Question

In $CS_{2}$, sulphur atoms are associated to form colloidal sol. $2.56\, g$ of sulphur colloidal sol in $100\, g\, CS_{2}$ shows osmotic pressure of $2.463$ atm at $300\, K$. How many sulphur atoms are associated in colloidal sol? (Solution constant $= 0.0821\, L$ atm mol $^{-1} K^{-1}$).

Answer 1

$\underset{\text{Molar mass 32x}}{xS \rightleftharpoons S_{x}}$ (associated colloidal sol) Osmotic pressure,
$\pi = MRT = \frac{n}{V}RT = \frac{wRT}{mV}$
Molar mass of $S_{x} = m \left(S_{x}\right) = \frac{wRT}{\pi V}$

$= \frac{2.56 \times0.0821 \times300}{2.463 \times0.01} = 256$
$\therefore 32 x = 256$
$x = 8$