Question

The bond length between \(\mathrm{C}-\mathrm{C}\) bond in sp 3 hybridized molecule is: (a) \(1.2 \AA\) (b) \(1.39 \mathrm{~A}\) (c) \(1.33 \AA\) (d) \(1.54 \AA\)

Short answer

The bond length is 1.54 Å, option (d).

Step-by-step solution

Understanding the Concept of sp³ Hybridization

In an sp³ hybridized carbon, the carbon atom forms four sigma bonds, typically oriented in a tetrahedral geometry. This is the most common state for carbon atoms in alkanes, where all the bonds are single covalent bonds formed with other carbons or hydrogens.

Common Bond Lengths of Carbon-Carbon Bonds

The typical bond length for a single covalent bond between two carbon atoms in an sp³ hybridized molecule is around 1.54 Å. This information is crucial in identifying the bond length among the provided options.

Comparing the Given Options

Now, compare each option against the typical C-C bond length in sp³ hybridized carbon molecules: - (a) 1.2 Å is too short for a C-C bond in sp³. - (b) 1.39 Å is closer to a C=C double bond in sp². - (c) 1.33 Å also resembles a double bond or sp² interaction. - (d) 1.54 Å matches our known bond length for a C-C single bond in sp³ hybridization.

Selecting the Correct Answer

Based on the typical bond length of 1.54 Å for an sp³ hybridized carbon-carbon single bond, option (d) 1.54 Å is the correct answer.

Key concepts

carbon-carbon bond length

The carbon-carbon bond length is the distance between the nuclei of two connected carbon atoms. In chemically bonded atoms, the bond length varies depending on the type and nature of the chemical bond. For a single covalent bond between two carbon atoms, which is common in alkanes, the sp3 hybridization plays a role.
The typical bond length for a single C-C bond in an sp3 hybridized molecule is about 1.54 Å. This length provides insight into molecular geometry and dictates the physical and chemical properties of the compound.
Understanding bond lengths helps in visualizing the 3D structure of molecules, which in turn aids in predicting reactivity and behavior in different chemical scenarios. The bond length in sp3 hybridized molecules is specifically designed to maintain equilibrium in the tetrahedral geometry.

sigma bonds

Sigma bonds are the strongest type of covalent chemical bond. Formed by the head-on overlap of atomic orbitals, these bonds allow for free rotation because the electronic overlap is symmetrical around the bond axis.
In sp3 hybridized molecules, such as alkanes, carbon forms sigma bonds exclusively. These bonds occur between the sp3 hybrid orbitals of carbon or between carbon and other atoms like hydrogen.

• Sigma bonds are significant in defining molecular stability.
• They determine the molecular shape as they dictate the bond angles, leading to the characteristic tetrahedral geometry.

Recognizing sigma bonds' contribution is essential to understanding molecular formation and structural delineation in organic chemistry.

tetrahedral geometry

Tetrahedral geometry is a fundamental concept in the shape and structure of molecules with sp3 hybridization. It describes a polyhedron with four faces, all of which are equilateral triangles. For carbon with sp3 hybridization, the electron clouds generated by its hybrid orbitals form a tetrahedral structure.
This geometric configuration allows for the atoms connected to carbon to be positioned at approximately 109.5° to each other. This uniformity ensures optimal spatial distribution of electrons, minimizing electron repulsion.

• The tetrahedral shape is integral to the configuration of alkanes.
• It explains the dense, stable structures these compounds exhibit.

Mastering tetrahedral geometry helps envision and comprehend the 3-dimensional structure of molecules, which is crucial for analyzing reactions and molecular interactions.

alkanes

Alkanes are the simplest form of hydrocarbons and a vital subject in organic chemistry. They consist solely of carbon and hydrogen atoms, connected by single covalent bonds. This makes them saturated hydrocarbons, where each carbon atom is in a sp3 hybridized state, optimizing four sigma bonds.
Common alkanes include methane, ethane, and propane. They exhibit consistent physical properties:

• They are often non-polar, leading to low solubility in water.
• Boiling and melting points increase with the number of carbon atoms.

The chemical stability of alkanes is attributed to their strong sigma bonds and tetrahedral geometry, which promotes a compact and resistant structure. Understanding alkanes is essential for grasping basic and advanced concepts in organic chemistry, such as bonding, reactions, and molecular structure.