Chemistry - Liquid Solution Question with Solution | TestHub

The formula for osmotic pressure is given by:

$\pi =\frac{WRT}{MV}$

Rearranging the formula to solve for the molar mass $M$ of the solute:

$M=\frac{WRT}{\pi V}$

Given values are:
$W=400\text{ mg}=0.4\text{ g}$
$V=300\text{ mL}=0.3\text{ L}$
$\pi =0.2\text{ atm}$
$T=300\text{ K}$
$R=0.0821{\text{ L atm K}}^{-1}{\text{ mol}}^{-1}$

Substituting the values into the formula:

$M=\frac{0.4\times 0.0821\times 300}{0.2\times 0.3}$

$M=\left(\frac{0.4}{0.2}\right)\times \left(\frac{300}{0.3}\right)\times 0.0821$

$M=2\times 1000\times 0.0821$

$M=164.2{\text{ g mol}}^{-1}$

Approximating to the nearest integer, we get $164{\text{ g mol}}^{-1}$.

Answer: $164\mathrm{g}{\mathrm{mol}}^{-1}$