Question

The hybridization of the two carbon atoms differs in an acetic acid, \(\mathrm{CH}_{3} \mathrm{COOH},\) molecule. (a) Designate the correct hybridization for each carbon atom in this molecule. (b) What is the approximate bond angle around each carbon?

Short answer

First carbon: \(\text{sp}^3\), \(109.5^\circ\); second carbon: \(\text{sp}^2\), \(120^\circ\).

Step-by-step solution

Understanding Molecular Structure

Acetic acid, \( \mathrm{CH}_3\mathrm{COOH} \), consists of two carbon atoms: one in the methyl group (\( \mathrm{CH}_3 \)) and the other in the carboxyl group (\( \mathrm{COOH} \)). The structural formula is important for determining hybridization.

Analyze the First Carbon Atom (Methyl Group)

The carbon atom in the methyl group (\( \mathrm{CH}_3 \)) is singly bonded to three hydrogen atoms and one carbon atom, making four sigma bonds. This indicates \( ext{sp}^3\) hybridization.

Analyze the Second Carbon Atom (Carboxyl Group)

The carbon atom in the carboxyl group (\( \mathrm{COOH} \)) forms one sigma bond with the adjacent carbon, one sigma bond with the oxygen via a double bond (also involving a pi bond), and one sigma bond with the hydroxyl oxygen. This results in three sigma bonds and a pi bond, suggesting \(\text{sp}^2\) hybridization.

Determine Bond Angles for the Methyl Carbon

The carbon in the methyl group is \( ext{sp}^3\) hybridized, which typically leads to a tetrahedral geometry. The bond angles around this carbon are approximately \({109.5^\circ}\).

Determine Bond Angles for the Carboxyl Carbon

The carbon in the carboxyl group is \( ext{sp}^2\) hybridized, usually resulting in a trigonal planar geometry. The bond angles around this carbon are approximately \({120^\circ}\).

Key concepts

Acetic Acid

Acetic acid, known chemically as \( \mathrm{CH}_3\mathrm{COOH} \), is a simple carboxylic acid often found in vinegar. It consists of two main groups: a methyl group \( (\mathrm{CH}_3) \) and a carboxyl group \( (\mathrm{COOH}) \). Understanding acetic acid's structure is crucial when studying its hybridization. The molecule is organic, meaning it has carbon as its backbone, and both carbon atoms in it exhibit different properties and forms of hybridization, which are essential for determining the molecule's overall geometry and chemical behavior. By studying each carbon atom, students can predict how the molecule interacts with other compounds and what bond angles the atoms might form.

sp3 Hybridization

The concept of \( \text{sp}^3 \) hybridization is key for understanding the structure of many organic compounds. In acetic acid, the carbon atom in the methyl group \( (\mathrm{CH}_3) \) is \( \text{sp}^3 \) hybridized. This means that its one 2s orbital combines with three 2p orbitals to form four new equivalent hybrid orbitals. These hybrid orbitals form sigma bonds:

• One with another carbon atom.
• Three with hydrogen atoms.

This hybridization leads to a tetrahedral geometry around the carbon. Tetrahedral geometry means the molecule's bonds are spreading out in space as much as possible, striving for an ideal bond angle of \( 109.5^\circ \). Each of these sigma bonds plays a role in the molecule's structural stability and reactivity.

sp2 Hybridization

The other carbon atom in acetic acid, found in the carboxyl group \( (\mathrm{COOH}) \), exhibits \( \text{sp}^2 \) hybridization. This involves mixing one 2s and two 2p orbitals to create three equivalent hybrid orbitals. Here is how the bonding works for the carboxyl carbon:

• It forms one sigma and one pi bond with an oxygen, resulting in a double bond.
• Another sigma bond connects it to the methyl carbon.
• The third sigma bond links it with a hydroxyl group \( (\mathrm{OH}) \).

\( \text{sp}^2 \) hybridization typically results in a trigonal planar shape. This shape is flatter compared to tetrahedral, leading to bond angles of about \( 120^\circ \). This planar geometry is critical for the compound’s ability to participate in certain chemical reactions, offering insights into its reactive nature and how it interacts with surrounding molecules.

Bond Angles

The bond angles are essential to understanding the spatial arrangement of atoms within a molecule. For acetic acid, these angles differ due to the different hybridizations present:

• The \( \text{sp}^3 \) hybridized carbon in the methyl group features a bond angle of around \( 109.5^\circ \), typical for tetrahedral shapes.
• The \( \text{sp}^2 \) hybridized carbon within the carboxyl group has bond angles approximately \( 120^\circ \), consistent with a trigonal planar geometry.

These bond angles help us predict the shape and reactivity of acetic acid. The three-dimensional arrangement allows the molecule to interact specifically with other molecules, which is key to its role in biological systems and chemical reactions. Understanding these angles also aids in visualizing how double bonds and molecular structures impact the molecular function and chemical properties.