Problem 53 - 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

(a) There are a total of 18 valence electrons in the propylene (C3H6) molecule. (b) 10 valence electrons are used to make σ bonds in the molecule. (c) 2 valence electrons are used to make π bonds in the molecule. (d) 6 valence electrons remain in nonbonding pairs within the molecule. (e) The hybridization of each carbon atom in the molecule is as follows: - Carbon 1 (C1): sp2 - Carbon 2 (C2): sp2 - Carbon 3 (C3): sp3

Step 1: (a) Total Number of Valence Electrons

To calculate the total number of valence electrons in the propylene molecule, we need to add up the number of valence electrons for each atom in the molecule. Here is the breakdown of valence electrons for each type of atom in propylene: - Carbon (C) has 4 valence electrons - Hydrogen (H) has 1 valence electron We have 3 carbon atoms and 6 hydrogen atoms in the propylene molecule (C3H6), so the total number of valence electrons is: \(3 \times 4 + 6 \times 1 = 12 + 6 = 18\)

Step 2: (b) Valence Electrons used for Sigma Bonds

Sigma bonds are single covalent bonds that form between atoms. In the propylene molecule, there are 3 carbon atoms and 6 hydrogen atoms, which means there are 3 C-H bonds and 2 C-C bonds, all of which are sigma bonds. Each sigma bond uses 2 valence electrons, so the total number of valence electrons used for sigma bonds is: \(5 \times 2 = 10\)

Step 3: (c) Valence Electrons used for Pi Bonds

Pi bonds are double or triple covalent bonds that form between atoms. In the propylene molecule, there is a double bond between two carbon atoms, which means there is 1 pi bond. Each pi bond uses 2 valence electrons, so the total number of valence electrons used for pi bonds is: \(1 \times 2 = 2\)

Step 4: (d) Valence Electrons in Nonbonding Pairs

To determine the number of valence electrons that remain in nonbonding pairs, we will subtract the valence electrons used for sigma bonds and pi bonds from the total number of valence electrons calculated previously: \(18 - 10 - 2 = 6\) So, there are 6 valence electrons in nonbonding pairs.

Step 5: (e) Hybridization for each Carbon Atom

Hybridization is the process of mixing atomic orbitals to produce new hybrid orbitals that have the properties of the original atomic orbitals. In the propylene molecule, we have three carbon atoms with different hybridizations: 1. For the first carbon atom (C1), we have sp2 hybridization. This is because there are 3 sigma bonds (1 C-C bond and 2 C-H bonds) and a pi bond, which means there are 3 hybrid orbitals (sp2) and 1 unhybridized p orbital. 2. For the second carbon atom (C2), we also have sp2 hybridization. This is because there are 3 sigma bonds (1 C-C bond, 1 C=C bond, and 1 C-H bond) and a pi bond, which means there are 3 hybrid orbitals (sp2) and 1 unhybridized p orbital. 3. For the third carbon atom (C3), we have sp3 hybridization. This is because there are 4 sigma bonds (1 C-C bond and 3 C-H bonds), which means there are 4 hybrid orbitals (sp3). In summary, the hybridizations for the three carbon atoms are as follows: - Carbon 1 (C1): sp2 - Carbon 2 (C2): sp2 - Carbon 3 (C3): sp3

Key Concepts

Valence Electrons

Valence electrons are the outermost electrons of an atom and are crucial in chemical bonding, as they are the ones involved in forming bonds with other atoms. In a molecule of propene (\(C_3H_6\)), we first count the valence electrons for each type of atom. Carbon, with an atomic number of 6, has 4 valence electrons, while hydrogen, having an atomic number of 1, has 1 valence electron.

• With 3 carbon atoms, the total number of valence electrons contributed by carbon is \(3 \times 4 = 12\)
• With 6 hydrogen atoms, the total number of valence electrons from hydrogen is \(6 \times 1 = 6\)

By adding these, the total number of valence electrons in a propene molecule is \(12 + 6 = 18\). Understanding this is key to predicting the molecule’s structure and bonding behaviors.

Sigma Bonds

Sigma (\(\sigma\)) bonds are the primary connections between atoms in a molecule. These bonds form when two atomic orbitals overlap head-on and share two electrons. In propene, sigma bonds form between the following:

• 3 bonds between each carbon and hydrogen (\(C-H\))
• 2 bonds between the carbons (\(C-C\))

Each sigma bond accounts for 2 of the molecule's total valence electrons. Thus, with 5 sigma bonds in propene, \(5 \times 2 = 10\) valence electrons are used. This understanding of sigma bonds helps clarify how atoms in propene are connected and stabilize the molecule.

Pi Bonds

Pi (\(\pi\)) bonds occur when two atoms in a molecule share electrons in an overlapping parallel arrangement of p orbitals, typically forming part of double or triple bonds. In propene, there’s a double bond between two of the carbon atoms, involving 1a pi bond.
The characteristics of a pi bond include:

• Each pi bond utilizes 2 valence electrons.
• In propene, 2 of the 18 total valence electrons are dedicated to the pi bond.

In contrast to sigma bonds, pi bonds provide additional bonding between atoms and add to a molecule's electron cloud, impacting molecular geometry and reactivity.

Hybridization

Hybridization helps explain how atoms form covalent bonds by combining different atomic orbitals into hybrid orbitals. This is essential in predicting molecule shapes and bond angles. In the case of propene:

• The first two carbon atoms (structurally adjacent) display sp2 hybridization, with bonds spanning three directions—each forms three sigma bonds and one pi bond.
• The third carbon atom, bonded only with sigma bonds, showcases sp3 hybridization which forms four sigma bonds.

Understanding hybridization can unravel the three-dimensional structure and properties of propene, demystifying its role as a polymer precursor.

Lewis Structure

A Lewis structure is a simplified representation showing all valence electrons in a molecule. It helps predict molecule shape, reactivity, and bonding characteristics. For propene:

• Draw the skeleton: Arrange carbon atoms in a chain and connect hydrogens to free valences.
• Add electrons: Disperse valence electrons to form bonds and fill octets where applicable.
• Identify bonds: Mark two lines for each double bond and one for each single bond.

The Lewis structure for propene confirms \(C_3H_6\) as a stable molecule with distinct sigma and pi bonds, vital in polymer science. Recognizing the Lewis structure offers insights into propene's reactivity and interaction potential in polymerization processes.