Q. Resonance structures for \(\mathrm{Co_3^{2-}}\).

Goal: Draw and explain the resonance structures for the carbonate ion, \( \mathrm{CO_3^{2-}} \).

1) Determine the total number of valence electrons

Carbon has \(4\) valence electrons. Each oxygen has \(6\) valence electrons, and there are three oxygens.

\[
\text{Total valence electrons} = 4 + 3(6) + 2 = 4 + 18 + 2 = 24
\]

2) Choose a reasonable bonding skeleton

In carbonate, carbon is typically the central atom and bonds to three oxygens. Start with three single bonds \( \mathrm{C-O} \). This uses \(3\) bonds total.

Each single \( \mathrm{C-O} \) bond has \(2\) electrons, so three single bonds use \(6\) electrons.

\[
\text{Electrons used in } 3 \text{ single bonds} = 3 \times 2 = 6
\]

3) Distribute electrons to satisfy the octet rule for oxygen first

With three single bonds, each oxygen has one bond to carbon. To reach the oxygen octet, each oxygen needs additional electrons.

For a neutral oxygen with one single bond, the oxygen must have \(3\) lone pairs to complete an octet (that is \(6\) nonbonding electrons plus \(2\) bonding electrons gives \(8\)).

So assign \(3\) lone pairs on each O.

That means each oxygen gets \(6\) nonbonding electrons.

Total nonbonding electrons assigned to three oxygens:
\[
3 \times 6 = 18
\]

Now count the used electrons: \(6\) bonding + \(18\) nonbonding = \(24\), which matches the total valence electrons. So that is the structure for a moment—but we must check formal charges.

4) Compute formal charges to find the resonance contributors

Because \( \mathrm{CO_3^{2-}} \) has a \(2-\) charge, we expect the charge to be distributed such that the overall formal charges sum to \(-2\).

4a) Formal charges for the “all single bonds” attempt

For carbon with four valence electrons in a structure where carbon has 3 single bonds:

Carbon has:
– No lone pairs
– 3 bonds total, so it “owns” \(3\) bonding pairs for formal charge purposes.

Formal charge formula:

\[
\mathrm{FC = V – (N + \tfrac{1}{2}B)}
\]

where \(V\) = valence electrons, \(N\) = nonbonding electrons, and \(B\) = bonding electrons.

For carbon:

\(V=4\), \(N=0\), \(B=6\) (since 3 single bonds = 6 bonding electrons). Then

\[
\mathrm{FC_C = 4 – \left(0 + \tfrac{1}{2}\cdot 6\right) = 4 – 3 = +1}
\]

For each oxygen:

Each oxygen has one single bond to carbon and 3 lone pairs.

So for one oxygen: \(V=6\), \(N=6\) (3 lone pairs), \(B=2\) (one single bond gives 2 bonding electrons). Then

\[
\mathrm{FC_O = 6 – \left(6 + \tfrac{1}{2}\cdot 2\right) = 6 – (6+1)= -1}
\]

So with all three single bonds:

\(\mathrm{FC_C=+1}\) and each oxygen is \(-1\). Total formal charge:

\[
(+1) + 3(-1) = -2
\]

That matches the overall charge. However, carbonate resonance is commonly represented by structures where one oxygen has a double bond while the other two have single bonds. Those resonance contributors are typically the most informative because they show better distribution of bonding electrons and typical octet satisfaction patterns.

5) Write the standard resonance structures for \( \mathrm{CO_3^{2-}} \)

In the most common resonance representation:

• One oxygen is double-bonded to carbon: \( \mathrm{C=O} \)
• The other two oxygens are single-bonded: \( \mathrm{C-O^-} \) on each of them

Resonance structure 1: double bond to oxygen 1; single bonds to oxygens 2 and 3

In words:

• One \( \mathrm{C=O} \) oxygen has two lone pairs
• Each single-bond oxygen has three lone pairs and carries a \(-1\) formal charge
• Carbon has formal charge \(0\) in this standard form

Resonance structure 2: double bond to oxygen 2

This is identical in form to structure 1, except the \( \mathrm{C=O} \) double bond is on a different oxygen.

Resonance structure 3: double bond to oxygen 3

Again identical, but the \( \mathrm{C=O} \) double bond is on the third oxygen.

6) Show the three resonance contributors explicitly (text form with charges)

Structure A:

\[
\mathrm{^{-}O\!-\!C(=O)\!-\!O^{-}}
\]

Structure B:

\[
\mathrm{O^{-}\!-\!C(=O)\!-\!^{-}O}
\]

Structure C:

\[
\mathrm{O^{-}\!-\!C(=O)\!-\!O^{-}}
\]

Important note about the text representations: Each resonance form has exactly:

• One \( \mathrm{C=O} \) double bond
• Two \( \mathrm{C-O^-} \) single bonds

and the \(-1\) formal charge appears on the two oxygens that are singly bonded to carbon.

7) Condensed “answer-ready” summary

Carbonate \( \mathrm{CO_3^{2-}} \) has three equivalent resonance structures, corresponding to which one of the three oxygens is double-bonded to carbon:

• \(\mathrm{O^{-} – C(=O) – O^{-}}\)
• \(\mathrm{O^{-} – C(=O) – O^{-}}\) (double bond on the second oxygen)
• \(\mathrm{O^{-} – C(=O) – O^{-}}\) (double bond on the third oxygen)

All three have the same overall formal-charge pattern: carbon is \(0\), and two oxygens are each \(-1\), totaling \(-2\).