At \( 27^\circ \text{C} \), 0.1 M, 1 L \( K_4[Fe(CN)_6] \) aqueous solution and 0.1 M, 1 L \( FeCl_3 \) aqueous solution are placed in a container separated by a semi permeable membrane AB. Assume complete dissociation of both the solutes. Which of the following statement is correct?
Ionic solutes in aqueous solution can pass through semi-permeable membrane.
Solution on side 'y' is hypotonic.
To cause the reverse flow of solvent during osmosis, external pressure (any value) should be applied to side 'x'.
Show Solution
The Correct Option isC
Solution and Explanation
Step 1: Understanding the Concept:
Osmosis involves the flow of solvent molecules across a semi-permeable membrane (SPM) from a region of lower solute concentration to a region of higher solute concentration. The true osmotic concentration is determined by the osmolarity (Molarity $\times$ van 't Hoff factor $i$). The solution with the lower osmolarity is deemed "hypotonic". Step 2: Key Formula or Approach:
Osmotic pressure: $\pi = i C R T$
Hypotonic means lower $\pi$ (and thus lower $i \times C$).
Hypertonic means higher $\pi$ (and thus higher $i \times C$). Step 3: Detailed Explanation:
Let's evaluate the side 'x':
Solution is $0.1 \text{ M K}_4[\text{Fe(CN)}_6]$.
Dissociation: $\text{K}_4[\text{Fe(CN)}_6] \to 4\text{K}^+ + [\text{Fe(CN)}_6]^{4-}$
Number of ions $i_x = 4 + 1 = 5$.
Effective concentration (Osmolarity) $= i_x \cdot C = 5 \times 0.1 = 0.5 \text{ M}$.
Let's evaluate the side 'y':
Solution is $0.1 \text{ M FeCl}_3$.
Dissociation: $\text{FeCl}_3 \to \text{Fe}^{3+} + 3\text{Cl}^-$
Number of ions $i_y = 1 + 3 = 4$.
Effective concentration (Osmolarity) $= i_y \cdot C = 4 \times 0.1 = 0.4 \text{ M}$.
Now analyze the options:
(A) Blue color formation requires the reaction of $\text{Fe}^{3+}$ with $[\text{Fe(CN)}_6]^{4-}$ to form Prussian blue. Since an SPM does not allow solute ions to pass through, they cannot mix. No color is formed.
(B) A semi-permeable membrane selectively allows solvent (water) to pass, completely blocking ionic solutes. False.
(C) Side 'y' has an osmolarity of $0.4 \text{ M}$, which is less than side 'x' ($0.5 \text{ M}$). Thus, the solution on side 'y' is hypotonic relative to 'x'. True.
(D) Reverse osmosis requires applying an external pressure specifically greater than the osmotic pressure difference to the hypertonic side ('x'). "Any value" is technically incorrect; it must exceed the threshold $\Delta \pi$. Step 4: Final Answer:
The statement "Solution on side 'y' is hypotonic" is correct.
