The stability off `K_(2)O,K_(2)O_(2) and KO_(2)` is in order `K_(2)O lt K_(2)O_(2) lt KO_(2)`. This increasing stability as the size of metal ion increases is due to stabilisation of

Options

A. larger cation by smaller anions through lattice energy effects
B. larger cation by larger anions through lattice energy effects
C. smaller cations by smaller anions through melting point
D. smaller cations by larger anions through melting point.

Answer

To solve the question regarding the stability of potassium oxide (K₂O), potassium peroxide (K₂O₂), and potassium superoxide (KO₂), we need to analyze the factors affecting their stability in relation to the size of the potassium ion (K⁺) and the nature of the anions involved.

### Step-by-Step Solution:

1. **Understanding the Compounds**:
- K₂O is potassium oxide, containing the oxide ion (O²⁻).
- K₂O₂ is potassium peroxide, containing the peroxide ion (O₂²⁻).
- KO₂ is potassium superoxide, containing the superoxide ion (O₂⁻).

2. **Analyzing Stability**:
- The stability of these compounds can be compared based on the nature of the anions and the size of the cation (K⁺).
- As the size of the cation increases, it can better stabilize larger anions due to its lower charge density.

3. **Lattice Energy Consideration**:
- Lattice energy plays a crucial role in the stability of ionic compounds. Larger cations (like K⁺) can stabilize larger anions (like O₂²⁻ and O₂⁻) more effectively due to their ability to distribute the charge over a larger volume.
- K₂O has the smallest anion (O²⁻), which is less stabilized by K⁺ compared to the larger anions in K₂O₂ and KO₂.

4. **Order of Stability**:
- The order of stability is K₂O < K₂O₂ < KO₂.
- K₂O is the least stable because the K⁺ ion does not stabilize the O²⁻ ion effectively.
- K₂O₂ is more stable than K₂O because the larger O₂²⁻ ion is better stabilized by K⁺.
- KO₂ is the most stable because the superoxide ion (O₂⁻) is effectively stabilized by the K⁺ ion.

5. **Conclusion**:
- The increasing stability of K₂O, K₂O₂, and KO₂ is due to the stabilization of larger anions (O₂²⁻ and O₂⁻) by the larger cation (K⁺) through lattice energy effects.

### Final Answer:
The stability of K₂O, K₂O₂, and KO₂ is in the order K₂O < K₂O₂ < KO₂ due to the stabilization of larger anions by the larger cation (K⁺) through lattice energy.