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 is in a plane perpendicular to the molecular plane (option c).

Step 1: Understanding the Structure of Ethene

Ethene (C_2H_4) consists of two carbon atoms each bonded to two hydrogen atoms and to each other by a double bond. The double bond is composed of a sigma (  () bond and a pi () bond.

Step 2: Relating Nodal Plane to Pi Bonds

The nodal plane in a pi bond is a plane where the probability of finding an electron is zero. It occurs due to the phase difference of the p-orbitals forming the pi bond.

Step 3: Determining the Nodal Plane Orientation

In ethene, the pi bond is formed by the overlap of two p-orbitals, which are perpendicular to the plane of the ethene molecule (which contains the sigma bonds). The nodal plane of the pi bond is thus perpendicular to the plane of the ethene and bisects the carbon-carbon sigma bond.

Step 4: Choosing the Correct Answer

Based on the understanding that the nodal plane is perpendicular to the molecular plane and bisects the carbon-carbon sigma bond, the correct choice is (c).

Key Concepts

Ethene Structure

Ethene, also known as ethylene, is a simple hydrocarbon composed of two carbon atoms and four hydrogen atoms, with the chemical formula \( C_2H_4 \). Each carbon atom in ethene is bonded to two hydrogen atoms and one other carbon atom, forming a double bond between the two carbon atoms. This double bond is crucial for the structural integrity and properties of ethene.

The structure of ethene can be visualized as being planar, with all atoms aligned in a single plane. Each carbon atom is \( sp^2 \) hybridized, which means that one 2s orbital mixes with two 2p orbitals, forming three \( sp^2 \) hybrid orbitals. These hybrid orbitals create sigma bonds by overlapping with the s orbitals of hydrogen atoms and one \( sp^2 \) hybrid orbital from the other carbon atom. The remaining unhybridized p orbitals on each carbon atom participate in forming a pi bond, which is an important aspect of ethene's structure.

The arrangement of these bonds gives ethene its characteristic planar geometry, with bond angles of approximately 120°. Understanding this structure is key to comprehending the behavior of the pi bonds and nodal planes in ethene.

Pi Bonds and Nodal Planes

Pi bonds are a type of covalent bond formed when two lobes of one p orbital overlap with two lobes of another p orbital from an adjacent atom. In ethene, the pi bond is formed by the side-to-side overlap of the unhybridized p orbitals on each carbon atom. The presence of this pi bond is what distinguishes a double bond from a single sigma bond.

A nodal plane is an area where there is a zero probability of finding an electron. In the context of a pi bond, the nodal plane occurs between the regions of the p orbitals that overlap. This plane passes through the internuclear axis of the two atoms connected by the pi bond, essentially dividing the overlapping p orbitals into separate phases.

In ethene, the nodal plane of the pi bond is perpendicular to the molecular plane of the molecule, which can be visualized as a flat sheet containing the sigma bond framework. This orientation means that while sigma bonds lie within the plane of the molecule, the pi bond's electron cloud is situated above and below this plane.

Sigma and Pi Bonds

Sigma and pi bonds are fundamental types of covalent bonds distinguished by their formation and orientation between atoms. In ethene, these bonds collectively stabilize the molecule, yet they have distinct characteristics.

• Sigma Bonds: A sigma bond is the strongest type of covalent bond and is formed through the head-on overlapping of orbitals. In ethene, all hydrogen-carbon bonds and one of the carbon-carbon bonds are sigma bonds. This type of bond is primarily responsible for holding the atoms together because it allows electrons to be concentrated between the bonded nuclei.


• Pi Bonds: A pi bond is weaker than a sigma bond and results from the lateral overlap of p orbitals. The pi bond in ethene contributes to the double bond between the carbon atoms, lying above and below the plane of the nucleus. This bond limits the rotational freedom around the carbon-carbon bond, resulting in the planar structure of ethene.

Understanding the differences between sigma and pi bonds, and their roles in molecular structures, helps in explaining the molecular geometry and reactivity of compounds like ethene. While sigma bonds provide strength and stability, pi bonds introduce additional complexity and functionality in chemical reactions.