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? Explain.

Short answer

In an sp hybridized atom, there are two unhybridized p orbitals remaining in the valence shell, and it can form a maximum of two π bonds. It is easier to twist or rotate around a single σ bond than around a double bond (σ + π) because of the symmetrical distribution of electron density around the bond axis in σ bonds and the need to break the π bond or move the atoms out of alignment with the parallel planes of electron density during rotation in double bonds.

Step-by-step solution

Part (a) - Unhybridized p orbitals and π bonds in sp hybridized atom

To determine the number of unhybridized p orbitals in an sp hybridized atom, we first need to understand the process of hybridization. In hybridization, atomic orbitals mix to form new, hybrid orbitals. In an sp hybridized atom, one s orbital and one p orbital mixes to form two sp hybrid orbitals. The valence shell of a carbon atom has one s and three p orbitals (s, px, py, pz) before hybridization. For sp hybridization, only one of the p orbitals hybridizes with the s orbital. Let's determine the remaining p orbitals. Start with total p orbitals: 3 Subtract the p orbitals used in hybridization: 3-1=2 The atom has two unhybridized p orbitals left in the valence shell after sp hybridization. Now, let's determine the number of π bonds the atom can form. Each unhybridized p orbital can participate in the formation of one π bond. Therefore, the sp hybridized atom can form a maximum of two π bonds.

Part (b) - Twisting or rotating around a single σ bond vs a double bond (σ + π)

Two bonded atoms can experience rotation around the bond axis. Let's analyze the ease of twisting around a single σ bond versus a double bond (σ + π). In a single σ bond, the orbital overlap is symmetrical around the bond axis, and the electron density is evenly distributed in a cylindrical shape. This allows for bond rotation with relative ease, as the overlapping orbitals maintain contact with one another during rotation. Thus, it's relatively easy to twist or rotate around a single σ bond. In contrast, a double bond consists of a σ bond and a π bond. While the σ bond is still symmetrical around the bond axis, the π bond involves electron density located above and below the bond axis in parallel planes. This means that rotation around the bond axis in a double bond requires breaking the π bond or moving the atoms out of alignment with the parallel planes of electron density. As a result, it is more challenging to twist or rotate around a double bond (σ + π) compared to a single σ bond because the overlapping p orbitals in the π bond must lose contact during the rotation. This leads to a higher energy barrier for rotation in a double bond. In conclusion, it would be easier to twist or rotate around a single σ bond than around a double bond (σ + π).

Key concepts

Unhybridized p Orbitals

When delving into the realm of chemistry, particularly the structure of molecules, we encounter the term 'unhybridized p orbitals'. These orbitals are crucial in understanding molecular geometry and the type of bonds atoms can form. An unhybridized p orbital is a region of space in an atom where the likelihood of finding an electron is high and which has retained its original form and energy level during the process of hybridization.

In sp hybridization, the valence shell of an atom, let's say carbon for simplicity, starts with one s orbital and three p orbitals. After hybridization, where one s and one p orbital mix to create two equivalent sp orbitals, we find that the remaining two p orbitals are unhybridized. They are ready to play their part in chemical bonding, particularly in the formation of \(\pi\) bonds, giving molecules like ethene its planar structure and unique chemical properties. Visualizing these orbitals as perpendicular to the plane of the sp hybridized orbitals can aid in comprehending molecular geometries.

Pi (\(\pi\)) Bonds

Diving deeper into chemical bonding, \(\pi\) bonds are a key feature of molecular architecture. These bonds result from the overlap of parallel unhybridized p orbitals from two adjacent atoms. Imagine two p orbitals, one from each atom, lining up side by side above and below the plane of the atoms. Unlike \(\sigma\) bonds, \(\pi\) bonds form additional bonds between atoms already connected by a \(\sigma\) bond, creating double or triple bonds and imparting unique properties to the molecule.

For instance, in sp hybridized atoms, the two unhybridized p orbitals allow the atom to form up to two \(\pi\) bonds, each involving different p orbitals. One of the fascinating aspects of \(\pi\) bonds is their influence on a molecule's reactivity. Due to their location above and below the plane of the atoms, \(\pi\) bonds are more exposed and thus more reactive than the more protected \(\sigma\) bonds. This characteristic plays a central role in many chemical reactions, such as those in organic chemistry.

Sigma (\(\sigma\)) Bonds

To get a full picture of molecular binding, we must not overlook \(\sigma\) bonds. These are the most common type of chemical bond in molecules and form through the 'head-on' overlapping of atomic orbitals. The orbitals might be s orbitals, p orbitals, or a combination thereof, but the resultant bonding orbital wraps around the bond axis like a snug cylinder of electron density. This structure grants \(\sigma\) bonds significant strength and the freedom to allow rotating about the bond axis.

The capability of \(\sigma\) bonds to permit rotation plays a critical role in the dynamic behavior of molecules. Imagine a single bond as a swivel connecting two parts; as long as it's only a \(\sigma\) bond, the parts can twist and turn freely. However, introduce a \(\pi\) bond, and you've essentially locked the swivel – rotation now requires the energy to break and reform the \(\pi\) bond, which isn't a trivial task. This is why the movement around double and triple bonds is much more restricted compared to single bonds, thereby affecting the 3-dimensional conformation of molecules and ultimately, their chemical properties and reactions.