Problem 166 - A Complete Resource Book in Chemistry for JEE Main

Question

Underlined carbon is sp \(^{3}\) hybridized in (a) \(\mathrm{CH}_{3} \mathrm{CH}=\underline{\mathrm{CH}}_{2}\) (b) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{NH}_{2}\) (c) \(\mathrm{CH}_{3} \mathrm{CONH}_{2}\) (d) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CN}\)

Step-by-Step Solution

Answer

The sp³ hybridized carbon is in compound (b) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \underline{\mathrm{NH}}_{2}\).

Step 1: Understand sp³ hybridization

sp³ hybridization occurs when a carbon atom forms four sigma (σ) bonds, resulting in a tetrahedral geometry with bond angles of about 109.5°. It involves mixing one s orbital and three p orbitals to form four equivalent hybrid orbitals.

Step 2: Analyze each compound

Identify if the underlined carbon in each compound forms four sigma bonds, which indicates sp³ hybridization: - For (a) \(\mathrm{CH}_{3} \mathrm{CH}=\underline{\mathrm{CH}}_{2}\), the underlined carbon is part of a double bond, suggesting sp² hybridization, not sp³.- For (b) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \underline{\mathrm{NH}}_{2}\), the underlined carbon forms single bonds with neighboring atoms, suggesting sp³ hybridization.- For (c) \(\mathrm{CH}_{3} \underline{\mathrm{CO}}\mathrm{NH}_{2}\), the underlined carbon is part of a carbonyl group, suggesting sp² hybridization.- For (d) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \underline{\mathrm{C}}\equiv\mathrm{N}\), the underlined carbon forms a triple bond with nitrogen, suggesting sp hybridization.

Step 3: Match the condition

The only compound where the underlined carbon is sp³ hybridized is (b) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \underline{\mathrm{NH}}_{2}\), as all bonds to the underlined carbon are single bonds, consistent with sp³ hybridization.

Key Concepts

sp³ Hybridization

In chemistry, understanding hybridization is crucial to predict the shape and bonding behavior of molecules. When we talk about sp³ hybridization, we specifically refer to the mixing of one s orbital and three p orbitals in a carbon atom. This combination creates four identical sp³ hybrid orbitals.
This concept is vital because it leads to the formation of four sigma (σ) bonds around the carbon atom, giving it a distinctive geometry. In sp³ hybridization, each bond is a result of the head-on overlap of orbitals, creating a strong sigma bond.
An sp³ hybridized carbon leads to a molecule with a tetrahedral shape. Consequently, all bond angles measure approximately 109.5°, creating a three-dimensional structure. This configuration is standard in many organic molecules, reflecting the versatility and stability of carbon.

Sigma Bonds

Sigma bonds (σ bonds) are the strongest type of covalent chemical bond. They form when two orbitals overlap head-on. In the context of sp³ hybridization, these bonds are formed between hybridized orbitals of carbon and other atoms.

• They allow for the free rotation of bonded atoms around the bond axis.
• Each sp³ hybridized carbon forms four sigma bonds, contributing to the stability and geometry of the molecule.

Sigma bonds are essential for understanding the linking between atoms in many organic molecules. They form the backbone of carbon-containing compounds, enabling complex structures and chemical reactions to occur. This characteristic makes them critical to the structure of organic chemistry and the chemistry of life.

Tetrahedral Geometry

When a carbon atom undergoes sp³ hybridization, it acquires a tetrahedral geometry. This unique shape occurs because the atom forms four identical sigma bonds that repel each other equally, leading to a symmetrical shape.

• Tetrahedral geometry involves bond angles of about 109.5°.
• It allows for the maximum spatial distribution of bonded valence electrons around the carbon atom.

This geometry is not limited to carbon-based molecules but is especially significant in organic chemistry. For example, in the methane molecule (CH₄), each hydrogen atom is positioned to form a tetrahedron around the central carbon atom. This spatial arrangement affects how molecules interact and react with one another, playing a pivotal role in chemical pathways and synthesis.