Question

The osmotic pressure of a solute is 600 mm at 300 K. The solution is diluted and the temperature is raised to 400 K and the solution shows an osmotic pressure of 200 mm. The solution was diluted to $x$ times. $x$ is :

Answer 1

The initial concentration is $C=\frac{\Pi }{RT}=\frac{600mm}{R\times 300K}=\frac{2}{R}M$.

The final concentration is $C^{\prime }=\frac{\Pi }{RT}=\frac{200mm}{R\times 400K}=\frac{1}{2R}M$.
The ratio of the initial concentration to the final concentration is $\frac{C}{C^{\prime }}=\frac{\frac{2}{R}M}{\frac{1}{2R}M}=4$.
Hence, the solution is diluted to 4 times.
$x=4$.