Problem 71 - Chemistry Principles and Practice

Question

If the \(z\) axis is defined as the bond axis, draw a picture that shows the overlap of each of the following pairs of orbitals; then indicate whether a \(\sigma\) or \(\pi\) bond forms. (a) \(p_{z}, p_{z}\) (b) \(p_{y}, p_{y}\) (c) sp hybrid formed from \(p_{z}\) and \(s\) orbitals, \(p_{z}\)

Step-by-Step Solution

Answer

(a) Forms a \(\sigma\) bond; (b) Forms a \(\pi\) bond; (c) Forms a \(\sigma\) bond.

Step 1: Identify Orbital Orientation

Recognize that the orbitals have different orientations based on their names. For example, the orbital with the subscript \(z\) is aligned along the \(z\)-axis, while the \(y\) is aligned along the \(y\)-axis.

Step 2: Analyze Overlap and Bond Type for (a)

For the pair \(p_{z}, p_{z}\), both orbitals are aligned along the \(z\)-axis. When these orbitals overlap end-to-end, they form a single bond along the axis, known as a \(\sigma\) bond.

Step 3: Analyze Overlap and Bond Type for (b)

For the pair \(p_{y}, p_{y}\), these orbitals are aligned parallel to the \(y\)-axis. They overlap side-to-side, forming a bond above and below the \(z\)-axis, resulting in a \(\pi\) bond.

Step 4: Analyze Overlap of sp Hybrid and (c)

The \(sp\) hybrid orbital formed from \(p_{z}\) and \(s\) orbitals is directed along the \(z\)-axis due to the incorporation of \(p_{z}\). Overlap is end-on with \(p_{z}\) orbitals, forming a \(\sigma\) bond along the \(z\)-axis.

Key Concepts

Sigma Bond

A sigma bond (\( \sigma \) bond) is a primary type of covalent bond and is characterized by the end-to-end overlap of atomic orbitals.When orbitals are aligned along the same axis, they can effectively overlap, leading to the formation of a strong sigma bond.The electron density for sigma bonds is concentrated directly between the nuclei of the bonding atoms.

Some key features of sigma bonds include:

• Formation between s-s, s-p, or p-p orbitals when they overlap along the inter-nuclear axis.
• The strongest type of covalent bond due to maximum electron density overlap.
• Form the first bond between two atoms – each additional bond is a different form, such as a pi bond.

Remember that the sigma bond's direct overlap along the axis contrasts with the side-to-side overlap seen in pi bonds.

Pi Bond

A pi bond (\( \pi \) bond) forms from the side-to-side overlap of p orbitals.This type of bond occurs in addition to an existing sigma bond, providing additional strength to a multiple bond (such as double or triple bonds).Pi bonds are characterized by their electron cloud, which lies above and below the axis connecting two nuclei.

Key characteristics of pi bonds:

• They involve the sideways overlapping of p orbitals.
• Weaker than sigma bonds due to less overlap.
• Found in double and triple bonds along with a sigma bond, adding stiffness but reducing rotational freedom.

In summary, pi bonds supplement sigma bonds to enhance the bonding in molecules with multiple bonds.

Orbital Overlap

Orbital overlap is fundamental in chemical bonding, where two atomic orbitals come together to create a new orbital configuration. The extent and nature of this overlap determine the strength and type of bond that forms.

Here's how orbital overlap generally works:

• For sigma bonds, the overlap is end-to-end, maximizing electron density between the bonded nuclei.
• For pi bonds, the overlap is side-to-side, occurring above and below the axis connecting the bonded atoms.
• The type of orbitals involved (s, p, d, f) dictates how orbitals overlap and the type of bond they form.

Understanding orbital overlap helps in visualizing how different atomic interactions form the bonds in molecules.

Hybrid Orbitals

Hybrid orbitals are combinations of standard atomic orbitals that blend together within an atom.This blending allows atoms to form more stable and directional bonds, ideal for complex molecular geometries.For instance, \( sp \) hybrid orbitals are created by the combination of one s and one p orbital.

Important aspects of hybrid orbitals:

• They form by mixing different orbitals, like s and p orbitals, to create new, equivalent hybrid orbitals.
• These hybrid orbitals align themselves to minimize repulsions and maximize bonds.
• Common hybrids include \( sp, sp^2, \) and \( sp^3 \) orbitals, each giving rise to different geometries and bonding possibilities.

In conclusion, hybridization is vital for understanding molecular shapes and predicting how atoms join to form stable compounds.