Problem 69 - Chemistry The Molecular Science

Question

In addition to \(\mathrm{CO}\) and \(\mathrm{CO}_{2}\), there are other carbon oxides. One is tricarbon dioxide, \(\mathrm{C}_{3} \mathrm{O}_{2},\) also called carbon suboxide, a foul-smelling gas. (a) Write the Lewis structure of this compound. (b) What is the value of the \(\mathrm{C}\) -to-C-to-O bond angle in carbon suboxide? (c) What is the value of the \(\mathrm{C}\) -to-C-to-C bond angle in tricarbon dioxide?

Step-by-Step Solution

Answer

(a) Linear O=C-C-C=O structure. (b) C-to-C-to-O bond angle is 180°. (c) C-to-C-to-C bond angle is 180°.

Step 1: Count total valence electrons

To draw the Lewis structure, first count the total valence electrons in the molecule. Carbon has 4 valence electrons each and oxygen has 6. Thus, for \( \mathrm{C}_3\mathrm{O}_2 \), the total valence electrons are \( (3 \times 4) + (2 \times 6) = 18 \) electrons.

Step 2: Draw skeleton structure

Determine the arrangement of atoms. Carbon, being less electronegative, will be in the middle. Arrange them as \( \mathrm{O}-\mathrm{C}-\mathrm{C}-\mathrm{C}-\mathrm{O} \) to start forming bonds.

Step 3: Assign initial bonds

Connect the atoms with single bonds in the skeleton structure: \( \mathrm{O}-\mathrm{C}-\mathrm{C}-\mathrm{C}-\mathrm{O} \), using up 4 electrons (2 for each bond), leaving 14 electrons to be assigned.

Step 4: Complete the octets

Fill the octets of the outer oxygen atoms first, by adding 6 more electrons to each oxygen. This uses 12 more electrons (6 for each oxygen). Now, 2 electrons remain.

Step 5: Form multiple bonds

With 2 electrons left, and to complete the octets and account for all valence electrons, form multiple bonds. Make carbon-oxygen double bonds on both ends: \( \mathrm{O}=\mathrm{C}-\mathrm{C}-\mathrm{C}=\mathrm{O} \).

Step 6: Verify structure and electron count

Ensure that all atoms have filled octets and the total electrons match the calculated 18. Each oxygen is double-bonded to carbon, completing their octet, and the central carbons also have a complete octet.

Step 7: Determine \( \mathrm{C}\)-to-C-to-O bond angle

In a linear arrangement like \( \mathrm{O}=\mathrm{C}-\mathrm{C}=\mathrm{O} \), the \( \mathrm{C}\)-to-C-to-O angles are 180° because of their sp-hybridization, indicating a linear structure.

Step 8: Determine \( \mathrm{C}\)-to-C-to-C bond angle

The molecule \( \mathrm{O}=\mathrm{C}-\mathrm{C}=\mathrm{O} \) forms a linear shape. Thus, the \( \mathrm{C}\)-to-C-to-C bond angle is also 180°, indicating linear geometry through the tricarbon chain.

Key Concepts

Valence Electrons

Understanding valence electrons is crucial for drawing Lewis structures. Valence electrons are the outermost electrons of an atom and determine its ability to bond with other atoms. For carbon oxides like tricarbon dioxide (\(\mathrm{C_3O_2}\)), you calculate the total number of valence electrons by considering each atom in the molecule.
For carbon, which has 4 valence electrons, and oxygen, with 6 valence electrons, the total can be calculated as follows:

• 3 carbon atoms contribute \(3 \times 4 = 12\) electrons.
• 2 oxygen atoms contribute \(2 \times 6 = 12\) electrons.

Adding these together, tricarbon dioxide has 18 valence electrons, which are allocated to bonding as you create the Lewis structure. Proper distribution ensures that each atom achieves a stable electron configuration, often an octet for main group elements, resulting in a correctly drawn structure.

Molecular Geometry

Molecular geometry explains the shape of a molecule, determined by the arrangement of atoms and electron pairs around a central atom. For tricarbon dioxide (\(\mathrm{C_3O_2}\)), this understanding helps in predicting angles between bonds.
The fundamental shape is established from the linear structure \(\mathrm{O} = \mathrm{C} - \mathrm{C} - \mathrm{C} = \mathrm{O}\) from the Lewis structure. In this molecule, each carbon is sp-hybridized, contributing to a linear geometry. Therefore, the bond angles between \(\mathrm{C}\) to \(\mathrm{C}\) to \(\mathrm{O}\) are 180°, as well as the \(\mathrm{C}\) to \(\mathrm{C}\) to \(\mathrm{C}\) angles, creating a line of atoms.

Hybridization

Hybridization is a concept explaining how atomic orbitals mix to form new, hybrid orbitals, which accommodate molecule bonding. This is vital for understanding the linear arrangement in tricarbon dioxide (\(\mathrm{C_3O_2}\)).
Each carbon atom in this molecule undergoes sp hybridization. This is because carbon forms two double bonds in sequence, meaning it needs two sp hybrid orbitals to align with the attached atoms.

• sp Hybridization: Combines one s orbital and one p orbital from carbon to create two sp hybrid orbitals, facilitating 180° bond angles.

The sp hybrid orbitals result in a straight line configuration, giving the molecule its rigid linear shape, with the electrons in the p orbitals forming pi bonds in the double pairing with oxygens.

Tricarbon Dioxide

Tricarbon dioxide, or carbon suboxide, is a unique and lesser-known oxide of carbon with a pungent smell and the chemical formula \(\mathrm{C_3O_2}\). It's fascinating due to its distinctive linear structure and bonding characteristics.
The molecule can be expressed in the Lewis structure as \(\mathrm{O} = \mathrm{C} - \mathrm{C} - \mathrm{C} = \mathrm{O}\), where the carbon and oxygen atoms are double-bonded, creating a series of conjugated bonds. Some key aspects include:

• Linear Geometry: Both the C-C-O and C-C-C bond angles are 180°.
• Stability: Each oxygen achieves a full octet, and each carbon in the central chain participates in bonding maximizing overlap of molecular orbitals.

This unique symmetry and bond arrangement results in a compound with properties distinct from other more common carbon oxides.