ved = 25 mg = 0.025 g

Volume of the solution = 2 L

Temperature = 25°C = 298 K

Molar Mass Calculation:

The molar mass of $\mathrm{K}_2 \mathrm{SO}_4$ = $2 \times 39 + 32 + 4 \times 16 = 174 \, \mathrm{g/mol}$

Dissociation in Water:

$\mathrm{K}_2 \mathrm{SO}_4$ dissociates completely as:

$ \mathrm{K}_2 \mathrm{SO}_4 \longrightarrow 2 \mathrm{K}^{+} + \mathrm{SO}_4^{2-} $

Number of ions produced per formula unit = 3 (2 $\mathrm{K}^{+}$ and 1 $\mathrm{SO}_4^{2-}$)

Osmotic Pressure Calculation using Van’t Hoff Factor (i):

Van’t Hoff factor $i = 3$

The formula for osmotic pressure is:

$ \pi = iCRT $

Here, $C = \frac{n}{V}$, where $n$ is the moles of solute, and $V$ is the volume in liters.

Calculate moles of $\mathrm{K}_2 \mathrm{SO}_4$:

$ n = \frac{0.025 \, \mathrm{g}}{174\, \mathrm{g/mol}} $

Substitute the known values into the osmotic pressure formula:

$ \pi = 3 \times \frac{0.025}{174} \times \frac{1}{2} \times 0.0821 \times 298 $

Solving for $\pi$, we find:

$ \pi = 5.27 \times 10^{-3} \, \mathrm{atm} $

Thus, the osmotic pressure of the solution is $5.27 \times 10^{-3} \, \mathrm{atm}$.

Liquid Solution

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