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Chemistry · 2023 · 3 marks
CBSE 2023 · Region 4 · Set 1 · Q29
If benzoic acid ( M =122 g mol^-1) is associated into a dimer when dissolved in benzene and the osmotic pressure of a solution of 6.1 g of benzoic…
If benzoic acid $\displaystyle \left(\mathrm{M}=122 \mathrm{~g} \mathrm{~mol}^{-1}\right)$ is associated into a dimer when dissolved in benzene and the osmotic pressure of a solution of $\displaystyle 6.1$ g of benzoic acid in $\displaystyle 100$ mL benzene is $\displaystyle 6.5$ atm at $\displaystyle 27^{\circ} \mathrm{C}$, then what is the percentage association of benzoic acid ? (Given : $\displaystyle \mathrm{R}=0.0821 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ )
Marking-scheme solution
\[\begin{aligned}
\pi & =i \frac{n_{B}}{V} \mathrm{R} T \\
6 \cdot 5 & =i \times \frac{W_{B}}{\mathrm{M}_{B}} \times \frac{1000}{V} \times 0.0821 \\
6 \cdot 5 & =i \times \frac{6 \cdot 1}{122} \times \frac{1000}{100 ~ L} \times 0.0821 \times 300 \mathrm{~K} \\
i & =\frac{6.5 \times 122}{6 \cdot 1 \times 0.0821 \times 300 \times 10}=0.528 \\
\alpha & =\frac{1-i}{1-\dfrac{1}{n}}=\frac{1-0.528}{1-\dfrac{1}{2}}=0.944 \text { or } 94.4 \%
\end{aligned}
\]
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CBSE Class 12 Chemistry past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.