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.

Options

A. `V_("final")=5V_("initial")`
B. `V_("initial")gtV_("final")`
C. `V_("final")=4V_("initial")`
D. `V_("final")=6V_("initial")`

Answer

A

Explanation

For initial solution,
`becausepi=(500)/(760)atm,T=283K`
`:.(500)/(760)xxV_("Initial")=nxxRxx283` . . . (i)
After dilution
`:. (105)/(760)xxV_("Final")=nxxRxx298` . . . (ii)
From Eqs. (i) and (ii), we get
`(V_("Initial"))/(V_("Final"))=(1)/(5)i.e.` solution was diluted to 5 times.