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 intial solution ,
`pi = (500)/(760) atm , T = 273 + 10 = 283 K`
Let volume of solution is `V_(1)`
`pi = (n)/(V) RT`
`(500)/(760) = (n)/(V_(1)) xx R xx 283`
After dilution , let the volumes `V_(2)` and temperature is raised to `25^(@)C`
` pi = (105.3)/(760) atm , T = 273 + 25 = 298 K`
Dividing eq(i) by eq(ii) .
`(500)/(105.3) = (V_(2))/(V_(1)) xx (283)/(298)`
or `" "(V_(2))/(V_(1)) (500 xx 298)/(105.3 xx 283) = 5`
`therefore ` The solution was diluted 5 times.