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What should be the osmotic pressure of a solution of urea in water at 30°C which has boiling point 0.052 K higher than pure water? Assume molarity and molality to be the same. \[{{K}_{b}}\] for water is 0.52 K \[kg\,mo{{l}^{-1}}\].
(a)- 0.487 atm
(b)- 1.487 atm
(c)- 2.487 atm
(d)- 3.487 atm

Last updated date: 17th Jun 2024
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Hint: The physical properties of a solution that depends on the number of particles present in a given volume of the solution or the mole fraction of the solute present in the solution are called colligative properties.

Complete step by step solution:
Osmotic pressure of a solution is one of the colligative properties. It is defined as the external pressure that must be applied on the solution in order to stop the flow of the solvent into the solution through a semipermeable membrane. It is given by the equation,
\[\pi =iCRT\]
where, \[\pi \] = osmotic pressure
i = Van’t Hoff factor
C = molar concentration of the solute in the solution
R = universal gas constant
T = temperature
We have been given in the above problem,
Difference in boiling point (\[\Delta T\]) = 0.052K
\[{{K}_{b}}\] for water is 0.52 K \[kg\,mo{{l}^{-1}}\]
We also know, \[\Delta T\]= \[{{K}_{b}}\times m\]
where, \[{{K}_{b}}\] = molal elevation constant,
m = molality
Therefore, by making use of above two relationship, we can calculate molality by rearranging as,
Molality (m) = \[\dfrac{\Delta T}{{{K}_{b}}}\]= \[\dfrac{0.052}{0.52}\]= 0.1
In the above problem, we have been given that, molality = molarity.
Therefore, molarity = 0.1 = C
Now, since we have got the value of C, we can calculate the osmotic pressure (\[\pi \]) by using relation
\[\pi =iCRT\]
    =1 ×0.1×0.0821×303
    =2.487 atm.
Therefore, the osmotic pressure of a solution of urea in water at 30°C is calculated to be 2.487 atm.

Hence, option (c) is correct.

Note: Semipermeable membrane only allows the movement of solvent molecules through it. Solute particles cannot pass through this membrane. Osmotic pressure is also applicable to gases and supercritical fluids.