Problem 59 - Chemistry: The Central Science in SI Units, Global Edition

Question

Vinyl chloride, \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl}\), is a gas that is used to form the important polymer called polyvinyl chloride (PVC). Its Lewis structure is (a) What is the total number of valence electrons in the vinyl chloride molecule? (b) How many valence electrons are used to make \(\sigma\) bonds in the molecule? (c) How many valence electrons are used to make \(\pi\) bonds in the molecule? (d) How many valence electrons remain in nonbonding pairs in the molecule? (e) What is the hybridization at each carbon atom in the molecule?

Step-by-Step Solution

Answer

(a) The total number of valence electrons in the vinyl chloride molecule is 18. (b) 10 valence electrons are used to make σ bonds in the vinyl chloride molecule. (c) 2 valence electrons are used to make π bonds in the vinyl chloride molecule. (d) 6 valence electrons remain in nonbonding pairs in the vinyl chloride molecule. (e) The hybridization at each carbon atom in the vinyl chloride molecule is sp².

Step 1: Calculate the total number of valence electrons.

To find the total number of valence electrons, we add up the valence electrons of each atom within the vinyl chloride molecule, \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl}\). Carbon has 4 valence electrons, hydrogen has 1 valence electron, and chlorine has 7 valence electrons. There are two carbon atoms, three hydrogen atoms, and one chlorine atom in the molecule. So, the total number of valence electrons is: Total valence electrons = (2 × 4) + (3 × 1) + (1 × 7) = 8 + 3 + 7 = 18 (a) The total number of valence electrons in the vinyl chloride molecule is 18.

Step 2: Calculate the number of valence electrons used to make σ bonds.

There are single bonds between C-C, C-H, and C-Cl in the molecule. Each single bond is a σ bond. The 3 single bonds to hydrogen atoms use 2 valence electrons each (as one electron comes from hydrogen and one comes from carbon) and the single bond between carbon and chlorine also uses 2 valence electrons (one from carbon and one from chlorine). The C-C σ bond also uses 2 valence electrons. So, the total number of valence electrons used in making σ bonds is: Total σ electrons = (3 × 2) + 2 + 2 = 6 + 2 + 2 = 10 (b) 10 valence electrons are used to make σ bonds in the vinyl chloride molecule.

Step 3: Calculate the number of valence electrons used to make π bonds.

The vinyl chloride molecule has a double bond (C=C) between the two carbon atoms. One of the bonds is a σ bond, which we already counted in Step 2, and the other bond is a π bond. Therefore, there's only one π bond in the molecule, and it uses 2 valence electrons. (c) 2 valence electrons are used to make π bonds in the vinyl chloride molecule.

Step 4: Calculate the number of nonbonding pairs of electrons.

Subtract the total number of valence electrons used in making σ and π bonds from the total number of valence electrons in the molecule: Total nonbonding pairs of electrons = Total valence electrons - Total σ electrons - Total π electrons = 18 - 10 - 2 = 6 (d) 6 valence electrons remain in nonbonding pairs in the vinyl chloride molecule.

Step 5: Determine the hybridization of each carbon atom.

The first carbon atom (C1) forms 3 sigma bonds (to the other carbon atom and two hydrogen atoms) and one π bond (with the other carbon atom). Since it forms 3 sigma bonds, its hybridization is sp². The second carbon atom (C2) forms 2 sigma bonds (to the chlorine atom and the first carbon atom) and one π bond (with the first carbon atom). Since it forms 2 sigma bonds, its hybridization is sp². (e) The hybridization at each carbon atom in the vinyl chloride molecule is sp².

Key Concepts

Valence Electrons

Valence electrons are the outermost electrons of an atom and are crucial in bonding because they can be shared or transferred between atoms. In the vinyl chloride molecule, understanding valence electrons is key to determining how atoms bond and interact. The vinyl chloride formula is \(\text{C}_2\text{H}_3\text{Cl}\), which means it contains two carbon atoms, three hydrogen atoms, and one chlorine atom.

To find the total number of valence electrons in vinyl chloride, we consider the following:

• Carbon (C) has 4 valence electrons. With two carbon atoms, the contribution is \(2 \times 4 = 8\) electrons.
• Hydrogen (H) has 1 valence electron. With three hydrogen atoms, the contribution is \(3 \times 1 = 3\) electrons.
• Chlorine (Cl) has 7 valence electrons. With one chlorine atom, it contributes 7 electrons.

Summing these up, the total number of valence electrons in vinyl chloride is \(8 + 3 + 7 = 18\). Knowing this helps us map out how these electrons are used in bonds and the geometry of the molecule.

Sigma Bonds

Sigma (\(\sigma\)) bonds are the strongest type of covalent chemical bond. They are formed by the head-on overlapping of atomic orbitals and allow free rotation around them. In vinyl chloride, \(\sigma\) bonds form the backbone structure of the molecule. Let's look at how these are formed.

In vinyl chloride, several \(\sigma\) bonds exist:

• Three \(\sigma\) bonds are formed between the carbon and hydrogen atoms (C-H).
• One \(\sigma\) bond is formed between the two carbon atoms (C-C).
• One \(\sigma\) bond exists between a carbon atom and the chlorine atom (C-Cl).

Each \(\sigma\) bond involves 2 valence electrons — one from each atom participating in the bond. Therefore, the total number of valence electrons used in \(\sigma\) bonds in vinyl chloride is \((3 \times 2) + 2 + 2 = 10\). These \(\sigma\) bonds secure the primary structure of the molecule, ensuring stability and allowing the molecule to maintain its shape.

Pi Bonds

Pi (\(\pi\)) bonds are a type of covalent bond that occur when two lobes of an orbital on one atom overlap another lobes of an orbital on a different atom, typically in a side-on fashion. This overlapping happens alongside the axis of the atoms and is often seen in double bonds, providing resonance and rigidity to the molecule.

In vinyl chloride, there is one \(\pi\) bond formed between the two carbon atoms in the C=C double bond. This bond introduces additional electron density between the atoms and limits the rotation around the bond.

Unlike \(\sigma\) bonds, the \(\pi\) bond in vinyl chloride utilizes 2 valence electrons that form from the sidewise overlap of p-orbitals. So, in the case of vinyl chloride, the total number of valence electrons used in the formation of \(\pi\) bonds is 2. Recognizing the existence of a \(\pi\) bond can help in understanding the structural rigidity and chemical reactivity of the molecule.

Hybridization

Hybridization is a concept that helps us understand the shapes of molecules and the distribution of electrons within them. It involves the mixing of atomic orbitals to form new hybrid orbitals. These hybrid orbitals allow for the formation of \(\sigma\) bonds and help determine molecular geometry.

In vinyl chloride, the hybridization of each carbon atom is crucial for understanding its geometry:

• The first carbon atom (C1) forms three \(\sigma\) bonds (two with hydrogen atoms and one with the second carbon atom) and one \(\pi\) bond. This implies hybridization of \(\text{sp}^2\), which is optimal for the planar configuration needed for the double bond.
• The second carbon atom (C2) similarly forms two \(\sigma\) bonds (one with chlorine and one with the first carbon atom) and one \(\pi\) bond. Its hybridization is \(\text{sp}^2\) too.

This sp² hybridization results in a planar molecule, which is essential for the properties and reactivity of vinyl chloride. Understanding hybridization provides insight into both the electronic arrangement and the three-dimensional structure of the molecule.