Problem 181 - A Complete Resource Book in Chemistry for JEE Main

Question

In which of the following compounds, the underlined carbon has \(\mathrm{sp}^{3}\) hybridization? (a) \(\mathrm{CH}_{3}-\underline{\mathrm{CH}}=\mathrm{CH}_{2}\) (b) \(\mathrm{CH}_{3} \mathrm{CO} \mathrm{NH}_{2}\) (c) \(\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{OH}\) (d) \(\mathrm{CH}_{3} \mathrm{COOH}\)

Step-by-Step Solution

Answer

Compound (c) has the underlined carbon with \\(\mathrm{sp}^{3}\\) hybridization.

Step 1: Understanding Hybridization

Hybridization is the concept of mixing atomic orbitals to form new hybrid orbitals. The type of hybridization depends on the number of sigma bonds and lone pairs around a carbon atom. For \(\mathrm{sp}^{3}\) hybridization, the carbon forms four sigma bonds, as seen in single bonds.

Step 2: Analyzing Compound (a)

The compound is \(\mathrm{CH}_{3}-\underline{\mathrm{CH}}=\mathrm{CH}_{2}\). The underlined carbon is bonded to one hydrogen atom and is also part of a double bond (\(\pi\) bond) with the next carbon. Therefore, it forms three sigma bonds and one \(\pi\) bond, indicating \(\mathrm{sp}^{2}\) hybridization.

Step 3: Analyzing Compound (b)

In \(\mathrm{CH}_{3} \mathrm{CO} \mathrm{NH}_{2}\), the underlined carbon is not specified, but considering the structure, the carbon adjacent to the oxygen in the ketone group forms one double bond and two single bonds, resulting in \(\mathrm{sp}^{2}\) hybridization. However, the second carbon in the chain is not underlined, thus the question does not specify the carbon effectively.

Step 4: Analyzing Compound (c)

For \(\mathrm{CH}_{3}-\underline{\mathrm{CH}_{2}}-\mathrm{OH}\), the underlined carbon forms four single bonds: three with hydrogen and one with the other carbon atom, fitting the criteria for \(\mathrm{sp}^{3}\) hybridization.

Step 5: Analyzing Compound (d)

In the structure \(\mathrm{CH}_{3} \underline{\mathrm{CO}} \mathrm{OH}\), the underlined carbon in the carboxylic acid group forms one double bond with oxygen (\(\pi\) bond) and two single bonds, indicating \(\mathrm{sp}^{2}\) hybridization.

Key Concepts

sp3 hybridization

When we talk about \( \text{sp}^3 \) hybridization, we're focusing on how a carbon atom mixes its orbitals. Carbon has atomic orbitals shaped like spheres and dumbbells, specifically the \( s \) and \( p \) orbitals. In \( \text{sp}^3 \) hybridization, one \( s \) orbital combines with three \( p \) orbitals to create four equivalent orbitals known as \( \text{sp}^3 \) hybrid orbitals.

Here's what these hybrid orbitals do:

🔹 They form single bonds with other atoms, like hydrogen or carbon. These are often called sigma bonds. 🔹 Each \( \text{sp}^3 \) hybrid orbital forms a sigma bond, allowing for a tetrahedral geometry around the carbon. 🔹 An example is in compound (c) \( \mathrm{CH}_{3}-\underline{\mathrm{CH}_{2}}-\mathrm{OH} \), where the underlined carbon forms four single (sigma) bonds: three with hydrogen and one with another carbon.

This setup ensures every bond angle is about 109.5 degrees, giving organic molecules their 3D shapes and influencing their reactivity. It’s essential in molecules that make up life, like in sugars and simple alcohols.

sigma bonds

Sigma bonds, often symbolized as \( \sigma \) bonds, form the backbone of organic molecules. These are the strongest type of covalent bond and occur when two orbitals overlap directly between two nuclei.

🔹 Unlike a \( \pi \) bond, a sigma bond allows for free rotation of the bonded atoms because the electron density is concentrated directly between the bonding nuclei.
🔹 In a carbon single bond, there is just one sigma bond.🔹 For instance, in the compound \( \mathrm{CH}_{3}-\underline{\mathrm{CH}_{2}}-\mathrm{OH} \), each carbon-hydrogen or carbon-carbon single bond is a sigma bond.

Another interesting point is that in multiple bonds (like double or triple bonds), the first bond is always a sigma bond. This is because sigma bonds maximize the orbital overlap, providing foundational strength to the bond. The stability and straightforwardness of sigma bonds make them the foundation of molecular architecture.

pi bonds

Pi bonds, represented as \( \pi \) bonds, are a bit different from sigma bonds. Forming the extra overlapping seen in double and triple bonds, they arise when parallel p orbitals from adjacent atoms overlap.

🔹 They are crucial in creating double and triple bonds in organic chemistry. 🔹 Unlike sigma bonds, pi bonds restrict the rotation of bonded atoms, which influences the shapes of molecules. This is vital in structural stability and functionality of unsaturated molecules like alkenes.
🔹 For example, in compound (a) \( \mathrm{CH}_{3}-\underline{\mathrm{CH}}=\mathrm{CH}_{2} \), the double bond consists of one sigma bond and one pi bond.

Pi bonds add to the overall bond energy but are generally weaker than sigma bonds because the electron density is spread above and below the plane of the nuclei. They are essential for the chemical reactivity of compounds, such as when double bonds react in addition reactions. Their presence dictates how molecules interact with each other and how they might change during chemical reactions.