Problem 92 - Chemistry: The Central Science in SI Units, Global Edition

Question

Ethyl propanoate, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COOCH}_{2} \mathrm{CH}_{3},\) gives a fruity pineapple-like smell. (a) Draw the Lewis structure for the molecule, assuming that carbon always forms four bonds in its stable compounds. (b) How many \(\sigma\) and how many \(\pi\) bonds are in the molecule? (c) Which CO bond is shortest in the molecule? (d) What is the hybridization of atomic orbitals around the carbon atom associated with that short bond? (e) What are the approximate bond angles around each carbon atom in the molecule?

Step-by-Step Solution

Answer

The Lewis structure for ethyl propanoate is: \(H - C - C - C = O\) \(| | |\) \(H H H - O - C - H\) \( | |\) \( H H H\) There are 11 sigma (\(\sigma\)) bonds and 1 pi (\(\pi\)) bond in the molecule. The C=O bond is the shortest CO bond in the molecule. The carbon atom associated with the shortest CO bond has sp hybridization. The approximate bond angles around each carbon in the molecule are: 1. CH3: 109.5° (sp3) 2. CH2: 109.5° (sp3) 3. C=O: 180° (sp) 4. CH3: 109.5° (sp3)

Step 1: a) Drawing the Lewis structure

To draw the Lewis structure for ethyl propanoate, follow these steps: 1. Write the skeletal structure: From the formula, we have \(\mathrm{CH}_{3} \mathrm{CH}_{2} \text{COOCH}_{2}\mathrm{CH}_{3}\). 2. Fill in the electron pairs around each atom to complete the octets for carbon and oxygen atoms and the duet for hydrogen atoms. The Lewis structure for ethyl propanoate is: \(H - C - C - C = O\) \(| | |\) \(H H H - O - C - H\) \( | |\) \( H H H\)

Step 2: b) Counting \(\sigma\) and \(\pi\) bonds

In the ethyl propanoate molecule, we have the following bonds: - 10 single (σ) bonds: 8 C-H bonds, 1 C-C bond, and 1 C-O bond. - 1 double (σ and π) bond: 1 C=O bond, which has one σ bond and one π bond. So, there are 11 sigma (\(\sigma\)) bonds and 1 pi (\(\pi\)) bond in the molecule.

Step 3: c) Identifying the shortest CO bond

The molecule has two CO bonds: one single bond (C-O) and one double bond (C=O). Double bonds are generally shorter than single bonds because they contain both a sigma and a pi bond, which pull the atoms closer together. Therefore, the C=O bond is shortest in the molecule.

Step 4: d) Determining the hybridization of the carbon atom

For the carbon atom associated with the shortest CO bond (the one with a double bond to oxygen), we can determine the hybridization by counting the electron domains around the atom: 1. One double bond (C=O): count as one electron domain. 2. One single bond (C-C): count as one electron domain. Thus, there are 2 electron domains around that carbon atom, so it undergoes sp hybridization.

Step 5: e) Approximate bond angles around each carbon atom

To determine the bond angles, we need to consider the hybridization of each carbon atom in the molecule: 1. First carbon (CH3): sp3 hybridization (four single bonds) - the bond angles around this carbon are approximately 109.5°. 2. Second carbon (CH2): sp3 hybridization (three single bonds and one free electron pair) - the bond angles around this carbon are also approximately 109.5°. 3. Third carbon (C=O): sp hybridization (one double bond and one single bond) - the bond angles around this carbon are approximately 180°. 4. Last carbon (CH3): sp3 hybridization (four single bonds) - the bond angles around this carbon are approximately 109.5°.

Key Concepts

Sigma and Pi Bonds

In molecules, bonds between atoms are formed through the overlap of atomic orbitals, and these bonds can be categorized as either sigma (\(\sigma\)) or pi (\(\pi\)) bonds. Understanding these bonds is crucial in sketching the structure and explaining the properties of organic compounds like ethyl propanoate.

**Sigma Bonds** Sigma bonds are the first type of bond formed between any two atoms. They are characterized by the direct overlap of orbitals along the bond axis, forming a strong connection. In ethyl propanoate (\(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COOCH}_{2}\mathrm{CH}_{3}\)), there are 11 sigma bonds. These include:

• Eight C-H sigma bonds from the methyl and methylene groups.
• One C-C sigma bond in the ethyl group.
• One C-O sigma bond in the ester group.
• One C-O sigma bond in the carbonyl group.

**Pi Bonds** Pi bonds occur when the side-by-side overlap of p orbitals forms a second bond accompanying a sigma bond, primarily in double or triple bonds. In this molecule, there is a single pi bond, located in the carbonyl group (\(C=O\)). This pi bond arises from the overlap of unhybridized p orbitals of carbon and oxygen, adding to the sigma bond and creating the C=O double bond.

Hybridization

Hybridization involves the mixing of atomic orbitals to form new hybrid orbitals that can create strong sigma bonds in a molecule. The type of hybridization depends on the number of electron domains around a central atom, which include bonds and lone pairs.

In ethyl propanoate, each carbon atom's hybridization varies based on its bonding environment:

• **sp³ Hybridization**:
  • The first carbon (\(\mathrm{CH}_3\)) and the last carbon (\(\mathrm{CH}_3\)) possess sp³ hybridization, as they are each bonded to four atoms in single bonds.
  • The central carbon in \(\mathrm{CH}_2\) is also sp³ because it forms three single bonds plus a bond to nearby atoms.
• **sp Hybridization**:
  • Carbon in the carbonyl group (\(C=O\)) displays sp hybridization. This results from only having two electron domains: one double bond (\(C=O\)) and one single bond (next carbon connected in the chain).

Knowing the hybridization helps predict the molecule's shape and properties.

Bond Angles

The bond angles in a molecule provide insight into its geometry and can be predicted through the hybridization of the atoms involved. Different hybridization leads to different molecular shapes, influencing bond angles.

For ethyl propanoate:

• **sp³ Hybridization (109.5°)**:
  • The carbon atoms within the \(\mathrm{CH}_3\) and \(\mathrm{CH}_2\) groups have bond angles approximately 109.5° because these atoms form four sigma bonds, creating a tetrahedral shape.
• **sp Hybridization (180°)**:
  • The bond angles around the carbonyl carbon (\(C=O\)) are about 180° due to sp hybridization. The combination of a double bond and a single bond makes this atom's electron pair geometry linear.

Understanding the bond angles helps explain the spatial orientation of the molecule, impacting its interaction with other molecules and its physical characteristics.

Carbon-Oxygen Double Bond

The carbon-oxygen double bond (\(C=O\)) in the ethyl propanoate is a crucial structural feature influencing the molecule's reactivity and physical properties. This bond consists of one sigma bond and one pi bond, making the bond both strong and polar.

**Shorter Bond Length** In general, double bonds like the carbon-oxygen bond are shorter than single bonds due to the additional pi bond. This bond pulls the two atoms closer together, resulting in a decrease in bond length. For ethyl propanoate, the \(C=O\) bond is indeed the shortest CO bond in the molecule.

**Reactivity and Polarity** The carbon-oxygen bond also brings significant chemical reactivity; this is due to the polar nature of the double bond. Oxygen is more electronegative than carbon, creating a dipole along the bond, where oxygen becomes slightly negative, and carbon slightly positive. This polarity influences the molecule's interactions, contributing to the characteristic aroma of ethyl propanoate.
Therefore, recognizing the properties of carbon-oxygen double bonds allows us to predict their behavior, reactivity, and role in the molecule's structure.