To determine the formal charges for each atom in the student's proposed Lewis structure of carbon dioxide (CO₂), we will follow the formal charge formula. Formal charge is calculated using the following equation:
[tex]\[ \text{Formal Charge} = \text{(Number of valence electrons)} - (\text{Number of lone pair electrons}) - \frac{1}{2} (\text{Number of bonding electrons}) \][/tex]
Given the structure for CO₂: O=C=O, where each oxygen has 2 lone pairs, we will calculate the formal charges for each atom step-by-step.
1. Left Oxygen (O) Atom:
- Valence Electrons: Oxygen has 6 valence electrons.
- Lone Pair Electrons: There are 4 lone pair electrons on the left oxygen.
- Bonding Electrons: The left oxygen forms a double bond with carbon, so it has 4 bonding electrons.
Using the formula:
[tex]\[
\text{Formal Charge of Left O} = 6 - 4 - \frac{1}{2}(4) = 6 - 4 - 2 = 0
\][/tex]
2. Carbon (C) Atom:
- Valence Electrons: Carbon has 4 valence electrons.
- Lone Pair Electrons: There are no lone pair electrons on carbon.
- Bonding Electrons: Carbon forms two double bonds with both oxygen atoms, so it has a total of 8 bonding electrons.
Using the formula:
[tex]\[
\text{Formal Charge of C} = 4 - 0 - \frac{1}{2}(8) = 4 - 0 - 4 = 0
\][/tex]
3. Right Oxygen (O) Atom:
- Valence Electrons: Oxygen has 6 valence electrons.
- Lone Pair Electrons: There are 4 lone pair electrons on the right oxygen.
- Bonding Electrons: The right oxygen forms a double bond with carbon, so it has 4 bonding electrons.
Using the formula:
[tex]\[
\text{Formal Charge of Right O} = 6 - 4 - \frac{1}{2}(4) = 6 - 4 - 2 = 0
\][/tex]
Hence, the formal charges for each atom in the CO₂ molecule are as follows:
[tex]\[
\begin{tabular}{|c|c|}
\hline
atom & formal charge \\
\hline
left O & 0 \\
\hline
C & 0 \\
\hline
right O & 0 \\
\hline
\end{tabular}
\][/tex]
