The measured osmotic pressure of a solution prepared by dissolving $17.4 \mathrm{mg}$ of $\mathrm{K}_2…
The measured osmotic pressure of a solution prepared by dissolving $17.4 \mathrm{mg}$ of $\mathrm{K}_2 \mathrm{SO}_4$ in $2 \mathrm{~L}$ of water at $27^{\circ} \mathrm{C}$ is $3.735 \times 10^{-3}$ bar.
The van't Hoff factor is
$\left(R=0.083 \mathrm{~L} \mathrm{bar} \mathrm{K}^{-1} \mathrm{~mol}^{-1}\right.$; atomic weights
$\mathrm{K}=39, \mathrm{~S}=32 ; \mathrm{O}=16$ )
2.84
3.0
2.0
2.32
Solution
Given, $\pi=3.735 \times 10^{-3}$ bar
Mass of $\mathrm{K}_2 \mathrm{SO}_4(\omega)=17.4 \mathrm{mg}$
Volume $=2 \mathrm{~L}$
Temperature $(T)=27^{\circ} \mathrm{C}=27+273=300 \mathrm{~K}$
From osmotic pressure of solution.
$
\begin{aligned}
\pi & =i C R T \\
i & =\text { van't-Hoff factor } \\
i & =\pi / C R T \\
& =\frac{\pi \times M \times V}{\omega \times R \times T}=\frac{3.735 \times 174 \times 2}{17.4 \times 0.083 \times 300}
\end{aligned}
$
Molar mass $(M) \mathrm{H}_2 \mathrm{SO}_4=174, i=3.0$