Question

The vapour pressure of water at 293 k is 2438 Pa and the vapour pressure of an aqueous solution is $ 2395.8\text{ Pa} $ . If solution density is $ 1080\text{ }kg/{{m}^{3}} $ at 313 k. Calculate the osmotic pressure at313 k. The molecular weight of solute =60 .
(A) $ 24.54\text{ Pa} $
(B) $ 24.54\times {{10}^{5}}\text{ Pa} $
(C) $ 0.955\text{ Pa} $
(D) None of these

Answer 1

Hint: The measure of the tendency of a material to change into the gaseous or vapour state is known as vapour pressure. The vapour pressure increases with increase in the temperature. The temperature at which the pressure at the surface of the liquid becomes equal to the pressure exerted by the surroundings is called the boiling point of the liquid.

Complete Step by step solution
The molecular weight of organic substances determine the basis of lowering of vapour pressure.
 $ \Rightarrow \dfrac{{{\text{P}}_{\text{s}}}-{{\text{P}}_{\text{o}}}}{{{\text{P}}_{\text{s}}}}=\dfrac{\text{n}}{\text{N}} $
Here,
 $ {{\text{P}}_{\text{s}}}= $ Vapour pressure of water
 $ {{\text{P}}_{\text{o}}}= $ Vapour pressure of aqueous solution
n = Number of moles
 $ \text{N = } $ Avogadro number
We know that,
 $ \text{N}=\dfrac{\text{W}}{\text{M}} $
Here,
 W = Weight of the solution
M = Molar mass
 $ \Rightarrow \dfrac{{{\text{P}}_{\text{s}}}-{{\text{P}}_{\text{o}}}}{{{\text{P}}_{\text{s}}}}=\dfrac{\text{n}\times \text{M}}{\text{W}} $
 $ \therefore \dfrac{\text{n}}{\text{W}}=\dfrac{\left( 2438-2395.8 \right)}{2438\times 18}=9.616\times {{10}^{-4}} $
We know that,
Concentration, $ \text{C = }\dfrac{\text{n}}{\text{W}}\times \text{d} $
 Where, $ d $ is the density of the solution.
Thus,
 $ \begin{align}
  & \Rightarrow \text{C = 9}\text{.616}\times \text{1}{{\text{0}}^{-4}}\times 1080 \\
 & \Rightarrow \text{C = 1}\text{.038} \\
\end{align} $
We know that, osmotic pressure =cRT
Now,
 $ \begin{align}
  & \Rightarrow \Pi \text{ =1}\text{.038}\times \text{0}\text{.0821}\times 313 \\
 & \Rightarrow \Pi =24.54\text{ atm} \\
 & \Rightarrow \Pi =24.54\times {{10}^{5}}\text{ Pa} \\
\end{align} $
Hence, the osmotic pressure of the solution at temperature 313 k is $ 24.54\times {{10}^{5}}\text{ Pa} $ .

Note The osmotic pressure of a solution can be defined as the pressure which is required to be applied to the solution in order to prevent the inward flow of water across a semipermeable membrane. A semipermeable membrane is a thin layer, which allows only certain types of molecules to pass through it. A semipermeable membrane only allows the movement of solvent particles through it the solvent particles cannot pass through it.