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")=5.4V_("original"))`

Explanation

Let original volume`="V"_(1)`
Volume of solution after dilution`="V"_(2)`
`pi_(1)="C"_(1),"RT"implies("w"_("B")"RT"_(1))/("V"_(1))`
`pi_(2)="C"_(2),"RT"implies("w"_("B")"RT"_(2))/("V"_(2))`
`(pi_(1))/(pi_(2))=("V"_(2)"T"_(1))/("V"_(1)"T"_(2))`
`("V"_(2))/("V"_(1))=(pi_(1))/(pi_(2))xx("T"_(1))/("T"_(2))`
`(500)/(105.3)xx(298)/(283)`
`=5"(app)"`
`therefore"V"_(2)=5"V"_(1)`
Hence solution is diluted to 5 times