Question: Assign formal charges to each carbon atom in the given species. All lone pairs have been drawn in.

a.

b.

c.

d.

The determination of formal charge is completed by using the given formula:

$\mathbf{Formal}\mathbf{}\mathbf{charge}\mathbf{}\mathbf{=}\mathbf{}\left(\mathrm{valence}{e}^{-}\right)\mathbf{-}\left(\mathrm{lone}\mathrm{pair}\mathrm{of}{e}^{-}\right)\mathbf{-}\left(\frac{1}{2}\times \mathrm{bonding}\mathrm{pair}\mathrm{of}{e}^{-}\right)$

a. The formal charge of ${\mathrm{CH}}_2$ carbon is calculated as follows:

• The total valence electrons of carbon are four.
• The number of lone pairs of electrons is zero.
• The total number of bonding pair electrons is 8 as all the carbon electrons are used.

Therefore,

$\begin{array}{rcl}\mathrm{Formal}\mathrm{charge}\mathrm{of}\mathrm{C}& =& 4-0-\left(\frac{1}{2}\times 8\right)\\ & =& 4-4\\ & =& 0\end{array}$

Hence, the formal charge of ${\mathrm{CH}}_2$carbon is zero.

Similarly, for CH carbon, the calculation of formal charge is as follows:

• The total valence electrons of carbon are four.
• The number of lone pairs of electrons is two.
• The total number of bonding pair electrons is 6 as all the carbon electrons are used.

Therefore,

$\begin{array}{rcl}\mathrm{Formal}\mathrm{charge}\mathrm{of}\mathrm{C}& =& 4-2-\left(\frac{1}{2}\times 6\right)\\ & =& 4-2-3\\ & =& -1\end{array}$

Hence, the formal charge of CH carbon is -1.

b. The formal charge of carbon is calculated as follows:

• The total valence electrons of carbon are four.
• The number of lone pairs of electrons is two.
• The total number of bonding pair electrons is four as all the carbon electrons are used.

Therefore,

$\begin{array}{rcl}\mathrm{Formal}\mathrm{charge}\mathrm{of}\mathrm{C}& =& 4-2-\left(\frac{1}{2}\times 4\right)\\ & =& 4-2-2\\ & =& 0\end{array}$

Hence, the formal charge of carbon is zero.

c. The calculation of formal charge for carbon is as follows.

• The total valence electrons of carbon are four.
• The number of lone pairs of electrons is 1.
• The total number of bonding pair electrons is 6 as all the carbon electrons are used.

Therefore,

role="math" localid="1648299817010" $\begin{array}{rcl}\mathrm{Formal}\mathrm{charge}\mathrm{of}\mathrm{C}& =& 4-1-\left(\frac{1}{2}\times 6\right)\\ & =& 4-4\\ & =& 0\end{array}$

Hence, the formal charge of carbon is zero.

d. The calculation of formal charge for carbon in is as follows:

• The total valence electrons of carbon are four.
• The number of lone pairs of electrons is zero.
• The total number of bonding pair electrons is 6 as all the carbon electrons are used.

Therefore,

role="math" localid="1648299908412" $\begin{array}{rcl}\mathrm{Formal}\mathrm{charge}\mathrm{of}\mathrm{C}& =& 4-0-\left(\frac{1}{2}\times 6\right)\\ & =& 4-3\\ & =& 1\end{array}$

Hence, the formal charge of carbon is +1.

The calculation of formal charge for carbon in as follows:

• The total valence electrons of carbon are four.
• The number of lone pairs of electrons is zero.
• The total number of bonding pair electrons is 8 as all the carbon electrons are used.

Therefore,

$\begin{array}{rcl}\mathrm{Formal}\mathrm{charge}\mathrm{of}\mathrm{C}& =& 4-0-\left(\frac{1}{2}\times 8\right)\\ & =& 4-0-4\\ & =& 0\end{array}$

Hence, the formal charge of ${\mathrm{CH}}_3$ carbon is zero.