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 bond types in each of these species. Here’s a step-by-step breakdown of the solution:

### Step 1: Draw the Lewis Structures
1. **ClO⁻ (Chlorite Ion)**:
- Chlorine (Cl) is bonded to one oxygen (O) with a single bond.
- The oxygen has three lone pairs.
- Structure: Cl - O⁻ (single bond).

2. **ClO₂⁻ (Chlorate Ion)**:
- Chlorine is bonded to one oxygen with a double bond and to another oxygen with a single bond.
- The singly bonded oxygen has two lone pairs, while the doubly bonded oxygen has no lone pairs.
- Structure: Cl = O (double bond) and Cl - O⁻ (single bond).

3. **ClO₃⁻ (Chlorate Ion)**:
- Chlorine is bonded to two oxygens with double bonds and one oxygen with a single bond.
- The singly bonded oxygen has one lone pair.
- Structure: Cl = O (double bond), Cl = O (double bond), and Cl - O⁻ (single bond).

4. **ClO₄⁻ (Perchlorate Ion)**:
- Chlorine is bonded to four oxygens with double bonds.
- There are no lone pairs on any of the oxygens.
- Structure: Cl = O (double bond) for all four oxygens.

### Step 2: Analyze Bond Types
- The bond length is influenced by the type of bond:
- **Single bonds** are longer than **double bonds**.
- As the number of double bonds increases, the bond length decreases.

### Step 3: Determine the Order of Bond Lengths
- **ClO⁻** has a single bond, which is the longest bond length.
- **ClO₂⁻** has one single bond and one double bond, making it shorter than ClO⁻.
- **ClO₃⁻** has two double bonds and one single bond, making it shorter than ClO₂⁻.
- **ClO₄⁻** has all double bonds, making it the shortest bond length.

### Conclusion
The order of O⁻ bond lengths from longest to shortest is:
**ClO⁻ > ClO₂⁻ > ClO₃⁻ > ClO₄⁻**.

### Final Answer
The correct order of O⁻ bond lengths is ClO⁻ > ClO₂⁻ > ClO₃⁻ > ClO₄⁻, which corresponds to option A.