Question

How to count formal charge in ${{\mathrm{NO}}_2}^{-}$?

Answer 1

Formal charge:-

• Formal charge of a compound can be calculated by the formula:

$\mathrm{FC}=\mathrm{V}-\mathrm{N}-\frac{\mathrm{B}}{2}$

• Here, FC= Formal charge, V= number of valence electrons in a free atom, N= total number of non-bonding electrons, B= total number of bonding electrons

Formal charge of ${{\mathrm{NO}}_2}^{-}$:-

• Structure of ${{\mathrm{NO}}_2}^{-}$is:

Step 1: Formal charge of Nitrogen

Here Nitrogen is the free atom and the number of valence electrons of it is 5.

Number of non-bonding electrons is 2 and bonding electrons are 6

$\therefore$Formal charge of Nitrogen is

$$\begin{gathered} \mathrm{FC}=\mathrm{V}-\mathrm{N}-\frac{\mathrm{B}}{2} \\ \Rightarrow \mathrm{FC}=5-2-\left(\frac{6}{2}\right) \\ \Rightarrow \mathrm{FC}=5-5 \\ \Rightarrow \mathrm{FC}=0 \end{gathered}$$

Step 2: Formal charge of double-bonded Oxygen

Here oxygen is the free atom and the number of valence electrons of it is 6.

Number of non-bonding electrons is 4 and bonding electrons are 4

$\therefore$Formal charge of double bonded oxygen is

$$\begin{gathered} \mathrm{FC}=\mathrm{V}-\mathrm{N}-\frac{\mathrm{B}}{2} \\ \Rightarrow \mathrm{FC}=6-4-\left(\frac{4}{2}\right) \\ \Rightarrow \mathrm{FC}=2-2 \\ \Rightarrow \mathrm{FC}=0 \end{gathered}$$

Step 3: Formal charge of single-bonded Oxygen

Here oxygen is the free atom and the number of valence electrons of it is 6.

Number of non-bonding electrons is 6 and bonding electrons are 2

$\therefore$Formal charge of single-bonded oxygen is

$$\begin{gathered} \mathrm{FC}=\mathrm{V}-\mathrm{N}-\frac{\mathrm{B}}{2} \\ \Rightarrow \mathrm{FC}=6-6-\left(\frac{2}{2}\right) \\ \Rightarrow \mathrm{FC}=0-1 \\ \Rightarrow \mathrm{FC}=-1 \end{gathered}$$

Step 4: Formal charge of ${{\mathrm{NO}}_2}^{-}$

Adding all the three different formal charges of Nitrogen and Oxygens we get the formal charge of ${{\mathrm{NO}}_2}^{-}$

$\therefore$Formal charge of ${{\mathrm{NO}}_2}^{-}$is

$$\begin{gathered} \mathrm{FC}=0+0+(-1) \\ \Rightarrow \mathrm{FC}=-1 \end{gathered}$$

Therefore, the formal charge of ${{\mathrm{NO}}_2}^{-}$ is $-1$