The shape of the carbon (lV) oxide molecule is

Analysis

The question asks for the molecular geometry (shape) of carbon(IV) oxide, also known as carbon dioxide ($CO_2$). To determine the shape, we must look at the bonding arrangement around the central atom.

Concept: VSEPR Theory

The Valence Shell Electron Pair Repulsion (VSEPR) theory states that electron pairs around a central atom arrange themselves as far apart as possible to minimize repulsion.

1. Lewis Structure: Carbon is the central atom. It has 4 valence electrons and forms two double bonds with two oxygen atoms ($O=C=O$).
2. Electron Domains: In $CO_2$, the carbon atom has two bonding domains (the two double bonds) and zero lone pairs.
3. Geometry: When a central atom has two bonding domains and no lone pairs, the electron pairs push each other to opposite sides to achieve maximum separation. This results in a bond angle of 180°.

Step-by-Step Solution

• Step 1: Identify the central atom: Carbon (C).
• Step 2: Determine the number of electron groups around the central atom: There are two double bonds connecting to oxygen atoms. In VSEPR theory, double bonds are treated as a single electron domain.
• Step 3: Determine the arrangement: With two electron domains and no lone pairs on the central carbon atom, the atoms must align in a straight line to minimize repulsion.
• Step 4: Conclusion: A 180° bond angle corresponds to a linear shape.

Comparison with other options:

• Pyramidal: Typical of molecules like ammonia ($NH_3$), which has a lone pair.
• Angular (Bent): Typical of molecules like water ($H_2O$), which has two lone pairs on the central atom.
• Tetrahedral: Typical of molecules like methane ($CH_4$), where the central atom has four single bonds.

Exam Tip

Remember the "Rule of 2": If the central atom has only two bonding pairs and no lone pairs (like $CO_2$ or $BeCl_2$), the shape is always linear. If you see a molecule with a central atom surrounded by four atoms with no lone pairs (like $CH_4$), it is always tetrahedral.