In which conversion , bond length decreases ?

Options

A. `N_(2) to N_(2)^(+)`
B. `N_(2) to N_(2)^(-)`
C. `CO to CO^(+)`
D. `O_(2) to O_(2)^(-)`

Answer

To determine in which conversion the bond length decreases, we need to analyze the hybridization changes in the given options. A decrease in bond length typically occurs when the hybridization changes from a lower s-character to a higher s-character, as higher s-character leads to stronger, shorter bonds.

### Step-by-Step Solution:

1. **Identify the Hybridization of the Atoms in Each Option**:
- **Option 1: Ammonia (NH₃) and Ammonium Ion (NH₄⁺)**
- For NH₃: Nitrogen has 5 valence electrons, and with 3 hydrogen atoms (1 valence electron each), the total is 8 valence electrons. This gives us 4 electron pairs (8/2 = 4), leading to sp³ hybridization.
- For NH₄⁺: The calculation is similar, but we subtract 1 for the positive charge. The total remains 8 valence electrons, resulting in sp³ hybridization as well.
- **Conclusion**: No change in hybridization.

2. **Option 2: Boron Trifluoride (BF₃) and Tetrafluoroborate Ion (BF₄⁻)**
- For BF₃: Boron has 3 valence electrons, and with 3 fluorine atoms (7 valence electrons each), we have a total of 24 valence electrons. This gives us 3 electron pairs (24/8 = 3), leading to sp² hybridization.
- For BF₄⁻: The calculation adds 1 for the negative charge, resulting in 32 valence electrons and 4 electron pairs (32/8 = 4), leading to sp³ hybridization.
- **Conclusion**: Hybridization changes from sp² to sp³.

3. **Option 3: Ethyne (C₂H₂) and Ethane (C₂H₆)**
- For C₂H₂: Each carbon is sp hybridized (2 electron pairs).
- For C₂H₆: Each carbon is sp³ hybridized (4 electron pairs).
- **Conclusion**: Hybridization changes from sp to sp³.

4. **Determine the Bond Length Changes**:
- In both options 2 and 3, the hybridization changes from a lower s-character (sp² in BF₃ and sp in C₂H₂) to a higher s-character (sp³ in BF₄⁻ and C₂H₆). This indicates that the bond lengths decrease in these conversions.

### Final Answer:
The bond length decreases in the conversions from BF₃ to BF₄⁻ and from C₂H₂ to C₂H₆.