Question

The osmotic pressure of urea solution at ${10}^{o}C$ is $200$ mm of $Hg$. It changes to $105.3$ mm of $Hg$ when diluted and the temperature raised to ${25}^{o}C$.

The extent of dilution is :

Answer 1

The osmotic pressure is given by the expression $\Pi =CRT$, where $\Pi ,C,R$ and $T$ are osmotic pressure, concentration, universal gas constant and temperature respectively.

Let ${\Pi }^{\prime }$ be the final osmotic pressure.
$\frac{\Pi }{{\Pi }^{\prime }}=\frac{CT}{C^{\prime }{T}^{\prime }}$ as $R$ and $T$ are constants.
$\frac{200}{105.3}=\frac{C(10+273)}{C^{\prime }(25+273)}$
$1.899=\frac{C}{C^{\prime }}\times 0.9496$
$\frac{C}{C^{\prime }}=1.999$

which can be,

$\frac{C}{C^{\prime }}=2$
Hence, the final concentration $C^{\prime }$ is one half of the initial concentration $C$.
Hence, the extent of dilution is two.