QJEEAdv04Ch178e: JEE Advanced 2004 Chemistry - Class 12 JEEAdv04Ch178e Solution: 1.22 g of benzoic acid is dissolved in 100 g of acetone and 100 …

(1) If molar mass of C₆H₅COOH is Mg mol ^{$-$ 1}, then no. of moles of dissolved C₆H₅COOH = ${{1.22} \over M}$ mol

$\therefore$ Molality (m) of the solution = ${{1.22} \over M} \times {{1000} \over {100}} = {{12.2} \over M}$ mol kg ^{$-$ 1}

We know, $\Delta$ T_b = k_b $\times$ m

Given : $\Delta$ T_b = 0.17 K and k_b = 1.7 K kg mol ^{$-$ 1}

$\therefore$ $0.17 = 1.7 \times {{12.2} \over M}$ or, M = 122

$\therefore$ Molecular mass of C₆H₅COOH is = 122

(2) If molar mass of C₆H₅COOH is M', then no. of moles of dissolved C₆H₅COOH = ${{1.22} \over {M'}}$ mol

Molality (m) of the solution = ${{1.22} \over {M'}} \times {{1000} \over {100}} = {{12.2} \over {M'}}$ mol kg ^{$-$ 1}

We know, $\Delta$ T_b = 0.13 K and k_b = 2.6 K kg mol ^{$-$ 1}

$\therefore$ $0.13 = 2.6 \times {{12.2} \over {M'}}$ or, M' = 244

$\therefore$ Molecular weight of C₆H₅COOH = 122

Now, van't Hoff factor (i) = ${{Calculated\,molecular\,weight} \over {Experimental\,molecular\,weight}} = {{122} \over {244}} = {1 \over 2}$

$i = {1 \over 2}$ indicates that C₆H₅COOH undergoes complete dimerisation in benzene.