Question

The osmotic pressure of a urea solution is 500 mm of Hg at $10{}^{o}C.$ The solution is diluted and its temperature is raised to $25{}^{o}C$ It is now found that osmotic pressure of the solution is reduced to 105.3 mm of Hg. The extent of dilution of the solution is

• A. 2 times
• B. 3 times
• C. 4 times
• D. 5 times

Answer 1

Answer: (D)

$\pi V=nRT$ or $\pi =\frac{n}{V}\times RT$ At $10{}^{o}C,\frac{500}{760}=\frac{n}{V}\times R\times 283$ ?(i) Suppose the solution is diluted x times, Then At $25{}^{o}C,\frac{105.3}{760}=\frac{n}{xV}\times R\times 298$ ?(ii) On dividing Eq. (i) by Eq (ii) $\frac{500}{760}\times \frac{760}{105.3}=x\times \frac{283}{298}$ $x=5,$ the solution has been diluted 5 times.