Problem 170 - A Complete Resource Book in Chemistry for JEE Main

Question

In the molecule \(\mathrm{CH}_{2}=\mathrm{C}=\mathrm{C}=\mathrm{CH}_{2}\), number of carbon atoms in sp hybrid state is

Step-by-Step Solution

Answer

2 carbon atoms are in sp hybridization state.

Step 1: Identify Hybridization Types

To determine the hybridization of each carbon atom in the molecule, recognize that sp, sp², and sp³ are the three types of hybridization that result from an s orbital mixing with one, two, and three p orbitals, respectively.

Step 2: Determine Each Carbon's Hybridization

In a molecule, a triple bond indicates sp hybridization, a double bond indicates sp² hybridization, and a single bond indicates sp³ hybridization. Each carbon in this molecule is only forming two bonds (double bonds) with its adjacent carbon atoms.

Step 3: Identify sp Hybridized Carbons

Since each carbon atom forms two sigma bonds and must be linear in geometry due to the presence of double bonds (both internal carbons are part of consecutive double bonds, i.e., C=C=C), they are sp hybridized. Thus, internal carbons are sp hybridized.

Step 4: Count sp Hybridized Carbon Atoms

Based on the hybridization rules, the two internal carbon atoms (C2 and C3 in the notation) are linked via a double bond to both of their adjacent carbons.

Key Concepts

Hybridization Types

In molecular chemistry, understanding hybridization is crucial. Hybridization is the mixing of atomic orbitals to form new hybrid orbitals. These orbitals are suitable for the pairing of electrons to form chemical bonds. There are several

• sp hybridization: Formed by mixing one s orbital and one p orbital, with a bond angle of 180°, resulting in linear geometry.
• sp² hybridization: Formed by mixing one s orbital with two p orbitals, resulting in trigonal planar geometry with bond angles of 120°.
• sp³ hybridization: Formed when one s orbital mixes with three p orbitals, resulting in tetrahedral geometry with bond angles of 109.5°.

Identifying the type of hybridization helps us understand how atoms in a molecule are bonded and arranged.

Sigma Bonds

Sigma bonds (c) are a fundamental type of covalent bond that appears in the formation of many molecules. They are the strongest type of covalent bond and form when atomic orbitals overlap directly between bonding atoms. This results in shared electron density "on the axis" connecting the two nuclei.
Here are some keys to remember about sigma bonds:

• They are formed from head-on overlapping of atomic orbitals.
• Only one sigma bond can exist between any two atoms.
• Sigma bonds allow for free rotation around the bond axis.
• In multiple bonds, such as double or triple bonds, one bond is a sigma bond, and the others are pi bonds (π bonds).

These bonds are the framework for the molecule, providing strength and stability.

Carbon Hybridization

Carbon can form a variety of hybridized states due to its ability to make four bonds, leading to diverse geometries:

• sp hybridization: Considered when carbon forms two sigma bonds, usually occurring in linear geometries as in acetylene (6CH). In sp hybridization, one s orbital combines with one p orbital.
• sp² hybridization: Seen in scenarios like ethene (c₂Hccc₂), where carbon forms three sigma bonds, resulting in a trigonal planar structure.
• sp³ hybridization: This occurs when carbon forms four sigma bonds, typically seen in methane, leading to a tetrahedral geometry.

It's through these hybridization types that carbon can form complex and diverse molecules, foundational to organic chemistry. In the exercise, determining the correct hybridization involves understanding the bonding and geometry of each carbon atom. In a series of linked double bonds, as identified in the exercise, sp hybridization occurs, revealing the linear nature and structure of the molecule.