Question

The osmotic pressure of urea solution at ${10}^{o}C$ is 200 mm becomes 105.3 mm when it is diluted and the temperature raised to ${25}^{o}C$.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 ${\pi }_1=200mm;T_1=283$

${\pi }_1=105.3mm,T_2=298$

Now, $\pi =\frac{n}{V}\left(RT\right)$

At $T_1,200=\frac{n}{V_1}R\times 283$ ....(i)

At $T_2,50=\frac{n}{V_2}R\times 298$ ....(ii)

Dividing (i) by (ii) ,we get

$\frac{200}{105.3}=\frac{V_2}{V_1}\times \frac{283}{298}\Rightarrow V_2=2V_1$

So, the correct option is $D$