Question

At ${10}^{0}C$, the osmotic pressure of urea solution is 500 mm. The solution is diluted and the temperature is raised to ${25}^{0}C$, so that the osmotic pressure became 105.3 mm. The number of times, the solution diluted is:

• A. $6$
• B. $5$
• C. $4$
• D. $3$

Answer 1

The correct option is B $5$

The expression for the osmotic pressure of solution is $\pi =iCRT$
A solution having volume $V_{1}L$ and n moles is at ${10}^{o}C$
The expression for the osmotic pressure becomes, $\frac{500}{760}=\frac{n}{v_1}\times 0.082\times 283$
The solution is then diluted to $V_{2}L$ and the temperature is raised to ${25}^{o}C$.
The expression for the osmotic pressure of the solution becomes $\frac{105.3}{760}=\frac{n}{v_2}\times 0.082\times 298$
Equation (i) is divided with equation (ii).
$\frac{\frac{500}{760}}{\frac{105.3}{760}}=\frac{\frac{n}{v_1}\times 0.082\times 283}{\frac{n}{v_2}\times 0.082\times 298}$
Thus $\frac{\left(i\right)}{\left(ii\right)}=\frac{V_2}{V_1}=5$
The solution is diluted to five times.