Q. \( \)Lewis dot structure for \( \mathrm{Co_3^{2-}} \).

We want the Lewis dot structure of the ion \( \mathrm{CO_3^{2-}} \) (carbonate). The goal is to draw a structure that places the correct number of valence electrons on the atoms and satisfies the usual octet rule as much as possible (with resonance).

Step 1: Count total valence electrons

Determine the number of valence electrons from each atom, then add for the charge.

\(\mathrm{C}\) has 4 valence electrons.

\(\mathrm{O}\) has 6 valence electrons each, and there are 3 oxygens.

The \(2-\) charge means we add 2 extra electrons.

Total valence electrons:

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

So, \(24\) valence electrons must be placed into the Lewis structure.

Step 2: Decide the central atom

In \(\mathrm{CO_3^{2-}}\), the carbon atom is the central atom because oxygen typically forms terminal positions around it.

So the basic skeleton is \( \mathrm{O – C – O} \) with a third oxygen attached, giving a planar arrangement (a “trigonal planar” idea).

Step 3: Place electrons to form initial single bonds

Connect carbon to each of the three oxygens with single bonds.

That means there are \(3\) C–O single bonds.

Each single bond uses \(2\) electrons, so:

\[
3 \text{ bonds} \times 2 \text{ electrons per bond} = 6 \text{ electrons used}
\]

Remaining electrons:

\[
24 – 6 = 18 \text{ electrons remaining}
\]

Step 4: Distribute remaining electrons to oxygen atoms

Give each oxygen an octet. For a typical Lewis structure setup, each oxygen needs \(8\) electrons around it.

At this stage, each oxygen has one single bond to carbon, which provides 2 electrons to that oxygen. Each oxygen still needs 6 more electrons to reach an octet.

Each oxygen will get \(3\) lone pairs (since each lone pair is 2 electrons):

\(3 \text{ lone pairs per oxygen} \times 2 = 6\) electrons added to each oxygen.

Thus each oxygen achieves an octet.

All \(18\) remaining electrons form lone pairs on the three oxygens, because \(3\) oxygens \(\times 3\) lone pairs each \(= 9\) lone pairs \(= 18\) electrons.

Step 5: Check carbon’s octet

Now check the electron count around carbon.

Carbon is bonded to three oxygens with three single bonds. Each single bond counts as 2 electrons shared with carbon, but for the octet check we consider bond electrons around carbon.

Carbon has:

\(3\) single bonds \(\Rightarrow\) \(3 \times 2 = 6\) electrons associated with carbon (or effectively carbon has 6 electrons around it from bonding).

That means carbon is short of an octet (it has 6), so we need to convert one of the bonds into a double bond.

Step 6: Convert to the correct carbonate structure (resonance)

For carbonate, the correct Lewis structures have:

• One C–O double bond
• Two C–O single bonds
• Oxygens with double-bonding have fewer lone pairs than the oxygens with single bonds
• Overall formal charge sum equals \(-2\)

One valid Lewis structure (place the double bond on one oxygen):

Draw \( \mathrm{C} \) in the center. Then:

• One oxygen forms a double bond with carbon: \( \mathrm{C{=}O} \)
• Two oxygens form single bonds with carbon: \( \mathrm{C-O} \)

Distribute lone pairs:

• The double-bonded oxygen has 2 lone pairs.
• Each single-bonded oxygen has 3 lone pairs.

Lewis structure (with one double bond):

The resonance forms are identical except which oxygen holds the double bond.

:O:—C(=O)—:O:

Using lone pair notation more clearly:

Let the double-bonded oxygen be \( \mathrm{O} \) on the top, then the structure can be represented as:

Structure 1:

\( \mathrm{O = C – O – O} \) with appropriate lone pairs, but the most standard drawing is:

\(\mathrm{CO_3^{2-}}\) forms three equivalent resonance structures, each with one \( \mathrm{C{=}O} \) and two \( \mathrm{C-O^-} \).

Step 7: Identify resonance (three equivalent structures)

Because the double bond can be placed on any one of the three oxygens, there are three resonance Lewis structures:

Resonance structure A: double bond between C and oxygen 1; the other two oxygens are single-bonded with \(\mathrm{O^-}\) charges.

Resonance structure B: double bond between C and oxygen 2; the other two oxygens are \(\mathrm{O^-}\).

Resonance structure C: double bond between C and oxygen 3; the other two oxygens are \(\mathrm{O^-}\).

Step 8: Show formal charges (to confirm correctness)

We can verify that the typical best Lewis resonance form has:

• The double-bonded oxygen has formal charge \(0\)
• Each single-bonded oxygen has formal charge \(-1\)

Then the total formal charge is:

\[
0 + (-1) + (-1) = -2
\]

which matches the ion charge \( \mathrm{CO_3^{2-}} \).

Final answer (what to draw)

The Lewis dot structure of \( \mathrm{CO_3^{2-}} \) consists of three equivalent resonance forms. Each form has one carbon-oxygen double bond and two carbon-oxygen single bonds, with lone pairs arranged so that the double-bonded oxygen has 2 lone pairs (formal charge 0) and each single-bonded oxygen has 3 lone pairs (formal charge \(-1\)).

In words: Draw \( \mathrm{C} \) at center with three surrounding oxygens. Make one \( \mathrm{C{=}O} \) and two \( \mathrm{C-O^-} \). Then indicate resonance by allowing the double bond to appear on any of the three oxygens.