The correct order of bond angle of `NO_(2)^(+),NO_(2) and NO_(2)^(-)` is

Options

A. `NO_(2)^(ɵ) gt NO_(2) gt NO_(2)^(o+)`
B. `NO_(2)^(o+) gt NO_(2) gt NO_(2)^(ɵ)`
C. `NO_(2)^(ɵ) gt NO_(2)^(o+) gt NO_(2)`
D. `NO_(2) gt NO_(2)^(ɵ) gt NO_(2)^(o+)`

Answer

To determine the correct order of bond angles for the ions \( NO_2^+, NO_2, \) and \( NO_2^- \), we can follow these steps:

### Step 1: Determine the Valence Electrons
- **For \( NO_2^+ \)**: Nitrogen has 5 valence electrons. The positive charge indicates the loss of one electron, leaving 4 valence electrons. Each oxygen atom requires 2 electrons for bonding, and with 2 oxygen atoms, all 4 electrons are used for bonding.

- **For \( NO_2 \)**: Nitrogen has 5 valence electrons. In this case, all 4 electrons are used for bonding with 2 oxygen atoms, leaving 1 unpaired electron.

- **For \( NO_2^- \)**: Nitrogen still has 5 valence electrons, but the negative charge indicates the addition of one electron, giving a total of 6 valence electrons. Again, 4 electrons are used for bonding, leaving 2 electrons as a lone pair.

### Step 2: Identify Bonding and Lone Pairs
- **\( NO_2^+ \)**: 2 bond pairs, 0 lone pairs.
- **\( NO_2 \)**: 2 bond pairs, 1 lone pair.
- **\( NO_2^- \)**: 2 bond pairs, 1 lone pair.

### Step 3: Analyze the Geometry and Bond Angles
Using VSEPR theory:
- **\( NO_2^+ \)**: With 2 bond pairs and no lone pairs, the geometry is linear, leading to a bond angle of approximately 180°.

- **\( NO_2 \)**: With 2 bond pairs and 1 lone pair, the geometry is bent. The bond angle is slightly less than 120° due to the presence of the lone pair, which causes greater repulsion.

- **\( NO_2^- \)**: Similar to \( NO_2 \), it has 2 bond pairs and 1 lone pair. The bond angle is also slightly less than 120°, but the presence of the lone pair may cause even more repulsion than in \( NO_2 \).

### Step 4: Determine the Order of Bond Angles
Based on the analysis:
- \( NO_2^+ \) has the largest bond angle (180°).
- \( NO_2 \) has a bond angle slightly less than 120°.
- \( NO_2^- \) also has a bond angle slightly less than 120°, but potentially smaller than that of \( NO_2 \) due to increased lone pair repulsion.

Thus, the correct order of bond angles is:
\[ NO_2^+ > NO_2 > NO_2^- \]

### Final Answer
The correct order of bond angles is \( NO_2^+, NO_2, NO_2^- \).

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