Problem 137 - A Complete Resource Book in Chemistry for JEE Main

Question

Consider the given statements about the molecule \(\left(\mathrm{H}_{3} \mathrm{C}\right)_{2} \mathrm{CH}-\mathrm{CH}=\mathrm{CH}-\mathrm{C} \equiv \mathrm{C}-\mathrm{CH}=\mathrm{CH}_{2} .\) 1\. Three carbon atoms are sp \(^{3}\) hybridized 2\. Three carbon atoms are sp \(^{2}\) hybridized 3\. Two carbon atoms are sp hybridized Of three statements (a) 1 and 2 are correct (b) 1 and 3 are correct (c) 2 and 3 are correct (d) 1,2 and 3 are correct

Step-by-Step Solution

Answer

The correct answer is (d) 1, 2 and 3 are correct.

Step 1: Analyze the structure

The molecule is structured as follows: \((\mathrm{H}_3\mathrm{C})_2 \mathrm{CH}-\mathrm{CH}=\mathrm{CH}-\mathrm{C} \equiv \mathrm{C}-\mathrm{CH}=\mathrm{CH}_2\). This structure includes various types of bonds such as single, double, and triple bonds which help in determining the hybridization of each carbon atom.

Step 2: Determine sp^3 hybridized carbons

In the molecule, the first group \((\mathrm{H}_3\mathrm{C})_2 \mathrm{CH}\) consists of carbon atoms with single bonds (\(\mathrm{C-C}\) and \(\mathrm{C-H}\) bonds). Carbon atoms with four single bonds are \(\text{sp}^3\) hybridized. Here, two \(\mathrm{CH}_3\) groups and one \(\mathrm{CH}\) group have carbon atoms that are \(\text{sp}^3\) hybridized.

Step 3: Determine sp^2 hybridized carbons

Carbon atoms with one double bond and two single bonds are \(\text{sp}^2\) hybridized. In this structure, the carbon between \(\mathrm{CH}-\mathrm{CH}=\mathrm{CH}\) and the \(\mathrm{CH}=\mathrm{CH}_2\) group each involve an \(\text{sp}^2\) hybridized carbon. There are three such carbons: \(\mathrm{CH-CH}=\mathrm{CH}\), \(\mathrm{CH}=\mathrm{CH}\), and part of \(\mathrm{CH}=\mathrm{CH}_2\).

Step 4: Determine sp hybridized carbons

Carbons involved in triple bonds are \(\text{sp}\) hybridized, having one triple bond and one single bond. In our molecule, the \(\mathrm{C} \equiv \mathrm{C}\) part has two \(\text{sp}\) hybridized carbons.

Step 5: Verify statements and conclude

From the analysis: There are three \(\text{sp}^3\) hybridized carbons, three \(\text{sp}^2\) hybridized carbons, and two \(\text{sp}\) hybridized carbons. Hence, statements 1, 2, and 3 are all correct.

Key Concepts

sp3 Hybridization

Hybridization is a concept in chemistry where atomic orbitals mix to form new hybrid orbitals suitable for pairing electrons for chemical bonding. The **sp³ hybridization** occurs when one s orbital mixes with three p orbitals. In the broad context of chemistry, this means that a carbon atom can form four equivalent, single bonds when it is **sp³ hybridized**. Such hybridization usually results in tetrahedral geometry, with bond angles of approximately 109.5°. In the given molecule, molecular segments such as **(H₃C)₂CH** have carbons with only single bonds. These carbons form four sigma bonds - for instance, bonding with hydrogen or another carbon. The single bonds lead to a saturated molecule, where no double or triple bonds are present. Key Points:

• Occurs with four single bonds
• Tetrahedral geometry
• Bond angle close to 109.5°

sp2 Hybridization

When a carbon atom is involved in **sp² hybridization**, one s orbital blends with two p orbitals, resulting in three hybrid orbitals. This allows the carbon atom to form three bonds, with one double bond and two single bonds. The geometric structure typically emerges as trigonal planar, with bond angles of around 120°. This type of hybridization often appears in unsaturated molecules, like those containing alkenes. In the structure given, carbon atoms linked by hybridization, as seen within the **CH=CH** and the **CH₂=CH** bonds, illustrate a clear example of **sp² hybridized** carbons. Each such carbon will be connected by a double bond, leading to a planar molecular geometry. Key Points:

• Includes one double bond
• Trigonal planar structure
• Bond angles around 120°

sp Hybridization

The simplest form of hybridization, known as **sp hybridization**, involves the merging of one s and one p orbital. This leads to the creation of two equivalent sp orbitals. With this type of hybridization, a carbon atom can form two bonds: typically one triple bond and one single bond. This arrangement imparts a linear geometry to the molecule or segment of it, which involves a bond angle of 180°. The linear structure is much like a straight line in a small molecular form. In the context of the provided molecule, the portion designated as **C≡C** illustrates **sp hybridization**. Here, each carbon participates in a triple bond, presenting a direct, straightforward line between them. Key Points:

• Forms one triple and one single bond
• Linear geometry
• Bond angle of 180°