Question

Osmotic pressure of urea solution is 380 mm at a temperature of ${10}^o$ C. The solution is diluted and the temperature is raised to ${30}^o$ C and the osmotic pressure is found to be 122 mm. The extent of dilution will be:

• A. $V_{final}=4V_{initial}$
• B. $3V_{final}=10V_{initial}$
• C. $V_{final}=5V_{initial}$
• D. $V_{final}=2V_{initial}$

Answer 1

The correct option is B $3V_{final}=10V_{initial}$

osmotic pressure(P) is directly proportional to temperature(T) and inversely proportional to volume of solution(V) if number of moles in the solution are kept constant ( i.e. the solution is diluted )

P1 = kTi/Vi ......where k is some constant

P2 = kTf/Vf......

taking ratio we have

P1 / P2 = (Ti x Vf)/(Tf x Vi)

substitute P1 = 380mm, P2 = 122mm, Ti = 10+273=283, Tf = 30+273=303

thus we have 3Vf = 10Vi.....OR

3Vfinal = 10Vinitial