Problem 112 - A Complete Resource Book in Chemistry for JEE Main

Question

The nodal plane in the \(\pi\) bond of ethene is located in (a) the molecular plane. (b) a plane parallel to the molecular plane. (c) a plane perpendicular to the molecular plane which bisects. The carbon- carbon \(\sigma\) bond at right angle. (d) a plane perpendicular to the molecular plane which contains the carbon- carbon bond.

Step-by-Step Solution

Answer

The nodal plane of the \( \pi \) bond in ethene is in a plane perpendicular to the molecular plane that bisects the carbon-carbon \( \sigma \) bond at a right angle (option c).

Step 1: Understanding the Problem

We need to determine which plane the nodal plane of the \( \pi \) bond in ethene is located in. Ethene, \( C_2H_4 \), has a double bond between the two carbon atoms consisting of one \( \sigma \) bond and one \( \pi \) bond.

Step 2: Explaining \( \pi \) Bonds

A \( \pi \) bond is formed by the sideways overlap of p orbitals from adjacent carbon atoms. This overlap occurs above and below the plane of the atoms, resulting in a nodal plane where no electron density exists.

Step 3: Identifying the Nodal Plane

The nodal plane of a \( \pi \) bond is located in the plane where the p orbitals do not overlap. This is the plane that bisects the two lobes of the \( \pi \) bond and passes through the atomic centers.

Step 4: Determining the Correct Plane

The nodal plane of the \( \pi \) bond is perpendicular to the plane of the \( \sigma \) bond formed by the s-orbitals. It bisects the carbon-carbon \( \sigma \) bond at a right angle, meaning it is option (c) from our choices.

Key Concepts

Pi Bonds

Pi bonds are an essential component in the study of organic chemistry, particularly when understanding molecules like ethene. These bonds form when two lobes of an orbital on one carbon atom overlap with two lobes of an orbital on another carbon atom. Unlike sigma bonds which occur along the bond axis, pi bonds are formed by the *side-to-side* overlap of **p orbitals**. This overlapping creates two regions of electron density:

• One located above the plane of the atoms involved in the bond.
• Another located below the plane of the atoms.

It's important to note that the presence of electron density above and below the molecular plane results in the characteristic nodal plane of pi bonds. The nodal plane is a region where the probability of finding electrons is zero. This means, in this area, the p orbitals do not overlap, offering a clear indication of pi bonding in action.

Sigma Bonds

In contrast to pi bonds, sigma bonds represent the foundational bonding found between atoms. These bonds form by the **head-on overlap** of atomic orbitals, such as s-s, s-p, or p-p orbital overlaps. This direct overlap is more robust and characterized as:

• Possessing greater bond strength compared to pi bonds.
• Providing the primary structure in molecular bonds like that found in ethene (\(C_2H_4\)).

In ethene, each carbon atom forms one sigma bond with another carbon atom and two additional sigma bonds with hydrogen atoms. This setup keeps all atoms in the same plane, contributing to the molecule’s stability.

Moreover, sigma bonds allow for free rotation of bonded atoms around the bond axis. However, in molecules like ethene, the existence of a pi bond restricts this rotation, maintaining the structural integrity and shape of the molecule.

Bonding in Ethene

Ethene, an organic compound with the formula \( C_2H_4 \), is a simple alkene with a structure that highlights the combination of both sigma and pi bonds. This dual bonding occurs between its two carbon atoms:

• A single sigma bond forms the backbone of their connection.
• A pi bond is formed atop this sigma bond, reinforcing the bond between carbons.

The presence of a pi bond introduces a fascinating characteristic to ethene: the formation of a **nodal plane**. This plane is perpendicular to the molecular plane and bisects the carbon-carbon sigma bond. As a result, the electron density of the pi bond exists entirely outside this nodal plane, in regions where the p orbitals overlap either above or below the plane of the molecule itself.

By understanding the bonding in ethene, we appreciate how the interplay of sigma and pi bonds contributes to the geometry and properties of organic molecules. This combination of bonding types is pivotal in providing ethene its flat, planar structure and stability, influencing its chemical reactivity and physical properties.