Problem 59 - Chemistry The Central Science In Si Units

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) 18 valence electrons. (b) 10 electrons in \( \sigma \) bonds. (c) 2 electrons in \( \pi \) bonds. (d) 6 nonbonding electrons. (e) Each carbon is \( \text{sp}^2 \) hybridized.

Step 1: Calculate Total Number of Valence Electrons

First, we need to determine the number of valence electrons in each atom within the molecule \( \text{C}_2\text{H}_3\text{Cl} \). Carbon has 4 valence electrons, hydrogen has 1, and chlorine has 7. The molecule consists of 2 carbon atoms, 3 hydrogen atoms, and 1 chlorine atom. Thus, the total number of valence electrons is:\[ 2(4) + 3(1) + 7 = 18 \text{ valence electrons} \]

Step 2: Determine Electrons in Sigma (σ) Bonds

Sigma bonds are single covalent bonds between atoms. In the vinyl chloride molecule, each carbon is bonded to two other atoms (one H, one C, or one Cl), and an additional \( \sigma \) bond exists between the two carbons. This gives us:- \( \text{C}-\text{H} \) (3 bonds)- \( \text{C}-\text{C} \) (1 bond)- \( \text{C}-\text{Cl} \) (1 bond)Total number of \( \sigma \) bonds in the molecule: 5Each \( \sigma \) bond uses 2 electrons, so the number of valence electrons used in \( \sigma \) bonds is:\[ 5 \times 2 = 10 \text{ electrons} \]

Step 3: Determine Electrons in Pi (π) Bonds

Pi bonds occur in double bonds, adding to the \( \sigma \) bond. The vinyl chloride molecule has one double bond, \( \text{C} = \text{C} \), which adds one \( \pi \) bond:- \( \text{C} = \text{C} \) (1 \( \pi \) bond)Each \( \pi \) bond uses 2 electrons, so the number of valence electrons used in \( \pi \) bonds is:\[ 1 \times 2 = 2 \text{ electrons} \]

Step 4: Calculate Nonbonding Electrons

Nonbonding electrons are those not involved in bonding (lone pairs). We have calculated that 10 electrons are used in \( \sigma \) bonds and 2 in \( \pi \) bonds. Subtract these from the total valence electrons to find the remaining electrons:\[ 18 - 10 - 2 = 6 \text{ nonbonding electrons} \]

Step 5: Determine Hybridization of Carbon Atoms

For hybridization, analyze each carbon atom. The carbon involved in a double bond (\( \text{C} = \text{C} \)) is \( \text{sp}^2 \) hybridized, and the carbon involved in single bonds to hydrogen and chlorine with one \( \pi \) bond is also \( \text{sp}^2 \) hybridized because it forms 3 \( \sigma \) bonds and participates in 1 \( \pi \) bond.

Key Concepts

Lewis structure

The Lewis structure is an incredible tool used to visualize the bonding in molecules. It displays the arrangement of atoms and electrons in a molecule, crucial for understanding chemical bonding and molecular geometry.
In constructing the Lewis structure of vinyl chloride \(\text{C}_2\text{H}_3\text{Cl}\), we begin by calculating the total valence electrons available. Carbon, hydrogen, and chlorine contribute 4, 1, and 7 valence electrons respectively. Summing these gives us a total of 18 valence electrons in the molecule.
The Lewis structure depicts each atom and the bonds formed between them, showing:

• 3 hydrogen atoms each form a single bond with carbon \((\text{C}-\text{H})\).
• The carbon atoms are double-bonded to each other \((\text{C} = \text{C})\), involving one sigma and one pi bond.
• Chlorine forms a single bond with one of the carbon atoms \((\text{C}-\text{Cl})\).

This visual representation assists in determining not only the type and number of bonds, but also regions of nonbonding pairs, known as lone pairs.

sigma bonds

Sigma (\( \sigma \)) bonds are the strongest type of covalent chemical bond. They occur when two atoms share a pair of electrons directly between them, creating a head-on overlap of atomic orbitals. In vinyl chloride, the sigma bonds are responsible for holding the basic framework of the molecule together.
In the molecule \(\text{C}_2\text{H}_3\text{Cl}\), several sigma bonds are present:

• Three \(\text{C}-\text{H}\) bonds, where each hydrogen forms a single sigma bond with carbon.
• One \(\text{C}-\text{Cl}\) bond, a single bond formed between carbon and chlorine.
• One \(\text{C}-\text{C}\) sigma bond found in the double bond between the two carbon atoms.

Each sigma bond contains 2 electrons, so in vinyl chloride, the 5 sigma bonds utilize a total of 10 valence electrons. These bonds are the backbone of many molecules, defining their primary structure.

pi bonds

Pi (\( \pi \)) bonds are a different type of covalent bond found in molecules that have multiple bonds, like double or triple bonds. They form when the sides of two adjacent p-orbitals overlap. This overlap occurs above and below the sigma bond axis.
In vinyl chloride, when looking at the chemical structure, you can identify one pi bond as part of the double bond \((\text{C} = \text{C})\) between the two carbon atoms. This pi bond is additional to the sigma bond formed between these two carbons.
Pi bonds are weaker than sigma bonds because the electron density is spread over a larger area and is less concentrated. In this molecule, the pi bond incorporates 2 electrons, adding to the total electron count in bonded states.
Understanding pi bonds is crucial, especially since they contribute to the molecule's reactivity, influencing how vinyl chloride interacts chemically during polymerization to form polyvinyl chloride (PVC).

hybridization

Hybridization is an essential concept that explains the mixing of atomic orbitals to form new hybrid orbitals, which can then form covalent bonds. This concept helps explain molecular geometry and bond properties.
In the vinyl chloride molecule, each carbon atom is \(\text{sp}^2\) hybridized. This hybridization occurs because each carbon is bonded in ways involving one pi bond and three sigma bonds.

• The \(\text{sp}^2\) hybridization creates a trigonal planar shape around each carbon, facilitating the overlap needed for pi bonding and the rest of the molecular structure.

This hybridization permits the proper orientation of the pi bond as well as the sigma bonds forming the stable frame of the molecule.
Using the concept of hybridization helps chemists predict bond angles, molecular shapes, and even potential reactions involving the molecules.