Question

What do you understand by osmosis and osmotic pressure? 1.26 g protein is present in 200 cm\(^3\) aqueous solution of protein. Molar mass of protein is 61,022 g mol\(^{-1}\). What will be osmotic pressure of this solution at 300 K?

Hint:

For dilute solutions, osmotic pressure follows \(\pi = CRT\), analogous to ideal gas law.

Answer 1

Step 1: Definitions.
- Osmosis: Flow of solvent molecules through a semipermeable membrane from lower solute concentration to higher solute concentration.
- Osmotic pressure: The pressure required to stop osmosis.
Step 2: Moles of protein.
\[ n = \frac{\text{Mass}}{\text{Molar mass}} = \frac{1.26}{61022} \approx 2.07 \times 10^{-5} \, mol \] Step 3: Concentration of solution.
Volume = 200 cm\(^3\) = 0.200 L.
\[ C = \frac{n}{V} = \frac{2.07 \times 10^{-5}}{0.200} = 1.035 \times 10^{-4} \, mol/L \] Step 4: Osmotic pressure formula.
\[ \pi = C R T = (1.035 \times 10^{-4})(0.0821)(300) \approx 0.103 \, atm \] Step 5: Conclusion.
Osmotic pressure = \(\mathbf{0.103 \, atm}\).