Step 1: Understanding the Concept:
Potassium (K) is an alkali metal belonging to Group 1 of the periodic table. Alkali metals have a single valence electron in their outermost shell, which they lose very easily to achieve a stable noble gas configuration.
Step 2: Detailed Explanation:
1. Alkali metals, including potassium, always exhibit an oxidation state of \(+1\) in their compounds.
2. In \(K_2O\) (Potassium oxide), oxygen is in the \(-2\) state. Calculation: \(2(x) + (-2) = 0 \implies x = +1\).
3. In \(K_2O_2\) (Potassium peroxide), oxygen is in the \(-1\) state (peroxide ion \(O_2^{2-}\)). Calculation: \(2(x) + 2(-1) = 0 \implies x = +1\).
4. In \(KO_2\) (Potassium superoxide), oxygen is in the \(-1/2\) state (superoxide ion \(O_2^{-}\)). Calculation: \(x + 2(-1/2) = 0 \implies x = +1\).
Step 3: Final Answer
The oxidation number of potassium remains \(+1\) in all three compounds.