At `17^(@)C`, the osmotic pressure of sugar solution is 580 torr. The solution is diluted and the temperature is raised to `57^(@)C`, when the osmotic pressure is found to be 165 torr. The extent of dilution is
a.2 times ,b.3 times ,c.4 times ,d.5 times

Explanation

c.Given
`T_(i)=17^(@)C=290 K,T_(f)=57^(@)C=330 K`
`pi(i)=580 "torr"=580/760 mm Hg`
`pi(f)=165 "torr"=165/760 mm Hg`
Using equation
`pi=CRT`
`580/760=C_(i) xx R xx 290` ….(i)
`165/760=C_(f) xx R xx 330` ….(ii)
Dividing Eq. (i) by Eq. (ii), we get
`C_(i)/C_(f)=2/1//2=4 rArr` Dilution = 4 times