Absolutely! Let's determine the formal charge for each atom in the structure [tex]\(\ddot{O} = \ddot{C} = O\)[/tex].
### Step-by-step solution:
#### Formal Charge Formula:
The formal charge is calculated using the formula:
[tex]\[ \text{Formal charge} = (\text{number of valence electrons in the free atom}) - (\text{number of non-bonding electrons}) - \frac{1}{2}(\text{number of bonding electrons}) \][/tex]
#### Leftmost Oxygen, [tex]\( \ddot{O} \)[/tex]:
1. Valence electrons: Oxygen has 6 valence electrons.
2. Non-bonding electrons: In the given structure, the leftmost oxygen has 6 non-bonding electrons (shown as 3 lone pairs).
3. Bonding electrons: It is bonded to one other atom (2 bonding electrons in one bond with the central oxygen).
Using the formal charge formula:
[tex]\[ \text{Formal charge} = 6 - 6 - \frac{1}{2} \times 2 = 6 - 6 - 1 = -1 \][/tex]
So, the formal charge on the leftmost O atom is -1.
#### Central Oxygen, [tex]\( =O= \)[/tex]:
1. Valence electrons: Oxygen has 6 valence electrons.
2. Non-bonding electrons: The central oxygen has 4 non-bonding electrons (shown as 2 lone pairs).
3. Bonding electrons: It is bonded to two other atoms (4 bonding electrons in total, 2 for each bond).
Using the formal charge formula:
[tex]\[ \text{Formal charge} = 6 - 4 - \frac{1}{2} \times 4 = 6 - 4 - 2 = 0 \][/tex]
So, the formal charge on the central O atom is 0.
#### Rightmost Carbon, [tex]\(C\)[/tex]:
1. Valence electrons: Carbon has 4 valence electrons.
2. Non-bonding electrons: The rightmost carbon has 0 non-bonding electrons.
3. Bonding electrons: It is bonded to two oxygen atoms with double bonds, meaning 4 electrons for each double bond, making a total of 8 bonding electrons.
Using the formal charge formula:
[tex]\[ \text{Formal charge} = 4 - 0 - \frac{1}{2} \times 8 = 4 - 0 - 4 = 0 \][/tex]
So, the formal charge on the rightmost C atom is 0.
### Summary:
- The formal charge on the leftmost O atom is -1.
- The formal charge on the central O atom is 0.
- The formal charge on the rightmost C atom is 0.
This matches the charges as follows:
- The formal charge on the leftmost O atom: [tex]\(-1\)[/tex]
- The formal charge on the central O atom: [tex]\(0\)[/tex]
- The formal charge on the rightmost C atom: [tex]\(0\)[/tex]
