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Osmotic pressure of urea solution is 56.6 mm Hg at a temperature of 10° C. The solution is diluted, and the temperature is raised to 40° C such that the osmotic pressure is found to be 31.3 mm Hg. The extent of dilution will be :

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$V_{final} = 10 V_{initial}$

$V_{final} = 2 V_{initial}$

$2 V_{final} = 3 V_{initial}$

$V_{final} = 20 V_{initial}$

answer is B.

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Detailed Solution

$\frac{π_{1}}{C_{1} T_{1}} = \frac{π_{2}}{C_{2} T_{2}} \Rightarrow \frac{56.6}{C_{1} \times 283} = \frac{31.0}{C_{2} \times 313} \Rightarrow C_{1} = 2 C_{2}$

Hence, volume must have doubled.

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