Problem 63 - Chemistry The Central Science

Question

Propylene, \(\mathrm{C}_{3} \mathrm{H}_{6},\) is a gas that is used to form the important polymer called polypropylene. Its Lewis structure is (a) What is the total number of valence electrons in the propylene 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

In the propylene molecule, there are a total of 18 valence electrons, with 16 valence electrons used to make σ bonds and 2 used to make π bonds. No valence electrons remain as nonbonding pairs. The hybridization states of the carbon atoms in the molecule are C1: sp2, C2: sp2, and C3: sp3.

Step 1: (a) Total number of valence electrons in the propylene molecule.

In order to find the total number of valence electrons in the propylene molecule, we can simply add the number of valence electrons from each individual atom. Carbon has 4 valence electrons, and hydrogen has 1 valence electron. Since there are 3 carbon atoms and 6 hydrogen atoms, the total number of valence electrons will be: \(3\times4(valence\,electrons\,from\,carbon) + 6\times1(valence\,electrons\,from\,hydrogen) = 12 + 6 = 18\). There are 18 valence electrons in the propylene molecule.

Step 2: (b) Valence electrons used to make σ bonds in the molecule.

A single bond is a σ bond. In the propylene molecule, we have the following bonds: - 2 C-C bonds (C1-C2 and C2-C3) - 6 C-H bonds In total, there are 8 σ bonds in the propylene molecule. Since each bond represents 2 electrons, this implies that 16 valence electrons are used to form σ bonds.

Step 3: (c) Valence electrons used to make π bonds in the molecule.

A double bond consists of one σ bond and one π bond. In propylene, there is a double bond between carbon-1 and carbon-2 (C1=C2). So, we have: 1 π bond in the molecule Since each bond represents 2 electrons, this would mean that 2 valence electrons are used to form π bonds in the molecule.

Step 4: (d) Valence electrons remaining as nonbonding pairs in the molecule.

As we've identified that 16 valence electrons are used to form σ bonds and 2 valence electrons are used to form π bonds, any remaining valence electrons must be nonbonding pairs. From (a), we know there are a total of 18 valence electrons in the molecule, and we've accounted for 16 + 2 = 18 electrons in (b) and (c), so no valence electrons remain as nonbonding pairs in the propylene molecule.

Step 5: (e) Hybridization at each carbon atom in the molecule.

There are 3 carbon atoms, each with a different hybridization state: 1. Carbon-1 (C1): It forms a single bond with one hydrogen (C-H), and a double bond with carbon-2 (C=C). This means it has 3 σ bonds (including one from the double bond) and one π bond, which requires an sp2 hybridization. 2. Carbon-2 (C2): It forms a single bond with carbon-3 (C-C) and two single bonds with hydrogen atoms (C-H). This means it has 3 σ bonds and one π bond (C1-C2 double bond), which also requires an sp2 hybridization. 3. Carbon-3 (C3): It forms a single bond with carbon-2 (C-C) and two single bonds with hydrogen atoms (C-H). This means it has 3 σ bonds, which requires an sp3 hybridization. Remember that in this case there is no π bond. So, the hybridization states of the three carbon atoms in the propylene molecule are: C1: sp2, C2: sp2, and C3: sp3.

Key Concepts

Valence Electrons

Valence electrons are the outermost electrons of an atom and are crucial in determining how an element will chemically bond with others. To determine the total number of valence electrons in a molecule like propylene (\(\mathrm{C}_{3}\mathrm{H}_{6}\)), we need to consider the valence electrons of each atom involved.

• Carbon, with an atomic number of 6, has 4 valence electrons.
• Hydrogen, with an atomic number of 1, has 1 valence electron.

In propylene, we have three carbon atoms and six hydrogen atoms. Therefore, the total number of valence electrons can be calculated as:\[3 \times 4 + 6 \times 1 = 12 + 6 = 18\] There are 18 valence electrons in total. These electrons will be distributed to form different bonds and remains as lone pairs in the molecule.

Sigma and Pi Bonds

Sigma (\(\sigma\)) and pi (\(\pi\)) bonds are types of covalent chemical bonds that differ in how their orbitals overlap. Sigma bonds are the first bonds formed between two atoms and are characterized by the head-on overlap of orbitals. They are strong and allow for free rotation around the bond axis.

• In the propylene molecule, each single bond is a sigma bond. This results in: two C-C \(\sigma\) bonds and six C-H \(\sigma\) bonds.
• This totals to eight \(\sigma\) bonds, using up 16 valence electrons.

On the other hand, pi bonds form when parallel orbitals overlap above and below the axis of the bond, typically occurring in addition to a sigma bond to form a double or triple bond.

• In propylene, there is one double bond between two carbon atoms (C1=C2), composed of one \(\sigma\) and one \(\pi\) bond.
• Therefore, 2 valence electrons are used to form the \(\pi\) bond.

Hybridization

Hybridization is the concept of mixing atomic orbitals into new hybrid orbitals suitable for the pairing of electrons to form chemical bonds. This helps explain the geometry of molecular structures.
Each carbon atom in propylene undergoes a different type of hybridization:

• **Carbon-1 (C1)**: Participates in three \(\sigma\) bonds, including a \(\sigma\) bond from a double bond with C2, requiring \(\text{sp}^2\) hybridization.
• **Carbon-2 (C2)**: Also forms three \(\sigma\) bonds, including one in the double bond, so it shares the same \(\text{sp}^2\) hybridization as C1.
• **Carbon-3 (C3)**: Forms only single \(\sigma\) bonds, resulting in \(\text{sp}^3\) hybridization.

The type of hybridization affects molecular geometry, with \(\text{sp}^2\) forming trigonal planar shapes and \(\text{sp}^3\) forming a tetrahedral structure.

Lewis Structure

The Lewis structure is a diagram that represents the arrangement of valence electrons around atoms in a molecule. It helps in visualizing the bonding between atoms and the presence of lone pairs of electrons.
In creating a Lewis structure for propylene:

• First, distribute a total of 18 valence electrons initially by forming bonds between the atoms.
• After forming all required bonds (two carbon-carbon single bonds, one carbon-carbon double bond, and six carbon-hydrogen bonds), use the remaining electrons to satisfy valency rules.
• All electrons must be accounted for by ensuring they are in bonds or as lone pairs.

In the case of propylene, all 18 valence electrons are used in bonds, leaving no lone pairs. Drawing Lewis structures involves checking that the octet rule and molecular geometry are respected for accurate representations.