Osmotic Pressure Comparison and Solution Hypotonicity Across Semi Permeable Membrane

To determine the correct statement, let us analyze the colligative properties (specifically osmotic pressure) of the solutions on both sides of the semi-permeable membrane.

1. Side 'x' ($\text{K}_4[\text{Fe}(\text{CN})_6]$ solution):

• Concentration, $C_x = 0.1\text{ M}$
• Dissociation equation for $\text{K}_4[\text{Fe}(\text{CN})_6]$: $\text{K}_4[\text{Fe}(\text{CN})_6]\text{ (aq)} \rightarrow 4\text{K}^+\text{(aq)} + [\text{Fe}(\text{CN})_6]^{4-}\text{(aq)}$
• Since dissociation is complete, the van 't Hoff factor is: $i_x = 1 + (5 - 1) \times 1 = 5$
• Total effective ion concentration on side 'x': $C_{\text{eff}, x} = i_x \times C_x = 5 \times 0.1\text{ M} = 0.5\text{ M}$
• Osmotic pressure of side 'x': $\Pi_x = i_x C_x R T = 0.5 R T$

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2. Side 'y' ($\text{FeCl}_3$ solution):

• Concentration, $C_y = 0.1\text{ M}$
• Dissociation equation for $\text{FeCl}_3$: $\text{FeCl}_3\text{ (aq)} \rightarrow \text{Fe}^{3+}\text{(aq)} + 3\text{Cl}^-\text{(aq)}$
• Since dissociation is complete, the van 't Hoff factor is: $i_y = 1 + (4 - 1) \times 1 = 4$
• Total effective ion concentration on side 'y': $C_{\text{eff}, y} = i_y \times C_y = 4 \times 0.1\text{ M} = 0.4\text{ M}$
• Osmotic pressure of side 'y': $\Pi_y = i_y C_y R T = 0.4 R T$

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3. Analysis of Options:

• Comparison of Osmotic Pressures: $\Pi_x = 0.5 RT > \Pi_y = 0.4 RT$ Since the osmotic pressure of the solution on side 'y' ($\Pi_y$) is lower than that on side 'x' ($\Pi_x$), the solution on side 'y' is hypotonic relative to side 'x' (and side 'x' is hypertonic relative to side 'y'). Therefore, Statement C is correct.

• Option A: A semi-permeable membrane (SPM) allows only solvent (water) molecules to pass through, preventing solute ions ($\text{Fe}^{3+}$ and $[\text{Fe}(\text{CN})_6]^{4-}$) from crossing. Thus, no complexation occurs, and no blue color is formed.

• Option B: Solute ions cannot pass through a semi-permeable membrane.

• Option D: To cause reverse osmosis, an external pressure greater than the net osmotic pressure difference ($\Delta \Pi = \Pi_x - \Pi_y$) must be applied to the hypertonic side (side 'x'), not just "any value".

Thus, the correct option is C.