The correct order of N-O bond lengths in NO, `NO_2^- , NO_3^-` and `N_2O_4` is

Options

A. `N_2O_4 gt NO_2^(-) gt NO_3^(-) gt NO`
B. `NO gt NO_3^(-) gt N_2O_4 gt NO_2^-`
C. `NO_3^(-) gt NO_2^(-) gt N_2O_4 gt NO`
D. `NO gt N_2O_4 gt NO_2^(-) gt NO_3^(-)`

Explanation

To determine the correct order of N-O bond lengths in the molecules NO, NO₂⁻, NO₃⁻, and N₂O₄, we will follow these steps:

### Step 1: Determine the Bond Order for Each Molecule
The bond order can be calculated using the formula:
\[ \text{Bond Order} = \frac{\text{Number of bonds}}{\text{Number of bonding sites}} \]

#### 1.1 For N₂O₄:
- Structure: N₂O₄ has a central nitrogen atom bonded to two oxygen atoms with double bonds and two oxygen atoms with single bonds.
- Number of bonds with oxygen: 6 (3 double bonds)
- Number of oxygen atoms: 4
- Bond Order:
\[ \text{Bond Order} = \frac{6}{4} = 1.5 \]

#### 1.2 For NO₂⁻:
- Structure: NO₂⁻ has a nitrogen atom bonded to two oxygen atoms, one with a double bond and one with a single bond, and carries a negative charge.
- Number of bonds with oxygen: 3 (1 double bond and 1 single bond)
- Number of oxygen atoms: 2
- Bond Order:
\[ \text{Bond Order} = \frac{3}{2} = 1.5 \]

#### 1.3 For NO₃⁻:
- Structure: NO₃⁻ has a nitrogen atom bonded to three oxygen atoms, one with a double bond and two with single bonds, and carries a negative charge.
- Number of bonds with oxygen: 4 (1 double bond and 2 single bonds)
- Number of oxygen atoms: 3
- Bond Order:
\[ \text{Bond Order} = \frac{4}{3} \approx 1.33 \]

#### 1.4 For NO:
- Structure: NO has a nitrogen atom bonded to one oxygen atom with a triple bond.
- Number of bonds with oxygen: 3 (1 triple bond)
- Number of oxygen atoms: 1
- Bond Order:
\[ \text{Bond Order} = \frac{3}{1} = 3.0 \]

### Step 2: Compare Bond Orders and Infer Bond Lengths
The bond order is inversely proportional to bond length; higher bond order means shorter bond length.

- NO: Bond Order = 3.0 (shortest bond length)
- N₂O₄: Bond Order = 1.5
- NO₂⁻: Bond Order = 1.5
- NO₃⁻: Bond Order ≈ 1.33 (longest bond length)

### Conclusion
Based on the bond orders, we can conclude the order of N-O bond lengths from shortest to longest:
1. NO (shortest bond length)
2. N₂O₄ and NO₂⁻ (same bond length)
3. NO₃⁻ (longest bond length)

Thus, the correct order of N-O bond lengths is:
**NO < N₂O₄ = NO₂⁻ < NO₃⁻**