Which of the following statement is correct for `NO_3^(-)` ion ?

Options

A. Sum of all formal charges = + 1
B. Formal charge on one of the oxygen atom = -2
C. Formal charge on nitrogen atom = +1
D. Average formal charge on oxygen atom `=-1/3`

Answer

To determine the correct statement regarding the nitrate ion \( \text{NO}_3^{-} \), we will calculate the formal charges of the atoms in the ion and analyze the provided statements.

### Step 1: Draw the Lewis Structure of \( \text{NO}_3^{-} \)
1. **Count the total number of valence electrons**:
- Nitrogen (N) has 5 valence electrons.
- Each Oxygen (O) has 6 valence electrons, and there are 3 Oxygens: \( 3 \times 6 = 18 \).
- The ion has an extra electron due to the negative charge.
- Total = \( 5 + 18 + 1 = 24 \) valence electrons.

2. **Construct the Lewis structure**:
- Place Nitrogen in the center and connect it to three Oxygen atoms.
- Form a double bond with one Oxygen and single bonds with the other two Oxygens.
- Distribute the remaining electrons to satisfy the octet rule.

### Step 2: Calculate the Formal Charges
The formula for formal charge is:
\[ \text{Formal Charge} = V - (N + \frac{B}{2}) \]
Where:
- \( V \) = number of valence electrons
- \( N \) = number of non-bonding electrons
- \( B \) = number of bonding electrons

#### For Nitrogen:
- Valence electrons (V) = 5
- Non-bonding electrons (N) = 0
- Bonding electrons (B) = 8 (4 from the double bond and 4 from the two single bonds)
\[ \text{Formal Charge on N} = 5 - (0 + \frac{8}{2}) = 5 - 4 = +1 \]

#### For Oxygen with a double bond (let's call it O1):
- Valence electrons (V) = 6
- Non-bonding electrons (N) = 4
- Bonding electrons (B) = 4 (2 from the double bond)
\[ \text{Formal Charge on O1} = 6 - (4 + \frac{4}{2}) = 6 - 6 = 0 \]

#### For the two Oxygens with single bonds (O2 and O3):
- Valence electrons (V) = 6
- Non-bonding electrons (N) = 6
- Bonding electrons (B) = 2 (1 from the single bond)
\[ \text{Formal Charge on O2} = 6 - (6 + \frac{2}{2}) = 6 - 7 = -1 \]
\[ \text{Formal Charge on O3} = 6 - (6 + \frac{2}{2}) = 6 - 7 = -1 \]

### Step 3: Sum of Formal Charges
- Total formal charge = \( +1 \) (N) + \( 0 \) (O1) + \( -1 \) (O2) + \( -1 \) (O3) = \( -1 \)

### Step 4: Analyze the Statements
1. **Sum of all formal charges is +1**: Incorrect (it is -1).
2. **Formal charges on one of the oxygen atoms is -2**: Incorrect (none have -2).
3. **Formal charge on nitrogen atom is +1**: Correct (as calculated).
4. **Average formal charge on oxygen atom is -1/3**: Incorrect (it is -2/3).

### Conclusion
The correct statement is:
- **Formal charge on nitrogen atom is +1**.