To assign a formal charge to each oxygen atom in the peroxide ion [tex]\(\left( O_2^{2-} \right)\)[/tex], we need to use the formal charge formula:
[tex]\[
\text{Formal charge} = \text{Valence electrons} - (\text{Number of non-bonding electrons} + \frac{1}{2} \times \text{Number of bonding electrons})
\][/tex]
Let’s follow these steps for each oxygen atom in the given Lewis structure:
[tex]\[
\left[\begin{array}{cc}
: & \cdots \\
O & - O : \\
\cdots & \cdots
\end{array}\right]^{2-}
\][/tex]
### Step-by-Step Calculation for the Left Oxygen Atom
1. Count the valence electrons for oxygen: Each oxygen atom has 6 valence electrons.
2. Count the non-bonding electrons on the left oxygen: The left oxygen atom has 6 non-bonding electrons (represented by dots).
3. Count the bonding electrons: The bond between the two oxygens consists of a single bond, which means there are 2 electrons shared between them.
Using the formal charge formula for the left oxygen:
[tex]\[
\text{Formal charge} = 6 - (6 + \frac{1}{2} \times 2)
\][/tex]
Simplify the expression:
[tex]\[
\text{Formal charge} = 6 - (6 + 1) = 6 - 7 = -1
\][/tex]
Thus, the formal charge on the left oxygen atom is [tex]\(-1\)[/tex].
### Step-by-Step Calculation for the Right Oxygen Atom
1. Count the valence electrons for oxygen: Each oxygen atom has 6 valence electrons.
2. Count the non-bonding electrons on the right oxygen: The right oxygen atom has 6 non-bonding electrons (represented by dots).
3. Count the bonding electrons: The bond between the two oxygens consists of a single bond, which means there are 2 electrons shared between them.
Using the formal charge formula for the right oxygen:
[tex]\[
\text{Formal charge} = 6 - (6 + \frac{1}{2} \times 2)
\][/tex]
Simplify the expression:
[tex]\[
\text{Formal charge} = 6 - (6 + 1) = 6 - 7 = -1
\][/tex]
Thus, the formal charge on the right oxygen atom is [tex]\(-1\)[/tex].
### Conclusion
In the provided Lewis structure for the peroxide ion [tex]\(\left( O_2^{2-} \right)\)[/tex], both oxygen atoms have a formal charge of [tex]\(-1\)[/tex].
[tex]\[
\begin{tabular}{|c|c|}
\hline
atom & formal charge \\
\hline
left $O$ & -1 \\
\hline
right $O$ & -1 \\
\hline
\end{tabular}
\][/tex]
