Question

The osmotic pressure of urea solution at ${10}^{\circ }C$ is 200 mm becomes 105.3 mm when it is diluted and temperature raised to ${25}^{\circ }C$. The extent of dilution is

• A. 8 times
• B. 5 times
• C. 4 times
• D. 2 times

Answer 1

The correct option is D 2 times

Let $\pi 1=200mm;T_1=283$
$\pi 1=105.3;T_2=298$
Now, $\pi =\frac{n}{V}RT$
At $T_1,200=\frac{n}{V_1}R\times 283....\left(i\right)$
At $T_2,105.3=\frac{n}{V_2}R\times 298....\left(ii\right)$
Dividing Eq. (i) by Eq. (ii), we get
$\frac{200}{105.3}=\frac{V_2}{V_1}\times \frac{283}{298}\Rightarrow V_2=2V_1$