1. Tardigrade
  2. Question
  3. Chemistry
  4. The osmotic pressure of a urea solution is 500 mm of Hg at 10 oC. The solution is diluted and its temperature is raised to 25 oC 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

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Q. 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

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Solution:

$ \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.