Acetic acid dimerises in benzene solution.The van't Hoff factor for the dimerisation of acetic acid is 0.8. The % of dimerisation of acetic acid is

Options

A. 0.2
B. 0.4
C. 0.6
D. 0.8

Answer

To solve the problem of determining the percentage of dimerization of acetic acid in benzene solution, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Dimerization**:
Acetic acid (CH₃COOH) dimerizes in solution to form a dimer (CH₃COOH)₂. This means that two molecules of acetic acid combine to form one dimer.

2. **Defining the Van't Hoff Factor (i)**:
The van't Hoff factor (i) is defined as the ratio of the total number of particles in solution after dissociation or association to the number of particles initially present. For dimerization, the van't Hoff factor is given as 0.8.

3. **Setting Up the Initial Conditions**:
Let's assume we start with 1 mole of acetic acid. Before dimerization, we have:
- Moles of CH₃COOH = 1
- Moles of (CH₃COOH)₂ = 0

4. **Defining Degree of Dimerization (α)**:
Let α be the degree of dimerization. This means that α moles of acetic acid will dimerize. After dimerization, the remaining moles of acetic acid will be:
- Moles of CH₃COOH remaining = 1 - α
- Moles of (CH₃COOH)₂ formed = α/2 (since 2 moles of acetic acid form 1 dimer).

5. **Calculating Total Moles After Dimerization**:
The total number of moles after dimerization can be expressed as:
\[ \text{Total moles} = (1 - α) + \frac{α}{2} \]

6. **Setting Up the Equation for Van't Hoff Factor**:
The van't Hoff factor can be expressed as:
\[ i = \frac{\text{Total moles after dimerization}}{\text{Initial moles}} = \frac{(1 - α) + \frac{α}{2}}{1} \]
Given that \( i = 0.8 \), we can set up the equation:
\[ 0.8 = (1 - α) + \frac{α}{2} \]

7. **Solving the Equation**:
Rearranging the equation:
\[ 0.8 = 1 - α + \frac{α}{2} \]
\[ 0.8 = 1 - \frac{α}{2} \]
\[ \frac{α}{2} = 1 - 0.8 = 0.2 \]
\[ α = 0.4 \]

8. **Calculating Percentage of Dimerization**:
The percentage of dimerization can be calculated as:
\[ \text{Percentage of dimerization} = α \times 100 = 0.4 \times 100 = 40\% \]

### Final Answer:
The percentage of dimerization of acetic acid is **40%**.