Question

Van’t Hoff factor (i) for centimolal solution of \( \mathrm{K_3[Fe(CN)_6] }\) is 3.333. What is its percentage dissociation?

• A. 80%
• B. 70%
• C. 33.33%
• D. 77.7%

Hint:

For electrolytes, always identify total ions formed before applying Van’t Hoff factor formula.

Answer 1

The Correct Option is D

Step 1: Understanding dissociation of the electrolyte.
Potassium ferricyanide dissociates as:
\[ \mathrm{K_3[Fe(CN)_6] \rightarrow 3K^+ + [Fe(CN)_6]^{3-}} \] Thus, total number of ions formed \( n = 4 \).

Step 2: Writing relation between Van’t Hoff factor and degree of dissociation.
\[ i = 1 + (n - 1)\alpha \]

Step 3: Substituting given values.
\[ 3.333 = 1 + (4 - 1)\alpha \] \[ 3.333 = 1 + 3\alpha \] \[ \alpha = \frac{2.333}{3} = 0.777 \]

Step 4: Converting into percentage.
\[ % \text{ dissociation } = 0.777 \times 100 = 77.7% \]

Step 5: Conclusion.
The percentage dissociation is 77.7%.