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 which statement is correct for the \( \text{NO}_3^{-} \) ion, we need to analyze its structure and calculate the formal charges of its constituent atoms.

### Step-by-Step Solution:

1. **Identify the Structure of \( \text{NO}_3^{-} \)**:
- The nitrate ion (\( \text{NO}_3^{-} \)) consists of one nitrogen atom and three oxygen atoms. The nitrogen atom is centrally located, and it is bonded to three oxygen atoms.

2. **Draw the Lewis Structure**:
- The nitrogen atom forms one double bond with one oxygen atom and single bonds with the other two oxygen atoms. One of the oxygen atoms carries a negative charge.

3. **Calculate the Formal Charge**:
- The formula for calculating the formal charge (FC) is:
\[ \text{FC} = \text{Valence Electrons} - \text{Non-bonding Electrons} - \frac{1}{2} \times \text{Bonding Electrons} \]

4. **Calculate the Formal Charge for Nitrogen**:
- Nitrogen has 5 valence electrons.
- There are no non-bonding electrons on nitrogen.
- The bonding electrons (from three bonds) total 8 (6 from the double bond and 2 from the single bonds).
- Thus, the formal charge on nitrogen is:
\[ \text{FC}_{N} = 5 - 0 - \frac{8}{2} = 5 - 0 - 4 = +1 \]

5. **Calculate the Formal Charge for Each Oxygen**:
- For the singly bonded oxygen (with a negative charge):
- Valence electrons = 6
- Non-bonding electrons = 6 (3 lone pairs)
- Bonding electrons = 2 (1 bond)
\[ \text{FC}_{O1} = 6 - 6 - \frac{2}{2} = 6 - 6 - 1 = -1 \]
- For the doubly bonded oxygen:
- Valence electrons = 6
- Non-bonding electrons = 4 (2 lone pairs)
- Bonding electrons = 4 (2 bonds)
\[ \text{FC}_{O2} = 6 - 4 - \frac{4}{2} = 6 - 4 - 2 = 0 \]
- The other singly bonded oxygen (without charge):
- Valence electrons = 6
- Non-bonding electrons = 6 (3 lone pairs)
- Bonding electrons = 2 (1 bond)
\[ \text{FC}_{O3} = 6 - 6 - \frac{2}{2} = 6 - 6 - 1 = -1 \]

6. **Sum of Formal Charges**:
- The sum of the formal charges is:
\[ +1 \text{ (from N)} + (-1) + 0 + (-1) = +1 - 2 = -1 \]
- This matches the overall charge of the nitrate ion, which is -1.

7. **Conclusion**:
- The formal charge on nitrogen is +1, and the formal charge on one of the oxygen atoms is -1. The average formal charge on the oxygen atoms can be calculated as:
\[ \text{Average FC on O} = \frac{-1 + 0 - 1}{3} = -\frac{2}{3} \]
- Thus, the correct statement is that the formal charge on nitrogen is +1.

### Final Answer:
- The correct statement for \( \text{NO}_3^{-} \) is: **The formal charge on nitrogen is +1.**