Question

Acetic acid dimerises in Benzene solution. The Van’t Hoff factor for the dimerization of Acetic acid is $0.8$. The percentage of dimerization of Acetic acid will be:
A. $20\%$
B. $40\%$
C. $60\%$
D. $80\%$

Answer 1

When Acetic acid is added to the solution of Benzene the dimerization of acid takes place. Also the Van’t Hoff factor is given for this dimerization of acid. Thus by using the relation between the van't Hoff factor and degree of association we can find the percentage of dimerization for acetic acid.

Formula used:
$i{\text{ = }}\dfrac{{1 - \alpha {\text{ + }}\dfrac{\alpha }{n}}}{1}$
Where, $i$ is known as the Van't Hoff factor, $\alpha$ is known as the degree of association and $n$ is the atomicity of a product. Here $n$ is equal to two.

Complete answer:
When acetic acid is added with benzene then a dimer of acetic acid is formed. This can be represented by using the chemical representation as,
${\text{C}}{{\text{H}}_{\text{3}}}{\text{COOH }} \rightleftharpoons {\text{ }}{\left( {{\text{ C}}{{\text{H}}_3}{\text{COOH}}} \right)_2}$
For the above reaction, we can use a relation between the degree of association and the Van't Hoff factor.
$i{\text{ = }}\dfrac{{1 - \alpha {\text{ + }}\dfrac{\alpha }{n}}}{1}$
Here, we are given with $i{\text{ = 0}}{\text{.8}}$ and since it forms a dimer so the value of $n$ is two. $i{\text{ = }}\dfrac{{1 - \alpha {\text{ + }}\dfrac{\alpha }{n}}}{1}$
On substituting the values we get the result as,
${\text{0}}{\text{.8 = }}\dfrac{{1 - \alpha {\text{ + }}\dfrac{\alpha }{2}}}{1}$
$\Rightarrow \alpha {\text{ = 0}}{\text{.4}}$
Hence the degree of association is ${\text{0}}{\text{.4}}$ , for finding the percentage of degree of association we can convert it into percentage as,
Percentage of association${\text{ = 0}}{\text{.4 }} \times {\text{ 100}}$
Percentage of association ${t{ = 40\% }}$
Therefore, the percentage of association is ${{ 40\% }}$. Therefore, the correct option is option (B).

Note:
$\alpha$ can be a degree of association or degree of dissociation. It depends on the reaction whether association takes place or dissociation takes place. The relation which we use in the above problem is valid for such reactions only. We can also derive the relation by calculating the total number of moles after some extent of association. When the particle of solute gets associated, $i$ will be less than one. When solute particles dissociate then the value of $i$ will be greater than one.