O – O bond length in` H_2O_2` is X than the `O -O` bond length in `F_2O_2`. The `O – H `bond length in` H_2O_2 `is Y than that of the O – F bond in `F_2O_2.` Choose the correct option for `X `and `Y `from those given below

Options

A. `X` : Longer `Y `: Shorter`
B. `X `: Shorter `Y` : Longer
C. `X `: Shorter `Y `: Shorter
D. `X` : Longer `Y` : Longer`

Answer

To solve the question regarding the bond lengths in hydrogen peroxide (H₂O₂) and fluorine peroxide (F₂O₂), we will analyze the bond lengths based on the electronegativity of the atoms involved.

### Step-by-Step Solution:

1. **Understanding the Structures**:
- H₂O₂ (hydrogen peroxide) has the structure where two oxygen atoms are bonded to each other and each oxygen is also bonded to a hydrogen atom.
- F₂O₂ (fluorine peroxide) has a similar structure, but instead of hydrogen, each oxygen is bonded to a fluorine atom.

2. **Comparing O-O Bond Lengths**:
- In H₂O₂, the O-O bond length is influenced by the presence of hydrogen atoms, which are less electronegative than oxygen. This means that the oxygen atoms will hold onto their electrons more tightly, resulting in a longer O-O bond length.
- In F₂O₂, the O-O bond length is influenced by the presence of fluorine atoms. Fluorine is more electronegative than oxygen, which means it will attract electrons more strongly, leading to a shorter O-O bond length compared to H₂O₂.
- Therefore, we conclude that the O-O bond length in H₂O₂ (let's denote it as X) is **greater** than the O-O bond length in F₂O₂.

3. **Comparing O-H and O-F Bond Lengths**:
- In H₂O₂, the O-H bond length is influenced by the fact that hydrogen is less electronegative than oxygen. This results in a relatively shorter O-H bond length.
- In F₂O₂, the O-F bond length is influenced by the high electronegativity of fluorine, which pulls the bonding electrons closer to itself, resulting in a longer O-F bond length compared to O-H.
- Therefore, we conclude that the O-H bond length in H₂O₂ (denote it as Y) is **shorter** than the O-F bond length in F₂O₂.

4. **Final Conclusions**:
- From the above analysis, we can summarize:
- X (O-O bond length in H₂O₂) is **greater** than the O-O bond length in F₂O₂.
- Y (O-H bond length in H₂O₂) is **shorter** than the O-F bond length in F₂O₂.

### Final Answer:
- X is larger (O-O bond length in H₂O₂ > O-O bond length in F₂O₂).
- Y is smaller (O-H bond length in H₂O₂ < O-F bond length in F₂O₂).