Question

Predict the ideal values for the bond angles about each carbon atom in the following molecule. Indicate the hybridization of orbitals for each carbon. $${\mathrm{CH}}_3{\mathrm{CCCH}}_2\mathrm{COOH}$$

Short answer

The ideal bond angles and hybridizations for each carbon atom in the molecule $C{H}_{3}CCC{H}_{2}COOH$ are: 1. First carbon atom (sp3 hybridization): 109.5° bond angles 2. Second carbon atom (sp2 hybridization): 120° bond angles 3. Third carbon atom (sp hybridization): 180° bond angles 4. Fourth carbon atom (sp3 hybridization): 109.5° bond angles 5. Fifth carbon atom (sp2 hybridization): 120° bond angles

Step-by-step solution

Draw the Lewis Structure

To begin, draw the Lewis structure of the molecule, which will help in understanding the bonds and hybridization states of each carbon atom. The molecule $C{H}_{3}CCC{H}_{2}COOH$ has the following Lewis structure: $$H_{3}C-C\equiv C-C-H_2-C(=O)-OH$$

Identify the carbon atoms

Next, identify the carbon atoms that we need to analyze. In this molecule, there are five carbon atoms: 1. The left-most carbon atom (in the -CH_3 group) 2. The second carbon atom connected by a single bond to the first carbon 3. The third carbon atom connected by a triple bond to the second carbon 4. The fourth carbon atom connected by a single bond to the third carbon (in the -CH_2 group) 5. The fifth carbon atom connected by a double bond to an oxygen atom (in the -COOH group)

Determine the hybridization state

Determine the hybridization state of each carbon atom by counting the number of electron domains (regions of electron density) around each atom: 1. First carbon atom: 4 electron domains (3 hydrogens and one bond to carbon) → sp3 hybridization 2. Second carbon atom: 3 electron domains (1 sigma bond to carbon, 1 sigma bond to adjacent carbon, and 1 pi bond) → sp2 hybridization 3. Third carbon atom: 2 electron domains (1 sigma bond to carbon and 2 pi bonds) → sp hybridization 4. Fourth carbon atom: 4 electron domains (2 hydrogens and 1 sigma bond to each adjacent carbon) → sp3 hybridization 5. Fifth carbon atom: 3 electron domains (1 sigma bond to carbon, 1 sigma bond to oxygen, and 1 pi bond) → sp2 hybridization

Predict the ideal bond angles

Based on the hybridization states of each carbon atom, we can now predict the ideal bond angles: 1. First carbon atom (sp3 hybridization): Tetrahedral geometry (109.5° bond angles) 2. Second carbon atom (sp2 hybridization): Trigonal planar geometry (120° bond angles) 3. Third carbon atom (sp hybridization): Linear geometry (180° bond angles) 4. Fourth carbon atom (sp3 hybridization): Tetrahedral geometry (109.5° bond angles) 5. Fifth carbon atom (sp2 hybridization): Trigonal planar geometry (120° bond angles) The ideal values for the bond angles about each carbon atom in the molecule $C{H}_{3}CCC{H}_{2}COOH$ are: 1. First carbon atom: 109.5° 2. Second carbon atom: 120° 3. Third carbon atom: 180° 4. Fourth carbon atom: 109.5° 5. Fifth carbon atom: 120°

Key concepts

Lewis Structure

A Lewis structure is a diagram that represents the arrangement of atoms within a molecule. It shows how the valence electrons are distributed among the atoms. By illustrating bonds between atoms and any lone pairs of electrons, the Lewis structure provides insight into the molecule's geometry and reactivity.
In the molecule ${\mathrm{CH}}_3{\mathrm{CCCH}}_2\mathrm{COOH}$, the Lewis structure helps identify the connectivity and electron sharing among carbon and other atoms, such as hydrogen and oxygen. Specifically, the structure shows:

• Single C-H bonds in $-{\mathrm{CH}}_3$
• Triple bond between two carbon atoms represented as $-\mathrm{C}\equiv \mathrm{C}-$
• Single and double bonds present in the $-\mathrm{COOH}$ functional group

Understanding the Lewis structure is the first step in determining hybridization and predicting bond angles.

Hybridization

Hybridization is a concept that describes the mixing of atomic orbitals to form new hybrid orbitals. These hybrid orbitals are responsible for the covalent bonding in molecules. The type of hybridization is determined by the number of electron domains (regions of electron density) surrounding an atom.
For the molecule ${\mathrm{CH}}_3{\mathrm{CCCH}}_2\mathrm{COOH}$:

• The first carbon (in $-{\mathrm{CH}}_3$) has four electron domains, indicating ${\text{sp}}^3$ hybridization which is formed from one $\text{s}$ and three $\text{p}$ orbitals.
• The second carbon has three electron domains, resulting in ${\text{sp}}^2$ hybridization, involving one $\text{s}$ and two $\text{p}$ orbitals.
• The third carbon is involved in a triple bond and has two electron domains, leading to $\text{sp}$ hybridization, using one $\text{s}$ and one $\text{p}$ orbital.
• The fourth carbon (in $-{\mathrm{CH}}_2$) also exhibits ${\text{sp}}^3$ hybridization.
• The fifth carbon, bonded to oxygen in the $-\mathrm{COOH}$ group, shows ${\text{sp}}^2$ hybridization.

Hybridization explains the geometry and bonding capabilities of the molecule.

Bond Angles

Bond angles refer to the angle formed between three atoms across at least two bonds. These angles determine the shape and geometry of the molecule. The hybridization of central atoms in a molecule dictates the ideal bond angles they can adopt.
For ${\mathrm{CH}}_3{\mathrm{CCCH}}_2\mathrm{COOH}$, the hybridization suggests:

• The first and fourth carbon atoms (both ${\text{sp}}^3$ hybridized) ideally have bond angles of 109.5°, characteristic of a tetrahedral shape.
• The second and fifth carbon atoms (${\text{sp}}^2$ hybridized) display ideal bond angles of 120°, arranged in a trigonal planar shape.
• The third carbon, being $\text{sp}$ hybridized, maintains a linear shape with an ideal bond angle of 180° due to it being involved in a triple bond.

Knowing the bond angles is crucial for predicting molecular geometry and the behavior of the compound in different chemical contexts.

Electron Domains

Electron domains are regions where electrons are most likely to be found. Electron domains include bonding pairs (single, double, triple bonds) and lone pairs of electrons surrounding an atom.
Understanding how many electron domains surround an atom helps us determine its hybridization and the subsequent molecular geometry.
For the given molecule ${\mathrm{CH}}_3{\mathrm{CCCH}}_2\mathrm{COOH}$:

• The first carbon atom has four electron domains: three from bonds with hydrogen, and one from a bond with carbon.
• The second and fifth carbons involve three electron domains: two from sigma bonds with adjacent atoms and one from a pi bond (in double bonds).
• The third carbon, part of a linear molecule due to a triple bond, has two electron domains contributing to its $\text{sp}$ hybridization.
• The fourth carbon also has four electron domains, similar to the first carbon.

Counting electron domains is a fundamental part of analyzing and predicting the molecular structure.