Molecules of benzoic acid `(C_(6)H_(5)COOH)` dimerise in benzene. ‘w’ g of the acid dissolved in 30g of benzene shows a depression in freezing point equal to 2K. If the percentage association of the acid to form dimer in the solution is 80, then w is : (Given that `K_(f)=5K Kg "mol"^(-1)` Molar mass of benzoic acid `=122 g "mol"^(-1)`)

Options

A. 2.4g
B. 1.5g
C. 1.0g
D. 1.8g

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the Dimerization of Benzoic Acid
Benzoic acid (C₆H₅COOH) dimerizes in benzene to form a dimeric structure. This means that two molecules of benzoic acid combine to form one dimer.

### Step 2: Calculate the Van 't Hoff Factor (i)
Given that 80% of benzoic acid associates to form dimers, we can calculate the van 't Hoff factor (i):
- Let x be the degree of association.
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