Question

At ${10}^{\circ }C$, the osmotic pressure of urea solution is $500mm$. The solution is diluted and the temperature is raised to ${25}^{\circ }C$, when the osmotic pressure is found to be $105.3mm$. Determine extent of dilution?

• A. Sol.$(V_{final}=5V_{original})$
• B. Sol.$(V_{final}=7V_{original})$
• C. Sol.$(V_{final}=3V_{original})$
• D. None of the above
  

Answer 1

The correct option is A Sol.$(V_{final}=5V_{original})$

The osmotic pressure $\pi =CRT$

For original solution

$500mm=C_{original}\times R\times (10+273)K$.....(1)

For diluted solution

$105.3mm=C_{final}\times R\times (25+273)K$.....(2)

Divide equation (1) with equation (2)

$\frac{500mm}{105.3mm}=\frac{C_{original}}{C_{final}}\frac{\times (10+273)K}{(25+273)K}$

$\frac{500mm}{105.3mm}=\frac{C_{original}}{C_{final}}\frac{\times (10+273)K}{(25+273)K}$

$\frac{C_{original}}{C_{final}}=5$

But $\text{Concentration}\propto \frac{1}{\text{Volume}}$

$\frac{V_{final}}{V_{original}}=5$

$V_{final}=5V_{original}$