A solution contains non-volatile solute of molecular mass $M_2$. Which of the following can be used to…

A solution contains non-volatile solute of molecular mass $M_2$. Which of the following can be used to calculate the molecular mass of the solute in terms of the osmotic pressure? Note: $m_2$ is the mass of the solute, $\mathrm{V}$ is the volume of the solution and $\pi$ is the osmotic pressure.
  1. $\mathrm{M}_2=\left(\frac{m_2}{\pi}\right) \mathrm{VRT}$
  2. $\mathrm{M}_2=\left(\frac{m_2}{\mathrm{~V}}\right) \frac{\mathrm{RT}}{\pi}$
  3. $\mathrm{M}_2=\left(\frac{m_2}{\mathrm{~V}}\right) \pi \mathrm{RT}$
  4. $\mathrm{M}_2=\left(\frac{m_2}{\mathrm{~V}}\right) \frac{\pi}{\mathrm{RT}}$

Solution

For dilute solution, the van't Hoff equation is: $\begin{aligned} \pi & =\frac{n}{\mathrm{~V}} \mathrm{RT} \\ \pi \mathrm{V} & =\frac{m_2}{\mathrm{M}} \mathrm{RT} \\ \Rightarrow \quad \mathrm{M} & =\frac{m_2 \mathrm{RT}}{\pi \mathrm{V}} \end{aligned}$ Van't Hoff explained that when solutes are dissolved in a solvent they dissociate into ions. Since colligative properties depend only on the number of solute particles, the dissociation of solute molecules into ions results in an increase in the number of particles and hence affects the colligative properties.

Asked in: NEET 2002

Practice more Solutions questions on Aicharya