`20.27g` of benzene containing `0.2965g` of benzoic acid (mol.wt. `=122`)freezes at `0.137^(@)` below the freezing point of pure benzene. If benzoic acid exists as dimer in benzene, find its degree of association. `K_(f)` for benzene is `5.12^(@)C.m^(-1)`

Explanation

To solve the problem, we need to determine the degree of association of benzoic acid in benzene, given the freezing point depression and the mass of the solute and solvent.

### Step-by-Step Solution:

1. **Calculate the moles of benzoic acid (C₇H₆O₂)**:
\[ \text{Moles of benzoic acid} = \frac{\text{mass}}{\text{molar mass}} = \frac{0.2965 \, \text{g}}{122 \, \text{g/mol}} = 0.00243 \, \text{mol} \]
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