Benzoic acid dimerises and its observed molecular wt. becomes 152.5, its van't Hoff factor will be

Options

A. 0.75
B. 0.875
C. 0.8
D. 1.125

Answer

To find the van't Hoff factor (i) for benzoic acid that dimerizes, we can follow these steps:

### Step 1: Understand the Dimerization Process
Benzoic acid (C6H5COOH) dimerizes, meaning that two molecules of benzoic acid combine to form a dimer. The reaction can be represented as:
\[ 2 \text{C}_6\text{H}_5\text{COOH} \rightleftharpoons \text{(C}_6\text{H}_5\text{COOH)}_2 \]

### Step 2: Determine the Molar Mass
The molar mass of a single molecule of benzoic acid is 122 g/mol. When two molecules dimerize, the observed molecular weight of the dimer is given as 152.5 g/mol.

### Step 3: Calculate the Van't Hoff Factor
The van't Hoff factor (i) is defined as the ratio of the actual number of particles in solution after dissociation to the number of formula units initially dissolved.

Using the formula:
\[ i = \frac{\text{actual molar mass}}{\text{observed molar mass}} \]

### Step 4: Substitute the Values
- Actual molar mass of benzoic acid = 122 g/mol
- Observed molar mass = 152.5 g/mol

Substituting these values into the formula:
\[ i = \frac{122 \, \text{g/mol}}{152.5 \, \text{g/mol}} \]

### Step 5: Perform the Calculation
Calculating the above expression:
\[ i = \frac{122}{152.5} \approx 0.8 \]

### Conclusion
The van't Hoff factor (i) for benzoic acid dimerization is approximately 0.8.

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