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

The correct option is C 5 times
Osmotic pressure of urea solution at ${10}^{0}C$
${\pi }_1=i{C}_{1}R{T}_1$ (i)
Osmotic pressure of urea solution at ${25}^{0}C$
${\pi }_2=i{C}_{2}R{T}_2$ (ii)
From eq 1 and 2 we will have
$\frac{{\pi }_1}{{\pi }_2}=\frac{C_1\times 283}{C_2\times 298}$
$\therefore C_2=\frac{283\times 105.3}{500\times 298}\times C_1$ that is
$C_2=\frac{C_1}{5}$