Problem 111 - General Chemistry: Principles and Modern Applications

Question

Carbon suboxide has the formula \(\mathrm{C}_{3} \mathrm{O}_{2} .\) The carbon- to-carbon bond lengths are \(130 \mathrm{pm}\) and carbon-to-oxygen, \(120 \mathrm{pm} .\) Propose a plausible Lewis structure to account for these bond lengths, and predict the shape of the molecule.

Step-by-Step Solution

Answer

The Lewis structure for Carbon Suboxide consists of a straight line of three carbons, with the terminal carbons each bonded to an oxygen atom (O=C=C=C=O). Each Oxygen atom has 6 electrons in its valence shell, and each carbon atom also has a complete octet. The overall shape of the molecule is linear.

Step 1: Count Total Valence Electrons

Start by calculating the total number of valence electrons. Carbon (C) has 4 valence electrons, and oxygen (O) has 6 valence electrons. Here, we have 3 Carbon atoms and 2 Oxygen atoms, so the total valence electrons is \(3*4 + 2*6 = 20\).

Step 2: Draw Skeleton & Distribute electrons

Draw a skeleton structure for the molecule. Arrange carbon and oxygen atoms such that the less electronegative atoms are in the center. Distribute the electrons among atoms to create bonds. Remember that each bond consists of 2 electrons. You will have three carbon atoms in a row with one oxygen bonded to either end: O=C=C=C=O.

Step 3: Complete Octet for Outer Atoms

Next, complete the octets for atoms starting with the outermost atoms first, in this case, the oxygen atoms. Since each oxygen is already bonded with a carbon (2 electrons), they each need 6 more electrons to complete its octet.

Step 4: Check the Leftover Electrons

Check if there are any leftover electrons after completing the octets. If there are no leftover electrons, then the lewis structure is complete. For this case, now every atom has a complete octet, and you've used all 20 electrons, so your lewis structure is complete.

Step 5: Predict Shape using VSEPR Theory

Now that you have the Lewis structure, you can use VSEPR (Valence Shell Electron Pair Repulsion) theory to predict the shape of the molecule. The carbons in the center form a straight line (linear), and each carbon-oxygen pair is also linear due to the double bond. So the overall shape of Carbon Suboxide is linear.

Key Concepts

Carbon Suboxide

Carbon suboxide is a fairly unique molecule with the chemical formula \( \mathrm{C}_{3} \mathrm{O}_{2} \). It is composed of three carbon atoms and two oxygen atoms. The Lewis structure for carbon suboxide is intriguing because it demonstrates a series of double bonds that link the atoms together. In the case of carbon suboxide, each of the terminal carbon atoms is double-bonded to an oxygen atom, while the central carbon atom is double-bonded to each of the terminal carbon atoms.

Due to its structure, carbon suboxide has certain physical properties and bond lengths. The bond lengths between carbon and carbon are reported to be 130 pm (picometres), while the bond lengths between carbon and oxygen are 120 pm. These bond lengths give us information about the type of bonding and the double bond character within the molecule. The shorter bond length for carbon-to-oxygen versus carbon-to-carbon suggests a strong double bond presence due to the higher electronegativity of oxygen.

VSEPR Theory

VSEPR theory, which stands for Valence Shell Electron Pair Repulsion theory, is fundamental in understanding the shape of molecules. It is based on the idea that groups of valence electrons around a central atom will arrange themselves as far apart as possible to minimize repulsion. This impacts the geometric structure of the molecule.

According to VSEPR theory, molecules are shaped because electron pairs, both bonding and non-bonding, repel each other and try to get as far away from each other as possible. For carbon suboxide, since we're dealing with double bonds and no lone pairs on the carbon atoms, the molecule adopts a linear shape to minimize repulsions. This is why both the carbon chain and the carbon-oxygen bonds are linear, with bond angles of 180 degrees.

Valence Electrons

Valence electrons are the electrons that reside in the outermost shell of an atom. They play a crucial role in chemical bonding and the overall properties of molecules. To predict the behavior of atoms in a molecule, like carbon suboxide, one must understand how to count valence electrons. For example, a carbon atom has 4 valence electrons and oxygen has 6. When creating a Lewis structure, it's the tally of these electrons that we use to form bonds.

In our case, we start with 12 valence electrons for the carbon atoms (4 each) and 12 for the oxygen atoms (6 each), resulting in a total of 20 valence electrons that need to be distributed in the molecule to form the Lewis structure. This understanding of valence electrons helps us to visualize how these atoms bond together and what kind of bonds they form, either single, double, or triple.

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms in a molecule. The geometry of a molecule can significantly affect its physical and chemical properties, such as polarity, reactivity, and color. For carbon suboxide, the linear molecular geometry is determined by the double bonds between carbon and oxygen, as well as between the central and terminal carbon atoms.

The linear configuration is a result of the double-bonded electron pairs repelling each other, as explained by VSEPR theory. With bond angles at 180 degrees, the molecule's shape remains straight. This geometry affects the way this molecule reacts with other molecules and also explains its physical properties such as the bond lengths mentioned earlier. Linear molecular geometries are common for diatomic elements and certain compounds, and carbon suboxide is an excellent example of this.