20 g of a substance were dissolved in 500 mL of water and the osmotic pressure of the solution was found to be 600 mm of mercury at 15 °C. The molar mass of the substance (in g mol−1) is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 1198
The osmotic pressure Π of a dilute solution is proportional to its molarity. Writing the moles of solute as w2/M2 gives the molar mass directly:
\( \displaystyle \Pi=\frac{w_2RT}{M_2V}\quad\Rightarrow\quad M_2=\frac{w_2RT}{\Pi V} \)
Convert the data to litre–atmosphere–kelvin units:
\( \displaystyle \Pi=\frac{600}{760}\,\mathrm{atm}=0.7895\,\mathrm{atm} \)
\( \displaystyle V=500\,\mathrm{mL}=0.5\,\mathrm{L},\quad T=15+273=288\,\mathrm{K} \)
\( \displaystyle w_2=20\,\mathrm{g},\quad R=0.0821\,\mathrm{L\,atm\,K^{-1}\,mol^{-1}} \)
Substituting:
\( \displaystyle M_2=\frac{20\times0.0821\times288}{0.7895\times0.5} \)
\( \displaystyle M_2=\frac{472.9}{0.3947}=1198\,\mathrm{g\,mol^{-1}} \)