The normality (N) of a solution is related to its molarity (M) by the equation:
$$ \text{Normality (N)} = \text{Molarity (M)} \times \text{n-factor} $$
where the n-factor (equivalent factor) is the number of equivalents of the substance per mole. For \( \text{KMnO}_4 \) acting as an oxidizing agent in acidic medium, the half-reaction is:
$$ \text{MnO}_4^- + 8\text{H}^+ + 5e^- \rightarrow \text{Mn}^{2+} + 4\text{H}_2\text{O} $$
In this reaction, each mole of \( \text{KMnO}_4 \) gains 5 moles of electrons. Therefore, the n-factor for \( \text{KMnO}_4 \) in acidic medium is 5.
Given that the molarity of the \( \text{KMnO}_4 \) solution is 1 M, its normality will be:
$$ \text{Normality (N)} = 1 \text{ M} \times 5 = 5 \text{ N} $$