Question

At \(300\ \mathrm{K}\), a decimolar solution of potassium ferrocyanide is \(50\%\) dissociated. The osmotic pressure (in atm) of the solution is \[ (R=0.082\ \mathrm{L\,atm\,K^{-1}\,mol^{-1}}) \]

• A. 6.83
• B. 3.87
• C. 7.38
• D. 7.83 \bigskip

Hint:

For electrolytes, \[ \boxed{i=1+\alpha(n-1)} \] where \begin{itemize} \item \(\alpha\) = degree of dissociation, \item \(n\) = total number of ions produced. \end{itemize} Then use \[ \boxed{\pi=iCRT.} \]

Answer 1

The Correct Option is C

Concept: Osmotic pressure \(\pi = iCRT\). Find van't Hoff factor \(i\) for K₄[Fe(CN)₆] at 50% dissociation.

Step 1: Dissociation: K₄[Fe(CN)₆] → 4K⁺ + [Fe(CN)₆]⁴⁻, n=5. α=0.5, i = 1+α(n-1) = 1+0.5(4) = 3. \(\pi = 3\times0.1\times0.082\times300 = 7.38\) atm.

Step 2: Write the final answer. \(\boxed{7.38\ \mathrm{atm}}\)