Question

(a) If the valence atomic orbitals of an atom are sp hybridized, how many unhybridized \(p\) orbitals remain in the valence shell? How many \(\pi\) bonds can the atom form? (b) Imagine that you could hold two atoms that are bonded together, twist them, and not change the bond length. Would it be easier to twist (rotate) around a single \(\sigma\) bond or around a double ( \(\sigma\) plus \(\pi\) ) bond, or would they be the same?

Short answer

In an sp hybridized atom, 2 unhybridized p orbitals remain, allowing the atom to form up to 2 π bonds. Rotating around a single σ bond is easier than around a double bond (σ plus π) due to the difference in bond overlap types, which permits free rotation around the σ bond axis and restricts rotation around the double bond axis.

Step-by-step solution

(a) Finding unhybridized p orbitals and possible π bonds for an sp hybridized atom

For an sp hybridized atom, one s orbital and one p orbital are mixed to form two sp hybrid orbitals. Since an atom in the second period or higher has three p orbitals in total, and one p orbital is involved in the hybridization, there are 3 - 1 = 2 unhybridized p orbitals remaining in the valence shell. Each of these unhybridized p orbitals can form a π bond with another p orbital, so the atom can form up to 2 π bonds.

(b) Comparing the ease of rotation around a single σ bond and a double bond (σ plus π)

Evaluating the ease of rotation around a single σ bond and a double bond requires us to consider the type of overlap that forms these bonds. A σ bond is formed by the end-to-end overlap of atomic orbitals. This overlap is strong but allows for rotation around the bond axis, as the atoms stay connected during the rotation. On the other hand, a π bond is formed by the parallel (side-by-side) overlap of unhybridized p orbitals, which results in regions of electron density above and below the internuclear axis. This type of overlap is weaker compared to a σ bond and does not allow for free rotation around the bond axis, as breaking the π bond would be energetically unfavorable. Considering these factors, it is easier to rotate around a single σ bond than a double bond (σ plus π).

Key concepts

Understanding Unhybridized p Orbitals

To fully grasp the behavior of electrons in an atom, it's crucial to understand what happens to the p orbitals during the process of hybridization. In sp hybridization, an atom combines one s orbital with one p orbital to create two equivalent sp hybrid orbitals. Since atoms in the second period and higher have three p orbitals in total, with one being consumed in hybridization, there are two unhybridized p orbitals remaining.

These unhybridized p orbitals are important for the formation of \( \pi \) bonds, as they maintain their perpendicular orientation to the axis of the sp hybrid orbitals. Picture the hybrid orbitals as two balloons tied at their ends, while the unhybridized p orbitals resemble two dumbbells perpendicular to the balloons. Each 'dumbbell' is capable of overlapping side-by-side with a dumbbell from another atom to form a \( \pi \) bond. This orientation is key to the bond's characteristics and how electrons are shared between atoms.

The Nature of Pi Bonds

Now, let's delve into the fascinating world of \( \pi \) bonds. These bonds are formed when the lobes of two unhybridized p orbitals align parallel to each other. When it comes to chemical bonding, the \( \pi \) bond is the 'sidekick' to the more robust \( \sigma \) bond. But don't let the 'sidekick' status fool you; \( \pi \) bonds are essential for the chemistry of double and triple bonds.

A \( \pi \) bond is less localized than a \( \sigma \) bond and exists above and below the internuclear axis—the line running through the centers of the two atoms. This distinctive electron cloud arrangement gives molecules with \( \pi \) bonds unique properties, such as the inability to rotate freely around double bonds, which affects molecular geometry and reactivity.

Sigma Bonds: The Building Blocks of Molecular Architecture

At the heart of molecular structure lies the \( \sigma \) bond, the simplest type of covalent bond. Created by head-on overlaps of atomic orbitals, \( \sigma \) bonds are the strongest type of covalent bonds due to their direct overlap. They serve as the backbone of the molecule, dictating the basic arrangement of atoms.

Unlike \( \pi \) bonds, \( \sigma \) bonds permit free rotation of the bonded atoms, which is why single-bonded atoms can twist and turn without breaking the bond. This freedom of movement has significant implications for the dynamic behavior of molecules. Imagine two dancers holding hands—their joined hands represent a \( \sigma \) bond, allowing them to spin and pivot freely. However, when a \( \pi \) bond forms alongside a \( \sigma \) bond in a double bond, that freedom is restricted. It's as if those dancers are now holding both hands overhead, creating a fixed form that can't easily twist.