Problem 7 - A Complete Resource Book in Chemistry for JEE Main

Question

Main axis of a diatomic molecule is \(\mathrm{Z}\), molecule orbitals \(\mathrm{p}_{\mathrm{x}}\) and \(\mathrm{p}_{y}\) overlap to form, which of the following orbital? (a) \(\pi\) molecular orbital (b) \(\sigma\) molecular orbital (c) \(\delta\) molecular orbital (d) no bond will form

Step-by-Step Solution

Answer

\( \pi \) molecular orbital

Step 1: Identify the Orbitals

The orbitals given are \( p_x \) and \( p_y \), which are p orbitals lying along the x-axis and y-axis, respectively, relative to the diatomic molecule.

Step 2: Understand Orbital Alignment

Since the main axis of the diatomic molecule is given as \( Z \), we understand that any bond formation considered here is relative to the z-axis. The alignment and shape of \( p_x \) and \( p_y \) are thus perpendicular to this main molecular axis.

Step 3: Determine Possible Bond Types

For p orbitals that are perpendicular to the bond axis \( Z \), when they overlap, they can only form a \( \pi \) molecular orbital. This occurs when side-by-side overlap of p orbitals takes place, rather than end-to-end.

Step 4: Confirm the Bond Formation

Based on the configuration and overlap nature (perpendicular to axis \( Z \)), the \( p_x \) and \( p_y \) orbitals will form a \( \pi \) molecular orbital due to their side-by-side overlap.

Key Concepts

σ molecular orbitals

Sigma (σ) molecular orbitals are one of the fundamental types of orbitals formed during chemical bonding. These orbitals result from the end-to-end overlap of atomic orbitals. Generally, when atomic orbitals overlap in a head-on manner along the internuclear axis—typically the z-axis in diatomic molecules—a strong bonding interaction is established, known as a σ bond.

Key characteristics of σ molecular orbitals include:

• They have a symmetrical electron distribution around the bond axis, which is why they are often very strong.
• A σ bond can contain electrons stemming from s, p, or even hybridized orbitals, such as sp, sp², or sp³.
• These orbitals are significant in determining a molecule’s shape and its bond angles because of their strong, direct interactions.

In many diatomic molecules, σ bonds serve as the "glue" holding the atoms together, which is critical for molecule stability.

π molecular orbitals

Pi (π) molecular orbitals are another crucial type of molecular orbital formed in chemical bonding. Unlike σ molecular orbitals, π orbitals result from the side-to-side overlap of atomic orbitals. Typically, they occur when p orbitals align parallel to each other, enabling an overlap that forms this unique bonding interaction.

Here are some important points about π molecular orbitals:

• They are usually formed by the lateral overlap of p orbitals, which are parallel to each other but perpendicular to the bond's main axis.
• Evident in molecules with double or triple bonds, π orbitals provide additional stability and are key in preventing rotation around the bond.
• These orbitals often exist alongside σ bonds to enhance the molecule's bonding capacity, but they are generally weaker than σ bonds due to their electron density being situated above and below the bond axis.

In molecular structures, π bonds lend rigidity and contribute significantly towards the double-bond character, particularly in the structure and function of unsaturated organic compounds.

p orbitals

P orbitals are a fundamental component of atomic structure and are essential in understanding molecular orbital theory. Each of these orbitals is shaped oblong, resembling a pair of lobes positioned on opposite sides of an atomic nucleus, with a nodal plane located at the nucleus itself.

Key facts about p orbitals include:

• Each atom has three p orbitals—denoted as p_x, p_y, and p_z—aligned along mutually perpendicular axes (x, y, and z).
• P orbitals are higher in energy than s orbitals and can be involved in both bonding and non-bonding interactions depending on the molecular context.
• Due to their shape, p orbitals can overlap side-by-side or end-to-end, leading to the formation of either π or σ molecular orbitals.

Significantly, p orbitals play a crucial role in the formation of chemical bonds, as they have the potential to create multiple types of bonds based on their orientation and overlap characteristics. Understanding p orbitals is key to predicting and explaining the geometry and properties of molecules.