Carbon suboxide `(C_3O_2)` has recently been shown as a component of the atmosphere of Venus. Which of the following formulation represents the correct ground state Lewis structure of carbon suboxide?

Options

A. `:O:C::C:C:O:`
B. `:overset(..)O::C::C:C::O:`
C. `:overset(..)O::C::C::C::overset(..)O:`
D. `:O:C:C:C:O:`

Explanation

To determine the correct ground state Lewis structure of carbon suboxide `(C3O2)`, we will follow these steps:

### Step 1: Determine the Total Number of Valence Electrons
- **Carbon (C)** has 4 valence electrons, and there are 3 carbon atoms:
\( 3 \times 4 = 12 \) valence electrons.
- **Oxygen (O)** has 6 valence electrons, and there are 2 oxygen atoms:
\( 2 \times 6 = 12 \) valence electrons.
- **Total valence electrons** for \( C3O2 \) = \( 12 + 12 = 24 \) valence electrons.

### Step 2: Arrange the Atoms
- The general structure of carbon suboxide is linear, with carbon atoms in the center and oxygen atoms on the ends.
- We can represent it as: \( O=C=C=C=O \).

### Step 3: Draw Single Bonds Between Atoms
- Start by placing single bonds between the carbon atoms and the oxygen atoms:
- Connect the first carbon to the first oxygen and the second carbon with single bonds.
- Connect the second carbon to the third carbon with a single bond.

### Step 4: Distribute Remaining Electrons to Satisfy the Octet Rule
- Each bond consists of 2 electrons.
- Initially, we have used \( 2 \times 4 = 8 \) electrons for the single bonds.
- This leaves us with \( 24 - 8 = 16 \) electrons to distribute.
- To satisfy the octet rule, we will convert some of the single bonds into double bonds:
- Convert the bonds between the carbon atoms and the oxygen atoms to double bonds.

### Step 5: Finalize the Structure
- After adjusting for double bonds, the structure will look like:
- \( O=C=C=C=O \)
- Each atom should now have a complete octet:
- Each carbon has 8 electrons (4 from double bonds).
- Each oxygen also has 8 electrons (4 from double bonds).

### Step 6: Verify the Structure
- Ensure that all atoms have a complete octet and that the total number of valence electrons used equals 24.

### Conclusion
The correct ground state Lewis structure for carbon suboxide \( (C3O2) \) is represented as \( O=C=C=C=O \).

---