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.

Explanation

Suppose initially the volume of solution `=V_(1)`
`"Given "T=10+273K = 283 K, pi=(500)/(7760)" atm"`
`pi="CRT"=(pi)/(V)=RT" "therefore" "(500)/(600)=(n)/(V_(1))Rxx283" …(i)"`
After dilution, suppose volume of solution `=V_(2)`
`"Given "T=25+273K=298K, pi=(105.3)/(760)" atm"`
`therefore" "(105.3)/(760)=(n)/(V_(2))Rxx298" (n = no. of moles which remains same) ...(ii)"`
Dividing eqn. (i) by eqn. (ii)
`(500)/(105.3)=(V_(2))/(V_(1))xx(283)/(293)" or "(V_(2))/(V_(1))=(500)/(105.3)xx(298)/(283)=5" or "V_(2)=5V_(1)`
Thus, solution has been diluted 5 times.