The correct order of `o^(-)` bond lengths in `ClO^(-), ClO_(2)^(-), ClO_(3)^(-) and ClO_(4)^(-)` is

Options

A. `ClO^(-) lt ClO_(2)^(-) lt ClO_(3)^(-) lt ClO_(4)^(-)`
B. `ClO_(4)^(-) lt ClO_(3)^(-) lt ClO_(2)^(-) lt ClO^(-)`
C. `ClO_(3)^(-) lt ClO_(4)^(-) gt Cl)O_(2)^(-) gt ClO^(-)`
D. `ClO_(4)^(-)=ClO_(3)^(-) = ClO_(2)^(-) = ClO^(-)`

Answer

To determine the correct order of O⁻ bond lengths in ClO⁻, ClO₂⁻, ClO₃⁻, and ClO₄⁻, we need to analyze the structures and bonding in each of these species.

### Step 1: Draw the Lewis Structures

1. **ClO⁻ (Chlorite ion)**:
- Chlorine (Cl) has 7 valence electrons.
- Oxygen (O) has 6 valence electrons.
- The negative charge contributes an additional electron.
- Total: 7 (Cl) + 6 (O) + 1 (charge) = 14 electrons.
- Structure: Cl is bonded to O with a single bond and has three lone pairs on O.

2. **ClO₂⁻ (Chlorite ion)**:
- Total valence electrons: 7 (Cl) + 2*6 (O) + 1 (charge) = 20 electrons.
- Structure: Cl is bonded to two O atoms, one with a double bond and one with a single bond. The single-bonded O has three lone pairs, and the double-bonded O has two lone pairs.

3. **ClO₃⁻ (Chlorate ion)**:
- Total valence electrons: 7 (Cl) + 3*6 (O) + 1 (charge) = 26 electrons.
- Structure: Cl is bonded to three O atoms, each with a double bond. There are no lone pairs on the O atoms.

4. **ClO₄⁻ (Perchlorate ion)**:
- Total valence electrons: 7 (Cl) + 4*6 (O) + 1 (charge) = 32 electrons.
- Structure: Cl is bonded to four O atoms, each with a double bond. There are no lone pairs on the O atoms.

### Step 2: Analyze Bond Lengths

- **Bond Lengths**: The bond length is influenced by the type of bond (single or double) and the number of resonance structures.
- ClO⁻ has one single bond, leading to the longest bond length.
- ClO₂⁻ has one double bond and one single bond, leading to a shorter bond length than ClO⁻.
- ClO₃⁻ has three double bonds, leading to even shorter bond lengths.
- ClO₄⁻ has four double bonds, resulting in the shortest bond lengths.

### Step 3: Order the Bond Lengths

Based on the analysis:
- ClO⁻ (longest bond length)
- ClO₂⁻
- ClO₃⁻
- ClO₄⁻ (shortest bond length)

### Final Order of O⁻ Bond Lengths

The correct order of O⁻ bond lengths is:
**ClO⁻ > ClO₂⁻ > ClO₃⁻ > ClO₄⁻**