Question

Draw sketches illustrating the overlap between the following orbitals on two atoms: (a) the \(2 s\) orbital on each atom, (b) the \(2 p_{z}\) orbital on each atom (assume both atoms are on the \(z\) -axis), \((\mathbf{c})\) the 2 s orbital on one atom and the \(2 p_{2}\) orbital on the other atom.

Short answer

In short, to illustrate the overlap between the orbitals on two atoms, you need to create three sketches: 1. For the overlap between 2s orbitals on each atom, draw two spherical orbitals around the nuclei and shade the overlapping area to represent the bonding region. 2. For the overlap between 2p_z orbitals on each atom, draw two dumbbell-shaped orbitals extending along the z-axis around the nuclei and shade the overlapping area to represent the bonding region. 3. For the overlap between 2s orbital on one atom and 2p_x orbital on the other atom, draw a spherical orbital around one nucleus and a dumbbell-shaped orbital extending along the x-axis around the other nucleus, then shade the overlapping area to represent the bonding region.

Step-by-step solution

Drawing 2s orbitals on each atom

2s orbitals are spherical in shape. To represent the overlap between the 2s orbitals on two different atoms, follow these steps: 1. Draw two circles to represent the nuclei of the two atoms. 2. Draw a spherical orbital (2s) around each nucleus. 3. Show the overlapping area filled with shading, which represents the bonding region between the two orbitals.

Drawing 2p_z orbitals on each atom

2p_z orbitals have a dumbbell shape, with the two lobes along the z-axis. To represent the overlap between the 2p_z orbitals on two different atoms, follow these steps: 1. Draw two circles to represent the nuclei of the two atoms, arranged along the z-axis. 2. Draw a 2p_z orbital around each nucleus, with the two lobes extending along the z-axis. 3. Show the overlapping area filled with shading, which represents the bonding region between the two orbitals.

Drawing 2s orbital on one atom and 2p_2 orbital on the other atom

In this scenario, we need to represent the overlap between the 2s orbital on one atom and the 2p_2 orbital on another atom. The 2p_2 orbital is a typo and should be corrected as 2p_x, 2p_y, or 2p_z orbital; for simplicity, let's assume it is the 2p_x orbital. To represent the overlap, follow these steps: 1. Draw two circles to represent the nuclei of the two atoms. 2. Draw a spherical orbital (2s) around one nucleus and a 2p_x orbital (with the two lobes extending along the x-axis) around the other nucleus. 3. Show the overlapping area filled with shading, which represents the bonding region between the two orbitals. Now you should have three sketches showing the overlap between the specified orbitals on the two atoms.

Key concepts

Orbital Overlap

Orbital overlap is a crucial concept in understanding how atoms bond to form molecules. It refers to the situation where atomic orbitals on different atoms "meet" or overlap in space, leading to a region where electron density is shared between the atoms. This shared electron density creates a chemical bond. In general, the more effective the overlap, the stronger the bond.

There are a few key points to consider about orbital overlap:

• Shape of Orbitals: The shape of the atomic orbitals influences how effectively they can overlap. For example, 2s orbitals are spherical, allowing them to overlap equally from all directions, while 2p orbitals have directional lobes which may affect the overlap.
• Type of Bond: The nature of the orbitals involved in overlapping determines the kind of bond formed. For instance, overlap of s orbitals with p orbitals can result in sigma (σ) bonds, while the side-on overlap of p orbitals can lead to pi (π) bonds.
• Bond Strength: Greater overlap typically results in stronger bonds because more electron density is concentrated between the nuclei of two bonded atoms.

By understanding the concept of orbital overlap, you can better predict and explain the properties of molecules as well as their chemical behavior.

Atomic Orbitals

Atomic orbitals are regions in an atom where there is a high probability of finding electrons. They are fundamentally important for understanding how atoms behave and interact with each other. Each orbital is defined by a unique set of quantum numbers that determine their size, shape, and orientation in space.

Key characteristics of atomic orbitals include:

• Types of Orbitals: The most common types are s, p, d, and f orbitals. Each type has a characteristic shape (e.g., s orbitals are spherical while p orbitals are dumbbell-shaped).
• Energy Levels: Electrons fill orbitals starting with the lowest energy level, following the Aufbau principle. This means 1s will fill before 2s, 2p, and so on.
• Orbital Hybridization: Sometimes orbitals mix to form new hybrid orbitals. This occurs to optimize bonding and molecular geometry, such as sp, sp2, and sp3 hybridizations that often participate in covalent bonding.

Understanding atomic orbitals provides insight into the distribution of electrons within an atom, which is a cornerstone of predicting chemical interactions.

Molecular Orbitals

Molecular orbitals are formed when atomic orbitals from different atoms combine during the formation of a molecule. Unlike atomic orbitals, which belong to individual atoms, molecular orbitals belong to the entire molecule. This concept explains the distribution of electrons across a molecule, rather than just an isolated atom.

Features of molecular orbitals include:

• Formation: Molecular orbitals are created when atoms combine, and their atomic orbitals overlap. The number of molecular orbitals created equals the number of atomic orbitals involved.
• Bonding and Antibonding Orbitals: Molecular orbitals can be bonding, which increase electron density between nuclei and stabilize the molecule, or antibonding, which decrease electron density and are destabilizing.
• Electron Configuration: Electrons fill molecular orbitals starting from the lowest energy level based on the principles of Hund’s rule and the Pauli exclusion principle, much like atomic orbitals.

Molecular orbital theory provides a more comprehensive explanation of bonding and properties of molecules compared to considering only atomic orbitals, helping predict molecular behavior with greater accuracy.