Question

Assertion :Lowering of vapour pressure is directly proportional to osmotic pressure of the solution. Reason: Osmotic pressure is a colligative property.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

Both assertion and reason are correct but the reason is not the correct explanation of assertion.
The relationship between the lowering of vapour pressure and osmotic pressure can be derived as follows:
Van't Hoff equation for dilute solutions is

$\pi =\frac{n}{V}RT.....\left(i\right)$

In case of a dilute solution. The volume of solution can be taken as equal to that of the solvent. If $N$ is the number of moles of the solvent of molecular weight M and density $\rho$, the volume V is given by

$V=\frac{NM}{\rho }.......\left(ii\right)$

or $\frac{n}{N}=\frac{\pi M}{\rho .R.T.}....\left(iii\right)$

From Raoult's law,

$\frac{P^{\circ }-P}{P^{\circ }}=\frac{n}{N}.......\left(iv\right)$

$\therefore \frac{P^{\circ }-P}{P^{\circ }}=\frac{\pi M}{\rho RT}$ [From $\left(iii\right)$ and $\left(iv\right)$]

or $(P^{\circ }-P)=\frac{\pi M}{\rho RT}\times P^{\circ }$

The factor $\frac{M{P}^{\circ }}{\rho RT}$ is constant at constant temperature.

$\therefore (P^{\circ }-P)\propto \pi$

or lowering of $V.P.\propto$ osmotic pressure

Thus assertion is correct.

Osmotic pressure is a colligative property is correct.