The osmotic pressure of urea solution is `500 mm` at `10^(@)C`. The solution is diluted and the temperature raised to `25^(@)C`, when the osmotic pressure is found to be `105.3 mm`. Find the extend if dilution.

Answer

5

Explanation

`because pi V = nST`
Initially `pi_(1) = (500)/(760)atm, T_(1) = 283K`
`(500)/(760) xx V_(1) = nS xx 283` …(1)
Let on dilution, the volume become `V_(2)` and temperature raise to `25^(@)C` i.e., `298K`
`pi_(2) = (105.3)/(760)`
Now `(105.3)/(760) xx V_(2) = nS xx 298` ...(2)
By eq. (1) and (2)
`(V_(1))/(V_(2)) = (283)/(298) xx (105.3)/(500)`
`:. V_(1)//V_(2) = 1//5`
or `V_(2) = 5V_(1)`
`:.` Solution is `5` times diluted.