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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]
[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]
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