Problem 61 - Chemistry: The Central Science in SI Units, Global Edition

Question

Consider the Lewis structure for acetic acid, which is known as vinegar: CCC(=O)O (a) What are the approximate bond angles about each of the two carbon atoms, and what are the hybridizations of the orbitals on each of them? (b) What are the hybridizations of the orbitals on the two oxygen atoms, and what are the approximate bond angles at the oxygen that is connected to carbon and hydrogen? (c) What is the total number of \(\sigma\) bonds in the entire molecule, and what is the total number of \(\pi\) bonds?

Step-by-Step Solution

Answer

\(a)\) The approximate bond angles around Carbon-1 and Carbon-2 are \(109.5^\circ\) and \(120^\circ\), respectively. The hybridizations of orbitals on Carbon-1 and Carbon-2 are \(sp^3\) and \(sp^2\), respectively. \(b)\) The hybridizations of orbitals on Oxygen-1 and Oxygen-2 are \(sp^3\) and \(sp^2\), respectively. The approximate bond angle at Oxygen-1 (connected to carbon and hydrogen) is \(109.5^\circ\). \(c)\) The total number of \(\sigma\) bonds in the entire molecule is 7, and the total number of \(\pi\) bonds is 1.

Step 1: Draw the Lewis Structure of Acetic Acid

We start by drawing the Lewis structure for acetic acid: H H | | H - C - C = O | | O O | H

Step 2: Determine Bond Angles and Hybridization of Orbitals on Carbon Atoms

First, let's label the carbon atoms. We can refer to the carbon atom connected to three hydrogen atoms as Carbon-1 (C1) and the other carbon atom as Carbon-2 (C2). For each carbon atom, we'll determine the bonding electron domains and identify the hybridization. Carbon-1 (C1): - It has three bonding electron domains (3 single bonds to 3 hydrogen atoms and 1 single bond to Carbon-2). - Hybridization: \(sp^3\) - Approximate bond angle: \(109.5^\circ\) (tetrahedral) Carbon-2 (C2): - It has three bonding electron domains (1 single bond to Carbon-1, 1 single bond to Oxygen, and 1 double bond to another Oxygen atom). - Hybridization: \(sp^2\) - Approximate bond angle: \(120^\circ\) (trigonal planar)

Step 3: Determine Bond Angles and Hybridization of Orbitals on Oxygen Atoms

Next, let's label the oxygen atoms. We'll refer to the oxygen atom connected to Carbon-2 and hydrogen as Oxygen-1 (O1) and the other oxygen atom as Oxygen-2 (O2). Oxygen-1 (O1): - It has three bonding electron domains (1 single bond to Carbon-2, 1 single bond to Hydrogen, and 1 lone pair). - Hybridization: \(sp^3\) - Approximate bond angle (between C2-O1-H): \(109.5^\circ\) Oxygen-2 (O2): - It has three bonding electron domains (1 double bond to Carbon-2 and 1 lone pair). - Hybridization: \(sp^2\) - The bond angles are not required for this oxygen; only those connected to both carbon and hydrogen are requested.

Step 4: Count Total Number of σ Bonds and π Bonds

Counting the bonds in the Lewis structure for acetic acid: Total number of \(\sigma\) bonds: - 4 single bonds from C1 - 2 single bonds from C2 - 1 single bond from O1 Total: 7 \(\sigma\) bonds Total number of \(\pi\) bonds: - 1 double bond from C2, which contains 1 \(\pi\) bond Total: 1 \(\pi\) bond Now we have all the information to answer the questions in the exercise: (a) The approximate bond angles around Carbon-1 and Carbon-2 are \(109.5^\circ\) and \(120^\circ\), respectively. The hybridizations of orbitals on Carbon-1 and Carbon-2 are \(sp^3\) and \(sp^2\), respectively. (b) The hybridizations of orbitals on Oxygen-1 and Oxygen-2 are \(sp^3\) and \(sp^2\), respectively. The approximate bond angle at Oxygen-1 (connected to carbon and hydrogen) is \(109.5^\circ\). (c) The total number of \(\sigma\) bonds in the entire molecule is 7, and the total number of \(\pi\) bonds is 1.

Key Concepts

Hybridization

Understanding hybridization is essential when discussing molecular structures and bonding. Hybridization refers to the concept where atomic orbitals mix to form new hybrid orbitals. These orbitals are crucial in forming bonds and determine the geometry of the molecules.

In the case of acetic acid, the two carbon atoms display different hybridization forms based on their bonding.

• **Carbon-1 (C1)**: With its four single bonds, C1 experiences an \(sp^3\) hybridization, typical for a tetrahedral shape, facilitating bond angles of approximately \(109.5^\circ\).
• **Carbon-2 (C2)**: This carbon atom shows an \(sp^2\) hybridization. It has a configuration of three bonding domains: two single bonds and one double bond. The \(sp^2\) hybridization is associated with a trigonal planar shape, resulting in a bond angle close to \(120^\circ\).

For the oxygen atoms in acetic acid:

• **Oxygen-1 (O1)**: It has an \(sp^3\) hybridization due to its three bonding domains and involvement with lone pair electrons, also leading to angles around \(109.5^\circ\).
• **Oxygen-2 (O2)**: Engaging in a double bond, O2 uses \(sp^2\) hybridization.

Recognizing the type of hybridization helps to predict molecular behavior, reactivity, and physical properties.

Bond Angles

Bond angles are a fundamental component in determining the 3D shape of molecules. They arise due to the spatial distribution of hybrid orbitals and the repulsion between electron pairs. Accurate knowledge of bond angles helps deduce the molecular geometry.

In acetic acid, the bond angles around each atom reveal much about the molecular structure:

• **Carbon-1 (C1)**: As part of a tetrahedral geometry, the bond angles are approximately \(109.5^\circ\). This wider angle allows evenly distributed orientation minimizing repulsion between the bond pairs.
• **Carbon-2 (C2)**: Due to its trigonal planar configuration, the bond angle is around \(120^\circ\). This planar arrangement is typical for structures with double bonds, giving incremented stability with minimal repulsion.
• **Oxygen-1 (O1)**: Also showing angles around \(109.5^\circ\), this is due to the \(sp^3\) hybridization.

Understanding these bond angles helps in predicting the overall molecular geometry, reactivity, and interaction with other molecules.

Sigma and Pi Bonds

Sigma (\(\sigma\)) and Pi (\(\pi\)) bonds form the cornerstone of understanding how atoms are held together in molecules and dictate much of a molecule's chemical behavior.

**Sigma Bonds (\(\sigma\))** are the first bonds formed between any two atoms. They are characterized by the head-on overlap of orbitals and are generally stronger. Sigma bonds allow free rotation around the bond axis, contributing to flexibility in molecular structures. In acetic acid, there are:

• 7 \(\sigma\) bonds formed from single bonds spread across C-C, C-H, and C-O bonds.

**Pi Bonds (\(\pi\))**, however, involve sideways or lateral overlap of p-orbitals. They usually form in addition to a sigma bond in double or triple bonds, limiting rotational freedom and adding rigidity. Pi bonds tend to be weaker than sigma bonds.

• In acetic acid, the C=O double bond includes 1 \(\pi\) bond.

Knowing the types and numbers of bonds in a molecule is crucial in understanding its structural behavior, reactivity, and interaction potential with other chemicals.