Problem 22 - A Complete Resource Book in Chemistry for JEE Main

Question

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

Step-by-Step Solution

Answer

The bond length is 1.54 Å (option d).

Step 1: Understanding sp3 Hybridization

SP3 hybridization occurs when one s-orbital and three p-orbitals combine, resulting in four equivalent hybrid orbitals. This geometry is commonly seen in single bonds, such as the carbon-carbon bond in methane (CH₄), where each carbon has a tetrahedral sp3 hybridization.

Step 2: Identifying Standard Bond Length

In a typical sp3 hybridized carbon-carbon single bond, such as in alkanes, the standard bond length is usually around 1.54 Å. This value is considered typical because the overlapping sp3 hybrid orbitals create a stable bond of this length.

Step 3: Comparing Options with Known Value

We compare the given options with the known \(\mathrm{C}-\mathrm{C}\) bond length of 1.54 Å for sp3 hybridized molecules. The only option that matches this precisely is option (d) 1.54 Å.

Step 4: Concluding the Answer

Since 1.54 Å is the typical bond length for a \(\mathrm{C}-\mathrm{C}\) bond in sp3 hybridized molecules and aligns with the given options, we conclude that the correct answer is option (d).

Key Concepts

sp3 Hybridization

In chemistry, sp3 hybridization is an important concept that describes how atoms bond in organic molecules. This type of hybridization involves the mixing of one s-orbital and three p-orbitals from the outer shell of an atom. The result is four equivalent sp3 hybrid orbitals. These orbitals are arranged in a tetrahedral geometry, which means they are spread out in a way that maximizes the distance between them. This arrangement minimizes electrostatic repulsion among the electrons.

A classic example of sp3 hybridization is seen in the molecule methane (CH₄). Here, the carbon atom undergoes sp3 hybridization, allowing it to form four equivalent single bonds with hydrogen atoms. Each of these bonds is the same length and strength, due to the equivalent hybrid orbitals involved. Understanding sp3 hybridization is crucial because it provides the foundational geometry for many organic molecules, showing why certain atoms are spaced as they are and how they come together to form compounds.

Carbon-Carbon Single Bond

In organic chemistry, the carbon-carbon (C-C) single bond is a fundamental building block of a wide variety of compounds. This bond is characterized by the sharing of one pair of electrons between two carbon atoms, which allows for the formation of a single covalent bond. The carbon-carbon single bond is notably versatile, as it can be found in a vast array of molecules, from simple hydrocarbons like ethane (C₂H₆) to complex polymers and biomolecules. Because carbon atoms can form this stable single bond with each other, they can create long chains and complex branching structures. This property is vital for the diversity and complexity found in organic molecules. In terms of hybridization, the carbon atom in a C-C single bond generally has sp3 hybridization. This type of bond is also known as a sigma bond (C3-bond), being the strongest type of covalent bond because of the end-to-end overlap of the atomic orbitals. As a result, sigma bonds allow for the free rotation of bonded atoms around the bond axis, contributing to the flexibility seen in many organic structures.

Bond Length in Organic Molecules

Bond length is a critical factor when examining the structure and stability of organic molecules. In the context of sp3 hybridization, the bond length between carbon atoms is typically about 1.54 Å. This measurement is considered standard for carbon-carbon single bonds in sp3 hybridized molecules, such as those found in alkanes. The reason sp3 hybridized carbon-carbon bond lengths are a specific value lies in the balance between the forces of attraction and repulsion among the bonding and non-bonding electrons. The tetrahedral geometry achieved through sp3 hybridization helps optimize this balance by positioning the hybrid orbitals such that they experience minimal electron cloud overlap besides the bonding region. Understanding bond lengths is essential, not only for predicting molecular shapes but also for assessing the energy required to break a particular bond. Shorter bonds are typically stronger, while longer bonds are weaker. Therefore, the knowledge of bond lengths helps chemists determine the reactivity and properties of a molecule. This understanding also aids in the interpretation of spectroscopic data, such as those obtained from X-ray diffraction or spectroscopy methods, which are used to estimate bond lengths and molecular structures.