Question

At ${10}^{0}C$ the osmotic pressure of urea solution is 500 mm of Hg .The solution is diluted and the temperature is raised to ${25}^{0}c$. When the osmotic pressure is found to be 105.3 mm of Hg. Determine extent of dilution.

• A. Two times
• B. Three times
• C. Four times
• D. Five times

Answer 1

The correct option is D Five times

${\pi }_1=MRT$

${\pi }_1=\frac{\omega }{(M.\omega t)}\times \frac{1}{V_1\left(lit\right)}\times R{T}_1$

${\pi }_1=\frac{K{T}_1}{V_1\left(lit\right)}$

${\pi }_2=\frac{K{T}_2}{V_2}$

$\frac{{\pi }_1}{{\pi }_2}=\frac{T_1{V}_2}{V_2{T}_2}$

$\frac{V_1}{V_2}=\frac{T_1{\pi }_2}{T_2{\pi }_1}$

$\Rightarrow \frac{283\times 105.3}{298\times 500}$

$V_1=0.2V_2$

$V_2=\frac{1}{0.2}{V}_1$

$V_2=5V_1$

Hence, the correct option is $D$