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

Answer

`(V_("final") =5V_("original"))`

Explanation

For initial solution,
`:' pi = (500)/(760) atm, T = 283 K`
`(500)/(760) xx V_(1) = n xx S xx 283` ..(i)
After dilution, let volume becomes `V_(2)` and temperature is raised to `25^(@)C` i.e, `298K`
`pi = (105.3)/(760) atm`
`(105.3)/(760) xx V_(2) = n xx S xx 298` ...(ii)
`:.` By Eqs. (i) and (ii), we get
`(V_(1))/(V_(2)) = (283)/(298) xx (105.3)/(500) (V_(1))/(V_(2)) = (1)/(5)`
`:. V_(2) = 5V_(1)`
i.e, solution was diluted to 5 times.