The molecular weight of benzoic acid in benzene as determined by depression in the freezing point method corresponds to

Options

A. Ionization of benzoic acid
B. Dimerization of benzoic acid
C. Trimerization of benzoic acid
D. Solvation of benzoic acid

Explanation

To solve the question regarding the molecular weight of benzoic acid in benzene as determined by the depression in the freezing point method, we will follow these steps:

### Step 1: Understand the Concept of Freezing Point Depression
The freezing point depression is a colligative property that depends on the number of solute particles in a solution. When a solute is added to a solvent, the freezing point of the solvent decreases. The formula for calculating the depression in freezing point (ΔTf) is given by:

\[ \Delta T_f = K_f \cdot m \]

where \( K_f \) is the cryoscopic constant of the solvent and \( m \) is the molality of the solution.

### Step 2: Determine the Molecular Weight of Benzoic Acid
The molecular formula of benzoic acid is \( C_6H_5COOH \). To calculate its molecular weight:

- Carbon (C): 12 g/mol, and there are 7 carbon atoms (6 from the benzene ring and 1 from the carboxylic group).
- Hydrogen (H): 1 g/mol, and there are 6 hydrogen atoms (5 from the benzene ring and 1 from the carboxylic group).
- Oxygen (O): 16 g/mol, and there are 2 oxygen atoms.

Calculating the total molecular weight:

\[ \text{Molecular weight} = (7 \times 12) + (6 \times 1) + (2 \times 16) = 84 + 6 + 32 = 122 \text{ g/mol} \]

### Step 3: Observed Molecular Weight from Freezing Point Depression
When benzoic acid is dissolved in benzene, the observed molecular weight calculated from the freezing point depression method is found to be 244 g/mol.

### Step 4: Calculate the Van't Hoff Factor (i)
The Van't Hoff factor (i) is calculated using the formula:

\[ i = \frac{\text{Actual molecular weight}}{\text{Observed molecular weight}} \]

Substituting the values:

\[ i = \frac{122 \text{ g/mol}}{244 \text{ g/mol}} = \frac{1}{2} \]

### Step 5: Interpret the Van't Hoff Factor
The Van't Hoff factor indicates the number of particles the solute breaks into in solution. Since \( i = \frac{1}{2} \), this suggests that 1 molecule of benzoic acid associates to form 2 particles in solution, which is indicative of dimerization.

### Step 6: Conclusion
Since the observed molecular weight is double the actual molecular weight, this indicates that benzoic acid undergoes dimerization in benzene. Therefore, the molecular weight of benzoic acid in benzene, as determined by the depression in the freezing point method, corresponds to the dimerization of benzoic acid.

### Final Answer
The molecular weight of benzoic acid in benzene as determined by the depression in the freezing point method corresponds to **dimerization of benzoic acid**.

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