Step 1: Equivalent weight calculation.
The equivalent weight of potassium permanganate \( KMnO_4 \) in the oxidation of ferrous ions depends on the change in oxidation state of manganese. For potassium permanganate, the change in oxidation state is 5 (from +7 to +2). The equivalent weight is calculated as:
\[
\text{Equivalent weight} = \frac{\text{Molar mass}}{\text{Change in oxidation state}} = \frac{158}{5} = 31.6
\]
Step 2: Conclusion.
Thus, the correct answer is 31.6.