of dissociation and the Van’t Hoff factor by examining the theoretical and practical dissociation of electrolytes in the solution.
Complete step by step answer:
Colligative properties: These are solution properties that rely solely on the quantity or concentration of the solute rather than the identity of the solute itself. Colligative properties include osmotic pressure, boiling point elevation, freezing point depression, and degree of dissociation, among others.
Scientists have noted that when polar or ionic solutes are dissolved in polar solvents, they dissociate, increasing the number of particles in the solution. As a result, the molar mass calculated appears lower than the theoretical molar mass, which is referred to as abnormal molar mass.
Conversely, certain solutes can react with one another when dissolved, causing them to associate and leading to a molar mass that is greater than the actual molar mass.
When the concentration of a polar solute is very high in a solution, determining the actual molar mass becomes challenging. Therefore, the abnormal molar mass is calculated first, and then the actual molar mass is derived using the Van’t Hoff factor, i.
Van’t Hoff factor i: This is the ratio of the observed colligative properties to the expected theoretical colligative properties.
Alternatively, it can be defined as the ratio of the actual or theoretical molar mass to the abnormal or experimental molar mass. It can also be described as the ratio of the total number of ions after dissociation or association to the total number of ions before dissociation or association.
The Van’t Hoff factor is greater than one for dissociation, less than one for association, and equal to one for solutes that are non-electrolytes.
As we know, solutes or electrolytes do not fully dissociate or associate when dissolved in a solvent; they only do so to a certain extent, referred to as the degree of dissociation, represented by the symbol α.
To obtain the relation between Van’t Hoff factor and degree of dissociation, consider an electrolyte that gives the following reaction
[latex]A_n \rightleftharpoons nA[/latex]
Let the degree of dissociation be α at the equilibrium condition which can be expressed as,
|
Initial |
1
|
0
|
|
Final |
1−α
|
nα
|
Therefore, the Van’t Hoff factor is defined as the ratio of the total number of particles following dissociation to the total number of particles prior to dissociation.
Hence, from this, the Van’t Hoff factor is defined as the ratio of total particles after dissociation to the total particles before dissociation:
[latex]i = 1 – \alpha(1 – n)[/latex]
Making the degree of dissociation the subject of the equation:
[latex]\alpha(1 – n) = 1 – i[/latex]
[latex]\alpha = \frac{i – 1}{n – 1}[/latex]
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.
Note:
From the previous explanation, we can infer that weak electrolytes dissociate only to a certain extent, denoted as α, when dissolved in a solution. Likewise, when two weak electrolytes capable of reacting with each other are combined in a solution, they associate only to a degree of α. This phenomenon is known as the degree of association, which is defined as the fraction of the solute that associates in a solution. The degree of association is represented as
[latex]\Large \alpha = \frac{1 – i}{1 – \frac{1}{n}}[/latex]