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

For initial solution,`pi=500/760`atm,`T=283 K`
Using `piV=nRT rArr 500/760xx(V_(1))=nxxRxx283` …(i)
After dilution, let volume becomes `V_(2)` and temperature is
raised to `25^(@)C,i.e., 298 K`.
`pi=105.3/760`atm
`105.3/760xx(V_(2))=nxxRxx298` ...(ii)
`:.` By Eqs.(i) and Eqs.(ii), we get
`V_(1)/V_(2)=(283)/(298)xx(105.3)/(500)`
`V_(1)/V_(2)=1/5 rArr V_(2)=5V_(1)`
i.e., the solution was diluted to 5 times.