Problem 146 - 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 carbons are sp \(^{3}\) hybridized 2\. three carbons are sp \(^{2}\) hybridized 3\. two carbons are sp hybridized Of these statements (a) 1 and 2 are correct (b) 1 and 3 are correct (c) 2 and 3 are correct (d) all are correct

Step-by-Step Solution

Answer

Statement 1 and 3 are correct: Option (b) is correct.

Step 1: Identify the Geometry of Carbon Atoms

First, analyze the hybridization of each carbon atom in the molecule \((\mathrm{H}_3\mathrm{C})_2 \mathrm{CH}-\mathrm{CH}=\mathrm{CH}-\mathrm{C} \equiv \mathrm{C}-\mathrm{CH}=\mathrm{CH}_2\). Hybridization depends on the number of regions of electron density (bonds and lone pairs) around the carbon atom.

Step 2: Determine sp³ Hybridized Carbons

Carbons with four single bonds (or a total of four sigma bonds) are sp³ hybridized. - The two \(\mathrm{CH}_3\) groups contain carbon sp³ hybridized.- The \(\mathrm{-CH}-\) (adjacent to \(\mathrm{CH}_3\)) is sp³ hybridized due to four sigma bonds.

Step 3: Determine sp² Hybridized Carbons

Carbons with three regions of electron density (one double bond and two single bonds or three sigma bonds) are sp² hybridized. - The carbon in \(-\mathrm{CH}=\mathrm{CH}-\) is sp² hybridized with one double bond (\(\pi\) and \(\sigma\)) and two sigma bonds.- The terminal \(\mathrm{=CH}_2\) is sp² hybridized due to one double bond and one single bond.

Step 4: Determine sp Hybridized Carbons

Carbons with two regions of electron density (one triple bond or one double bond with a single bond) are sp hybridized.- The \(\equiv \mathrm{C}-\) (triple bond carbon) is sp hybridized, as it is part of a triple bond with two pi bonds and one sigma bond.- The \(\mathrm{C}-\) directly attached to the triple-bonded carbon is also sp hybridized, with one triple bond and one single bond.

Step 5: Check the Conditions

Evaluate each condition: - The statement that three carbons are sp³ hybridized is true. - The statement that three carbons are sp² hybridized is not true; only two are sp² hybridized. - The statement that two carbons are sp hybridized is true.

Key Concepts

sp3 hybridization

In organic chemistry, sp³ hybridization occurs when a carbon atom forms four single bonds or a total of four sigma bonds. The sp³ hybridized carbon has a tetrahedral geometry with bond angles of approximately 109.5 degrees. This is because the molecule forms a three-dimensional shape where each bond is equidistant to minimize repulsions.

Here, in the molecule \(\mathrm{CH}_3\), \(\mathrm{C}\) is binded to three hydrogen atoms and another carbon atom forming only single bonds. This set-up makes the carbon in the \(\mathrm{CH}_3\) group sp³ hybridized.

Similarly, in the portion of the molecule where there is \(-\mathrm{CH}-\), it contains a carbon atom that is single-bonded to four neighboring atoms (three other carbons and one hydrogen). These bonds are all sigma bonds, so the carbon is sp³ hybridized.

• Tetrahedral Structure
• Approximately 109.5° Bond Angle
• Four Single Sigma Bonds

sp2 hybridization

sp² hybridization happens when a carbon is surrounded by three regions of electron density or specifically, one double bond and two single bonds. When this configuration exists, the carbon has a trigonal planar shape, with bond angles close to 120 degrees.

In the molecule, look for sections like \(-\mathrm{CH}=\mathrm{CH}-\), where each carbon atom is part of a double bond (composed of one sigma bond and one pi bond) along with two additional single bonds. This specific configuration illustrates the sp² hybridized carbon.

Also, when examining the terminal \(\mathrm{=CH}_2\), observe that this carbon configuration allows for one double bond combined with another single bond, confirming its sp² hybridization.

• Trigonal Planar Geometry
• Approximately 120° Bond Angle
• Presence of Double Bond (as \pi\ond)

sp hybridization

The concept of sp hybridization involves a carbon atom forming bonds in a linear structure. Typically, an sp hybridized carbon has two regions of electron density, usually in the form of a triple bond or a combination of a double bond and a single bond.

In this molecule's structure, the segment \(\equiv\mathrm{C}-\) represents a triple bond situation. This carbon is involved in one triple bond, meaning there are two pi bonds and one sigma bond from the carbon. The carbon directly attached to this triple-bonded carbon is also sp hybridized because it shares the same linear arrangement due to the single and triple bond formation.

This configuration results in a linear geometry, offering a bond angle of 180 degrees, showcasing the characteristics of sp hybridization clearly.

• Linear Structure
• 180° Bond Angle
• Presence of a Triple Bond (with 2 \pi\onds)