Question

A graph plotted between P vs. d (where, P is osmotic pressure of solution of a solute of molar mass m and d is its density at temperature T). Pick out the correct statements about the plots.

• A. $\left[\frac{P}{d}\right]$ is independent of molar mass
• B. the intercept of the plot $\frac{ST}{m}$
• C. the intercept of the plot is zero
• D. ${\left[\frac{P}{d}\right]}_{d\to 0}$ is independent of temperature

Answer 1

Answer: (C)

the intercept of the plot is zero

Osmosis is the diffusion of a fluid through a semipermeable membrane. When a semipermeable membrane (animal bladders, skins of fruits and vegetables) separates a solution from a solvent, then only solvent molecules are able to pass through the membrane.

The osmotic pressure of a solution is the pressure difference needed to stop the flow of solvent across a semipermeable membrane. The osmotic pressure of a solution is proportional to the molar concentration of the solute particles in solution.

$\pi =\frac{nRT}{V}=MRT=\frac{dRT}{M_1}$

Here, $\pi$ is the osmotic pressure.

$R$ is gas constant, $T$ is temperature, M is molarity of solute,

$n$ is the number of moles of solute present, d is density of solution.

When we are plotting $P$ vs $d$ graph, it is a straight line passing through origin $y=mx$.

So, intercept made by the plot will be zero.

$\frac{P}{d}=\frac{RT}{M_1}$

Fraction $\frac{P}{d}$ is dependent on temperature and molar mass as we can see above.