Problem 46 - Chemistry The Central Science

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), (c) the 2 s orbital on one atom and the 2\(p_{z}\) orbital on the other atom.

Step-by-Step Solution

Answer

To create the sketches illustrating the overlap of orbitals, first understand the shapes of 2s and 2\(p_{z}\) orbitals. The 2s orbital has a spherical shape, while the 2\(p_{z}\) orbital has a dumbbell shape oriented along the z-axis. The overlap of 2s orbitals on each atom forms a sigma bond with a higher electron density in the region of orbital overlap. When 2\(p_{z}\) orbitals on each atom overlap along the z-axis, they also form a sigma bond with electron density concentrated between the two nuclei. Lastly, the overlap of a 2s orbital on one atom and a 2\(p_{z}\) orbital on the other atom forms a sigma bond, with electron density concentrated around the region where the orbitals have overlapped.

Step 1: Understanding the shapes of orbitals

Before drawing the sketches of the overlapping orbitals, we must first understand the shapes of the 2s and 2\(p_{z}\) orbitals. The 2s orbital has a spherical shape that is bigger than the 1s orbital. It has a radial node separating the inner and outer lobes, which means that the probability density of finding an electron is higher on the outer lobe compared to the inner lobe. The 2\(p_{z}\) orbital, on the other hand, has a dumbbell shape and is oriented along the z-axis. It has two lobes with a nodal plane that lies along the x-y plane.

Step 2: Drawing the overlap of 2s orbitals on each atom

To draw the sketch of the overlapping 2s orbitals, start by drawing two atoms close to each other and sketch the spherical 2s orbital on each atom. As the atoms approach each other, their 2s orbitals will overlap in the region between the two nuclei, thus forming a sigma bond. The overlapping region appears as a cloud of electron density, with the higher density in the region of orbital overlap.

Step 3: Drawing the overlap of 2\(p_{z}\) orbitals on each atom

To draw the sketch of the overlapping 2\(p_{z}\) orbitals, first position two atoms along the z-axis. Next, draw the dumbbell-shaped 2\(p_{z}\) orbital on each atom with their lobes pointing towards each other. When both 2\(p_{z}\) orbitals overlap, they form a sigma bond along the z-axis, with electron density concentrated in the region between the two nuclei.

Step 4: Drawing the overlap of 2s orbital on one atom and the 2\(p_{z}\) orbital on the other atom

To draw the overlap of the 2s orbital on one atom (atom A) and the 2\(p_{z}\) orbital on the other atom (atom B), position the atoms close to each other with atom B on the z-axis. Then, sketch the 2s orbital on atom A and the 2\(p_{z}\) orbital on atom B, with the latter's lobes pointing towards atom A. In this configuration, the overlap between the 2s orbital and one of the 2\(p_{z}\) orbital's lobes will form a sigma bond. The density of electron cloud will be more concentrated around the region where the 2s and 2\(p_{z}\) orbitals have overlapped.

Key Concepts

2s orbital

The 2s orbital is one of the simplest types of atomic orbitals to understand because of its spherical shape. Imagine a globe around the nucleus of an atom. This is essentially what a 2s orbital looks like.
Unlike the 1s orbital, the 2s is larger due to its higher energy level. Inside this sphere, there's an area called a radial node. This is a region where the probability of finding an electron is zero.

• Shape: Spherical
• Nodal Surface: Presence of a radial node

When thinking about orbital overlaps, it's important to understand that the 2s orbital is like a cloud of possibility, where electrons might be found. When two atoms with 2s orbitals approach each other, these clouds overlap and create a region of electron density between the nuclei, which is key in forming a bond.

2pz orbital

The 2pz orbital is quite different from the 2s orbital in both shape and orientation. It's shaped like a dumbbell with two lobes, and it is oriented along the z-axis of an atom. Imagine a barbell lying along the z direction, with the center of the dumbbell at the nucleus.

• Shape: Dumbbell-shaped with two lobes
• Orientation: Z-axis
• Nodal Plane: Lies along the x-y plane

The 2pz orbital's distinct shape and alignment give it unique properties compared to s orbitals. The two lobes represent areas of high electron density on either side of the nucleus, separated by a nodal plane where the probability of finding an electron is zero. This characteristic is crucial for certain types of molecular interactions, especially when considering overlap with other orbitals to form sigma bonds.

sigma bond

Sigma bonds are the strongest type of covalent chemical bond. They form when atomic orbitals overlap in a region called an orbital overlap, where the highest electron density is found between the two bonded nuclei.

• Type of Bond: Covalent
• Formation: Overlap of orbitals directly between two atomic nuclei
• Strength: Strongest of covalent bonds

In a sigma bond, overlapping can occur in different combinations, such as: - 2s with 2s orbital overlap - 2pz with 2pz orbital overlap - 2s with 2pz orbital overlap Each of these overlaps can result in a sigma bond because of how these orbitals are oriented relative to each other. When one atom's 2s orbital overlaps with another atom's 2pz orbital, the overlapping takes place directly along the axis that connects the two nuclei. This alignment maximizes the overlap and electron density between the atoms, which results in a strong, stable bond.