Dimer of acetic acid in liquid benzene is in equilibrium with acetic acid monomer at certain temperature and pressure. If 25% of the dimer molecules are separated out then
(a)freezing point of the solution reduces
(b)average molar mass of solute increases
(c)boiling point of solution increases
(d)molar mass of solute decreases

Options

A. freezing point of the solution reduces
B. average moler mass of solute incerases
C. boiling point of solution increases
D. molarmass of solute decreases

Answer

To solve the problem, we need to analyze the effects of removing 25% of the dimer of acetic acid in liquid benzene on the properties of the solution. Here’s a step-by-step breakdown:

### Step 1: Understand Dimerization
- Acetic acid (CH₃COOH) can dimerize to form a dimer (C₂H₄O₂). In this process, two acetic acid molecules combine to form one dimer molecule through hydrogen bonding.
- The equilibrium between the dimer and monomer is represented as:
\[ 2 \text{CH}_3\text{COOH} \rightleftharpoons \text{C}_2\text{H}_4\text{O}_2 \]

### Step 2: Effect of Removing Dimer
- If 25% of the dimer molecules are removed, the concentration of dimer decreases.
- According to Le Chatelier's principle, the equilibrium will shift to the right to produce more dimer from the monomers to counteract the change.

### Step 3: Change in Van 't Hoff Factor (i)
- The Van 't Hoff factor (i) represents the number of particles the solute breaks into in solution.
- Initially, for dimerization, \( i < 1 \) because one dimer (1 particle) forms from 2 monomers (2 particles).
- When 25% of the dimer is removed, the number of dimer molecules decreases, leading to a further decrease in the Van 't Hoff factor (i), as there are fewer dimer particles compared to monomer particles.

### Step 4: Average Molar Mass of Solute
- The observed molar mass (M) of the solute can be calculated using the formula:
\[ M = \frac{M_0}{i} \]
where \( M_0 \) is the molar mass of the solute (acetic acid) and \( i \) is the Van 't Hoff factor.
- Since \( i \) is decreasing (due to the removal of dimer), the observed molar mass \( M \) will increase.

### Step 5: Analyze the Statements
- **(a)** Freezing point of the solution reduces: **False**. The freezing point depression is related to \( i \) and since \( i \) is decreasing, the freezing point depression will also decrease, but this does not mean the freezing point itself reduces.

- **(b)** Average molar mass of solute increases: **True**. As discussed, the observed molar mass increases due to the decrease in \( i \).

- **(c)** Boiling point of solution increases: **False**. Similar to freezing point, the boiling point elevation is also directly proportional to \( i \). If \( i \) decreases, the boiling point elevation decreases, but it does not mean the boiling point itself increases.

- **(d)** Molar mass of solute decreases: **False**. The molar mass of the solute (acetic acid) remains constant, but the observed molar mass increases due to the decrease in \( i \).

### Conclusion
The correct statement is:
**(b) Average molar mass of solute increases.**