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

Question

Main axis of a diatomic molecule is z, molecule orbitals \(\mathrm{p}_{x}\) and \(\mathrm{p}_{\mathrm{y}}\) 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

The orbitals will form a \(\pi\) molecular orbital.

Step 1: Understanding Molecular Orbitals

Molecular orbitals are formed by the overlap of atomic orbitals from two atoms. In the case of diatomic molecules, this involves considering the orientations of the p orbitals involved.

Step 2: Recognizing Orbital Types

The p orbitals can combine in two fundamental types of interactions: end-to-end (sigma, \(\sigma\)) and side-to-side (pi, \(\pi\)).

Step 3: Determine Overlap Interaction

Given that the \(\mathrm{p}_{x}\) and \(\mathrm{p}_{y}\) orbitals overlap, and considering they both extend parallel to the molecular axis (z-axis) when described as \(\mathrm{p}_{x}\) and \(\mathrm{p}_{y}\), they will overlap side-by-side, not end-to-end.

Step 4: Identify Resulting Molecular Orbital

Since \(\mathrm{p}_{x}\) and \(\mathrm{p}_{y}\) overlap side-by-side, they form a \(\pi\) molecular orbital.

Key Concepts

p orbitals overlap

In chemistry, the concept of orbital overlap is crucial for understanding how chemical bonds form. The p orbitals are a type of atomic orbital and have a specific orientation in space. Each set of p orbitals consists of three types, labeled as \( p_x \), \( p_y \), and \( p_z \). Each of these has a distinct shape, resembling a dumbbell, and is oriented along the respective axis of a coordinate system.

When discussing overlap, we consider how these orbitals from two atoms interact when they come close to one another. The overlap can occur in different manners. For example, when \( p_x \) and \( p_y \) orbitals approach each other, the interaction can be side-to-side along the same plane, which is an important consideration when predicting the type of molecular orbital that will result.

Some key points to remember about \( p \) orbital overlaps are:

• The shape and orientation of p orbitals determine how they can overlap.
• Side-by-side overlaps do not involve the central axis which results in different interactions compared to end-to-end overlaps.

pi molecular orbital

A pi (\( \pi \)) molecular orbital is formed when two atomic orbitals overlap side-by-side. This typically occurs with p orbitals, such as \( p_x \) or \( p_y \), that are oriented parallel to each other. The resulting molecular orbital does not lie along the axis of the bond (the z-axis in diatomic molecules), but rather, it is above and below this axis. This creates a type of bond that is characteristic of double and triple bonds in molecules.

The main features of \( \pi \) molecular orbitals include:

• They are less direct than \( \sigma \) bonds because the electron density is concentrated above and below the nuclei of the bonding atoms, not between them.
• \( \pi \) bonds provide additional strength to the bond, resulting in a higher total bond order.

The formation of a \( \pi \) bond in which the orbitals do not overlap head-on is a fascinating example of how electrons can stabilize atoms by allowing the sharing of electron density in areas that aren't directly between the involved atomic nuclei.

sigma molecular orbital

Sigma (\( \sigma \)) molecular orbitals are formed by the end-to-end overlap of atomic orbitals. Unlike \( \pi \) orbitals, \( \sigma \) molecular orbitals involve the direct head-on interaction of orbitals like \( s \) orbitals or \( p_z \) orbitals. This interaction results in electron density being concentrated along the line or axis connecting two nuclei, typically referred to as the molecular axis (z-axis in diatomic molecules).

Important characteristics of \( \sigma \) molecular orbitals include:

• They have more electron density directly between the two atomic nuclei compared to \( \pi \) bonds, leading to a stronger bond.
• \( \sigma \) bonds allow for free rotation around the bond axis, as the electron density holds the nuclei firmly together along the axis.

Understanding \( \sigma \) molecular orbitals is key in predicting and explaining why molecules physically orient themselves in certain ways and exhibit particular chemical properties.