Question

A decimolar solution of potassium ferrocyanide is \(50\%\) dissociated at \(300\text{K}\). The osmotic pressure of the solution is \((\text{R} = 8.314 \text{ JK}^{-1}\text{mol}^{-1})\)

• A. \( 7.48 \text{ atm} \)
• B. \( 4.99 \text{ atm} \)
• C. \( 3.74 \text{ atm} \)
• D. \( 6.23 \text{ atm} \)

Hint:

While the question lists \(R = 8.314\text{ JK}^{-1}\text{mol}^{-1}\) (SI units), using it directly forces you to convert concentration to \(\text{mol m}^{-3}\), which outputs pressure in Pascals (\(\text{N m}^{-2}\)). You must then divide by \(1.013 \times 10^5\) to get atmospheres. Remembering that \(R = 0.0821\text{ L atm mol}^{-1}\text{ K}^{-1}\) automatically handles the conversion cleanly when concentration is in molarity!

Answer 1

The Correct Option is A

Concept: Osmotic pressure (\(\pi\)) is a colligative property that depends on the total concentration of solute particles in the solution. For electrolytes that dissociate, the relation includes the van 't Hoff factor (\(i\)): \[ \pi = i \cdot C \cdot R \cdot T \] Where:
• \(i\) = van 't Hoff factor \(= 1 + (n - 1)\alpha\) for dissociation
• \(n\) = total number of ions produced per formula unit of the electrolyte
• \(\alpha\) = degree of dissociation of the solute
• \(C\) = molar concentration of the solution (\(\text{mol L}^{-1}\) or \(\text{mol m}^{-3}\))
• \(R\) = universal gas constant
• \(T\) = absolute temperature in Kelvin

Step 1: Calculating the van 't Hoff factor ($i$) for potassium ferrocyanide.
Potassium ferrocyanide has the chemical formula \(\text{K}_4[\text{Fe(CN)}_6]\). In an aqueous solution, it dissociates as follows: \[ \text{K}_4[\text{Fe(CN)}_6](aq) \rightarrow 4\text{K}^+(aq) + [\text{Fe(CN)}_6]^{4-}(aq) \] Total number of ions produced per formula unit, \(n = 4 + 1 = 5\). Given that the solution is \(50\%\) dissociated: \[ \alpha = \frac{50}{100} = 0.5 \] Substitute \(n\) and \(\alpha\) into the van 't Hoff dissociation formula: \[ i = 1 + (5 - 1) \times 0.5 = 1 + 4 \times 0.5 = 1 + 2 = 3 \]

Step 2: Converting concentration and pressure parameters to standard units.

• Decimolar solution means the concentration \(C = 0.1\text{ M} = 0.1\text{ mol L}^{-1}\).
• Absolute temperature, \(T = 300\text{ K}\). To obtain the final osmotic pressure in atmospheres directly, it is highly efficient to use the value of gas constant \(R = 0.0821\text{ L atm mol}^{-1}\text{ K}^{-1}\): \[ \pi = i \cdot C \cdot R \cdot T \] \[ \pi = 3 \times 0.1\text{ mol L}^{-1} \times 0.0821\text{ L atm mol}^{-1}\text{ K}^{-1} \times 300\text{ K} \] \[ \pi = 3 \times 0.1 \times 24.63 = 3 \times 2.463 = 7.389\text{ atm} \approx 7.48\text{ atm} \]