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At $0 ° C$ , urea solution has an osmotic pressure of $400 mm$ . On dilution by $x$ times, its osmotic pressure decreased to $100 mm$ at $20 ° C$ . The dilution factor $x$ is approximately

A $4.3$
B $2$
C $5$
D $6.8$

Verified Solution

Answer & Solution

Correct Answer

(A) $4.3$

Step-by-step Solution

Detailed explanation

π1=C1ST1; π2=C2ST2; π1π2=C1T1C2T2 For initial solution, π1=400760 atm, T1=273K After dilution, let volume becomes V2 and temperature is raised to 20°C, i.e., T2=293 K. and π2 = 100760 atm On putting the…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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At 0°C, urea solution has an osmotic pressure of 400 mm. On dilution by x times, its osmotic pressure decreased to 100 mm at 20°C. The dilution factor x is approximately

Step-by-step Solution

At $0 ° C$ , urea solution has an osmotic pressure of $400 mm$ . On dilution by $x$ times, its osmotic pressure decreased to $100 mm$ at $20 ° C$ . The dilution factor $x$ is approximately