Question

What are the hybrid orbitals of the carbon atoms in the following molecules? (a) \(\mathrm{H}_{3} \mathrm{C}-\mathrm{CH}_{3}\) (b) \(\mathrm{H}_{3} \mathrm{C}-\mathrm{CH}=\mathrm{CH}_{2}\) (c) \(\mathrm{CH}_{3}-\mathrm{C}=\mathrm{C}-\mathrm{CH}_{2} \mathrm{OH}\) (d) \(\mathrm{CH}_{3} \mathrm{CH}=\mathrm{O}\) (e) \(\mathrm{CH}_{3} \mathrm{COOH}\)

Short answer

(a) sp³, (b) sp³, sp², sp², (c) sp³, sp, sp, sp³, (d) sp³, sp², (e) sp³, sp²

Step-by-step solution

Analyze the molecule (a)

The molecule is \( \mathrm{H}_{3}\mathrm{C}-\mathrm{CH}_{3} \), commonly known as ethane. Each carbon atom is bonded to three hydrogen atoms and one other carbon atom. In ethane, each carbon atom forms four single bonds, indicating \( \mathrm{sp}^3 \) hybridization. \( \mathrm{sp}^3 \) hybridization involves the mixing of one \( s \) and three \( p \) orbitals.

Analyze the molecule (b)

The molecule \( \mathrm{H}_{3} \mathrm{C}-\mathrm{CH}=\mathrm{CH}_{2} \) is known as propene. The first carbon atom is bound to three atoms with single bonds, indicative of \( \mathrm{sp}^3 \) hybridization. The middle carbon forms a double bond with another carbon and two single bonds, suggesting it is \( \mathrm{sp}^2 \) hybridized. The last carbon forms two single bonds and one double bond, so it is \( \mathrm{sp}^2 \) hybridized as well.

Analyze the molecule (c)

In \( \mathrm{CH}_{3}-\mathrm{C}=\mathrm{C}-\mathrm{CH}_{2} \mathrm{OH} \), the first and last carbon are each bonded similarly to those in \( \mathrm{H}_{3} \mathrm{C}-\mathrm{CH} \), so they are \( \mathrm{sp}^3 \) hybridized. The two middle carbon atoms are involved in a triple bond with each other, and each forms one additional \( \sigma \) bond, leading to \( \mathrm{sp} \) hybridization.

Analyze the molecule (d)

The molecule \( \mathrm{CH}_{3} \mathrm{CH}=\mathrm{O} \) is acetaldehyde. The first carbon is bound to three hydrogen atoms and one carbon, leading to \( \mathrm{sp}^3 \) hybridization. The carbon in the carbonyl (C=O) is involved in a double bond with oxygen and single bond with another carbon atom, which characterizes \( \mathrm{sp}^2 \) hybridization.

Analyze the molecule (e)

The molecule \( \mathrm{CH}_{3} \mathrm{COOH} \) is acetic acid. The methyl group \( \mathrm{CH}_{3} \) carbon is \( \mathrm{sp}^3 \) hybridized as it forms three single bonds with hydrogen and one with carbon. The carbon in the carboxyl group (C=O) is \( \mathrm{sp}^2 \) hybridized because it is involved in a double bond with oxygen and single bonds with both another carbon and oxygen.

Key concepts

sp3 hybridization

The concept of \( sp^3 \) hybridization is fundamental in understanding how certain molecules, like ethane, form their structures. In \( sp^3 \) hybridization, one s orbital mixes with three p orbitals to create four equivalent hybrid orbitals. These orbitals arrange themselves in a tetrahedral geometry, allowing for the formation of four sigma bonds. This type of hybridization occurs when a carbon atom forms single bonds with other atoms.

• Example: In ethane \((\mathrm{C}_2\mathrm{H}_6)\), each carbon atom undergoes \( sp^3 \) hybridization. These carbon atoms are bonded to three hydrogen atoms and another carbon atom, forming the typical tetrahedral shape.
• \( sp^3 \) hybridized carbon atoms have bond angles of approximately 109.5° between them, which helps achieve a more stable configuration.

Understanding \( sp^3 \) hybridization is crucial for predicting the structure and reactivity of saturated hydrocarbons and many other organic molecules.

sp2 hybridization

\( sp^2 \) hybridization is another common type of hybridization, especially in organic chemistry, where a carbon atom forms a double bond. In this process, one s orbital mixes with two p orbitals, leading to three \( sp^2 \) hybrid orbitals and one unhybridized p orbital. This arrangement allows for the formation of a planar geometry with 120° bond angles.

