Question

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

a.

b.

c.

d.

Short answer

Answer

a. 0 and -1, respectively

b. 0

c. 0

d. 0 and +1, respectively

Step-by-step solution

Step-by-Step Solution Step 1: Determination of formal charge  

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

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

Calculation of formal charge

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.