Question

$36g$ of organic substance is present in one litre of solution at $200K$ .
The osmotic pressure of a solution is $1.8\times {10}^{5}Pa$ .
Calculate the molecular mass of the substance.
Take $R=8.3Jmo{l}^{-1}{K}^{-1}$

• A. $332gmo{l}^{-1}$
• B. $166gmo{l}^{-1}$
• C. $83gmo{l}^{-1}$
• D. $154gmo{l}^{-1}$

Answer 1

The correct option is A $332gmo{l}^{-1}$

Osmotic pressure:

$\pi =\frac{n}{V}\times RT$

Here n is number of moles

$n=\frac{\text{Given mass}}{\text{Molar mass}}=\frac{w_B}{m_B}$

$V=1L={10}^{-3}{m}^{3}R=8.3Jmo{l}^{-1}{K}^{-1}T=200K\pi =1.8\times {10}^{5}Pa{w}_B=36g$

$\Rightarrow \pi V=\frac{w_B}{m_B}\times RT{m}_B=\frac{w_B\times R\times T}{\pi \times V}$

$m_B=\frac{36\times 8.3\times 200}{1.8\times {10}^5\times {10}^{-3}}{m}_B=332gmo{l}^{-1}$