• Examples: In propene \((\mathrm{C}_3\mathrm{H}_6)\) and acetaldehyde \((\mathrm{CH}_3\mathrm{CHO})\), certain carbon atoms undergo \( sp^2 \) hybridization. These carbon atoms are involved in double bonding, which introduces rigidity and restricts rotation around the bond.
• This type of hybridization is seen in allotropes like graphite, giving them unique electronic and structural properties.

\( sp^2 \) hybridization contributes significantly to the reactivity and physical properties of alkenes, carbonyl compounds, and aromatic rings.

sp hybridization

Unlike \( sp^3 \) and \( sp^2 \) hybridization, \( sp \) hybridization occurs when a carbon atom forms triple bonds or two double bonds. One s orbital mixes with one p orbital to create two \( sp \) hybrid orbitals, leaving two unhybridized p orbitals. These orbitals align linearly, resulting in bond angles of 180°.

• Example: In molecules like ethyne \((\mathrm{C}_2\mathrm{H}_2)\) or the middle carbons of certain polyalkenes, the involved carbons exhibit \( sp \) hybridization.
• This linear geometry is characteristic of alkynes and contributes to their unique chemical properties, such as higher acidity compared to alkenes and alkanes.

Understanding \( sp \) hybridization is essential for comprehending the properties and reactivity of alkynes and other molecules containing C-C triple bonds.

ethane

Ethane is a simple alkane with the formula \( \mathrm{C}_2\mathrm{H}_6 \). In ethane, each carbon atom forms four single bonds, three with hydrogen atoms and one with the other carbon atom. This structure results from \( sp^3 \) hybridization.

• Ethane has a tetrahedral geometry around each carbon atom, with bond angles close to 109.5°.
• This gives ethane its characteristic non-polar nature and low reactivity due to the saturation of its bonds.
• It is often used as a starting material in the production of other organic compounds due to its availability and simplicity.

As an example of saturated hydrocarbons, ethane's properties are significant for understanding larger alkanes' behavior.

propene

Propene, also known as propylene, is an unsaturated hydrocarbon with the formula \( \mathrm{C}_3\mathrm{H}_6 \). It contains a double bond, which is central to its structure and reactivity. This molecule features different hybridizations at its carbon atoms.

• The first carbon in propene is \( sp^3 \) hybridized while the second and the third carbons are \( sp^2 \) hybridized due to the presence of a double bond.
• Propene's double bond makes it more reactive than saturated hydrocarbons like ethane, offering sites for addition reactions.
• This reactivity makes propene a key raw material in the chemical industry, notably in the production of plastics and other industrial chemicals.

Understanding the hybridization of propene is pivotal in predicting its chemical behavior and its reactions.

acetaldehyde

Acetaldehyde, with the molecular formula \( \mathrm{CH}_3\mathrm{CHO} \), is a simple aldehyde that plays an important role in organic chemistry. In terms of hybridization:

• The carbon in the \( \mathrm{CH}_3 \) group exhibits \( sp^3 \) hybridization, forming single bonds with three hydrogen atoms and one sigma bond with the carbon in the carbonyl group.
• The carbonyl carbon, however, is \( sp^2 \) hybridized. This allows it to form a strong double bond with the oxygen atom, which is crucial for the aldehyde's chemical reactivity.
• Acetaldehyde is a useful intermediate in the synthesis of various organic compounds, including acetic acid, perfumes, and flavors.

The hybridization impacts both structural properties and the reactivity, highlighting its importance in chemical processes and manufacturing.

acetic acid

Acetic acid, known for its formula \( \mathrm{CH}_3\mathrm{COOH} \), is an integral compound in organic chemistry, widely recognized as the main component of vinegar. Its hybridization imparts its unique characteristics:

• The carbon in the \( \mathrm{CH}_3 \) group is \( sp^3 \) hybridized, forming single bonds with hydrogen atoms and the other carbon atom in the molecule.
• The carboxyl carbon (\( \mathrm{COOH} \)) is \( sp^2 \) hybridized, allowing for the formation of a structural carboxylic acid group with a double bond to oxygen and a single bond to hydroxyl (\( \mathrm{OH} \)).
• This hybridization affects the acid's physical and chemical properties, giving acetic acid its acidic nature and participation in various hydrogen bonding interactions.

Understanding acetic acid's structure through its hybridization is essential for applications ranging from culinary uses to industrial processes.