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

(d) 1, 2, and 3 are correct.

Step 1: Identify the types of carbon-carbon bonds in the molecule

The given molecule can be broken down by examining it as \((\mathrm{H}_{3}\mathrm{C})_{2} \mathrm{CH}-\mathrm{CH}=\mathrm{CH}-\mathrm{C} \equiv\mathrm{C}-\mathrm{CH}=\mathrm{CH}_{2}\). Here, observe the bonds: there are single (\(-\)), double (\(=\)), and triple (\(\equiv\)) carbon-carbon bonds.

Step 2: Determine the hybridization for each type of bond

- \(sp^3\) hybridization: Carbon atoms with only single bonds (\(-\)) are \(sp^3\) hybridized.- \(sp^2\) hybridization: Carbon atoms with one double bond (\(=\)) are \(sp^2\) hybridized.- \(sp\) hybridization: Carbon atoms with a triple bond (\(\equiv\)) or two double bonds are \(sp\) hybridized.

Step 3: Count the sp hybridized carbon atoms

The carbon atoms involved in triple bonding \((\equiv)\) will be \(sp\) hybridized. There are two carbons in the triple bond \(-\mathrm{C}\equiv \mathrm{C}-\), making a total of 2 \(sp\) hybridized carbons.

Step 4: Count the sp2 hybridized carbon atoms

The carbon atoms with double bonds \((=)\) will be \(sp^2\) hybridized. There are three distinct double bonds \(\mathrm{-CH}=\mathrm{CH}-\mathrm{CH}=\mathrm{CH}_{2}\), making a total of 3 \(sp^2\) hybridized carbons.

Step 5: Count the sp3 hybridized carbon atoms

The carbon atoms with only single bonds \(-\), such as the initial \((\mathrm{H}_{3}\mathrm{C})_{2} \mathrm{CH}\), are \(sp^3\) hybridized. Counting the \(\mathrm{-CH}_{3}\) groups and adjacent single bonds, we find three carbon atoms are \(sp^3\) hybridized.

Step 6: Validate the statements

Statement 1 says three carbon atoms are \(sp^3\) hybridized, which is correct based on our step 5 analysis. Statement 2 says three carbon atoms are \(sp^2\) hybridized, which is also correct according to step 4. Statement 3 says two carbon atoms are \(sp\) hybridized, which matches our step 3 finding. Therefore, all statements (1, 2, and 3) are correct.

Key Concepts

sp hybridization

In the world of organic chemistry, hybridization plays a crucial role in determining the structure and bonding nature of molecules. Let's begin with the concept of **sp hybridization**. This type of hybridization involves the mixing of one s orbital and one p orbital from the same atom to form two sp hybrid orbitals. Each of these orbitals contains one electron and forms linear molecules.

Typically, carbon atoms that are sp hybridized form molecules with a triple bond between carbon atoms, indicated by a triple line (≡) in structural formulas. Such an arrangement allows the formation of a linear molecular shape, with a bond angle of 180 degrees.

Key characteristics of sp hybridization include:

• Molecules are linear in shape.
• Each carbon atom forms two bonds, usually composed of one triple bond and one single bond.
• The remaining unhybridized p orbitals form two pi bonds which are perpendicular to each other, contributing to the triple bond.

Understanding these aspects helps in identifying molecules where sp hybridization occurs, such as the section of our molecule that contains the carbon-carbon triple bond.

sp2 hybridization

Next, let's discuss **sp2 hybridization**, another common type of hybridization in organic molecules. This involves the mixing of one s orbital with two p orbitals to form three equivalent sp2 hybrid orbitals. As a result, molecules with sp2 hybridized atoms have a trigonal planar shape and a bond angle of approximately 120 degrees.

In sp2 hybridization, each carbon atom with a double bond (shown as =) is typically sp2 hybridized. The orientation of the bonds due to this hybridization allows for the distinct planar shape of the molecule, important for understanding molecular geometry and reactivity.

Characteristics of sp2 hybridization include:

• Molecules take on a trigonal planar shape.
• It involves carbon atoms with one double bond and two single bonds.
• The remaining unhybridized p orbital forms a pi bond over the plane of the bonded atoms, contributing to the double bond.

This knowledge assists in the recognition of double-bonded sections within molecular structures, as exemplified by several sections in the given organic molecule involving carbon-carbon double bonds.

sp3 hybridization

Finally, we have **sp3 hybridization**, which is one of the most prevalent hybridizations for carbon atoms in organic chemistry. This occurs when one s orbital mixes with three p orbitals to produce four equivalent sp3 hybrid orbitals. This allows for tetrahedral bonding arrangements with bond angles close to 109.5 degrees.

Carbon atoms that are bonded with only single bonds, depicted as a single line (-) in structural formulas, typically exhibit sp3 hybridization. The formation of these four sigma bonds provides stability and makes up structures that are quite common in organic molecules, like alkanes.

Key features of sp3 hybridization include:

• Molecules have a tetrahedral shape.
• The carbon atom forms four single bonds with other atoms.
• All four hybrid orbitals participate in sigma bonding, leading to a more saturated structure.

Recognizing sp3 hybridized carbons is helpful when deciphering parts of a molecule that consist solely of single bonds, as demonstrated by the arrangement of carbon atoms at the beginning of our given molecule with sections of only single carbon-carbon bonds.