Question

(i) Prove that osmotic pressure is a colligative property.
(ii) Calculate the molar concentration of urea solution if it exerts an osmotic pressure of 2.45 atmosphere at 300 K. [R = 0.0821 $l.atm.mo{{l}^{-1}}{{K}^{-1}}$ ]

Answer 1

Hint: The basic knowledge about the colligative properties of the solutions can help us solve the given statements. Knowing about the osmotic pressure as a colligative property, as it depends upon the amount of the substance. we can further move to solve the given illustration using the same information.

Complete answer:
Let us study about the colligative properties of the solutions;
Colligative properties- The properties of the solution depend on the ratio of the number of solute molecules to the number of solvent molecules and is independent of the nature of chemical species present in the same. Now, concentrating on osmotic pressure and keeping the fact alive about the colligative property;
Osmotic pressure is the tendency of solvent molecules to move in the direction of lower solvent activity. It is proportional to the molarity and temperature of the solution.
Also, molarity is the number of moles of solute in one litre of solution. Thus, osmotic pressure can be stated as,
\[\begin{align}
& \pi V=nRT \\
& \pi =CRT \\
\end{align}\]
where,
$\pi $ = osmotic pressure
$C=\dfrac{n}{V}$ = concentration of solution
n = number of moles of solute in the solution
V = volume of solution
R = universal gas constant
T = temperature of solution
Since, osmotic pressure is directly proportional to the number of moles of solute present; it represents the basic definition of colligative property. Hence, osmotic pressure is a colligative property.
Illustration-
Given that,
Osmotic pressure = $\pi =2.45atm$
Temperature = T = 300 K
R = 0.0821 $l.atm.mo{{l}^{-1}}{{K}^{-1}}$
Thus, using the formula for osmotic pressure, molar concentration can be given as,
$\begin{align}
& C=\dfrac{\pi }{RT}=\dfrac{2.45}{0.0821\times 300} \\
& C=0.099M \\
\end{align}$

Thus, molar concentration of urea solution is 0.099 M.

Note: There are four colligative properties i.e.
1. Relative lowering of vapour pressure
2. Elevation of boiling point
3. Depression of freezing point
4. Osmotic pressure
Also, while solving the illustration use units properly.