Question

(a) Draw a picture showing how two \(p\) orbitals on two different atoms can be combined to make a sigma bond. (b) Sketch a \(\pi\) bond that is constructed from \(p\) orbitals. (c) Which is generally stronger, a \(\sigma\) bond or a \(\pi\) bond? Explain. (d) Can two s orbitals make a \(\pi\) bond? Explain.

Short answer

(a) The σ bond is formed by the end-to-end overlapping of two p orbitals on two different atoms with their axes aligned along the internuclear axis. \( \begin{tikzpicture}\draw (-1,0) ellipse (0.5 and 1);\draw (1,0) ellipse (0.5 and 1);\node at (-1,1.5) {Atom A};\node at (1,1.5) {Atom B};\draw (-0.5,0) -- (0.5,0);\node[label=right:\(+\sigma\)] at (0,0.75) {};\end{tikzpicture} \) (b) A π bond is formed by the side-by-side overlapping of two p orbitals with their axes parallel to each other. \( \begin{tikzpicture}\draw (-1,-1) ellipse (0.5 and 1);\draw (1,-1) ellipse (0.5 and 1);\draw (-1,1) ellipse (0.5 and 1);\draw (1,1) ellipse (0.5 and 1);\node (A) at (-1, 2.5) {Atom A};\node (B) at (1, 2.5) {Atom B};\draw (A) -- (B);\node[label=below:\(+\pi\)] at (-1, 0) {};\node[label=below:\(+\pi\)] at (1, 0) {};\end{tikzpicture} \) (c) Generally, a σ bond is stronger than a π bond due to greater overlapping of orbitals and more effective electron shielding. (d) No, two s orbitals cannot make a π bond as they lack a defined axis and can only form σ bonds through direct overlapping of their electron clouds between the nuclei of the two atoms.

Step-by-step solution

(a) Drawing σ bond from p orbitals

To draw a sigma bond formed by two p orbitals, we must show the overlapping of the two p orbitals end-to-end. Let's consider two p orbitals on two different atoms, where their axes are aligned along the internuclear axis (the line connecting the centers of the two atoms). 1. Draw two p orbitals in parallel with their axes aligned perpendicular to the internuclear axis. 2. The p orbitals overlap end-to-end, forming a bond between the two atoms. 3. Label the bond as a σ bond. Here is a diagram illustrating this process: [latex] \begin{tikzpicture} \draw (-1,0) ellipse (0.5 and 1); \draw (1,0) ellipse (0.5 and 1); \node at (-1,1.5) {Atom A}; \node at (1,1.5) {Atom B}; \draw (-0.5,0) -- (0.5,0); \node[label=right:\(+\sigma\)] at (0,0.75) {}; \end{tikzpicture} [/latex]

(b) Sketching a π bond from p orbitals

To illustrate a pi bond formed by two p orbitals, we must show the overlap of the p orbitals side-by-side. Let's again consider two p orbitals on two different atoms, but now the axes are not aligned along the internuclear axis. 1. Draw two p orbitals with their axes parallel to each other and not overlapping. 2. The p orbitals overlap side-by-side, forming two regions (above and below the plane) of electron density. 3. Label the bond as a π bond. Here is a diagram illustrating the π bond: [latex] \begin{tikzpicture} \draw (-1,-1) ellipse (0.5 and 1); \draw (1,-1) ellipse (0.5 and 1); \draw (-1,1) ellipse (0.5 and 1); \draw (1,1) ellipse (0.5 and 1); \node (A) at (-1, 2.5) {Atom A}; \node (B) at (1, 2.5) {Atom B}; \draw (A) -- (B); \node[label=below:\(+\pi\)] at (-1, 0) {}; \node[label=below:\(+\pi\)] at (1, 0) {}; \end{tikzpicture} [/latex]

(c) Comparing σ bonds and π bonds strengths

Generally, a σ bond is stronger than a π bond. This is because the σ bond has greater overlapping of orbitals, resulting in a more stable bond. The electrons in a σ bond are also more localized between the two nuclei, leading to stronger and more effective internuclear electron shielding and thereby further stabilizing the bond. On the other hand, π bonds are formed with a weaker side-by-side interaction between atomic orbitals, leading to less effective electron shielding.

(d) Can two s orbitals make a π bond? Explanation

No, two s orbitals cannot make a π bond. This is because s orbitals are spherically symmetrical around the nucleus and do not possess a defined axis. The formation of π bonds occurs when p orbitals interact side-by-side (parallely) creating electron density above and below the internuclear axis. Since s orbitals lack a defined axis, they cannot form the required side-by-side overlapping necessary for creating a π bond. These s orbitals can only form σ bonds through the overlapping of their electron clouds directly between the nuclei of the two atoms.

Key concepts

Sigma Bond

Sigma (\( \sigma \)) bonds are the strongest type of covalent chemical bond. In these types of bonds, the overlapping occurs end-to-end, allowing electron density to be concentrated in a region directly between the nuclei of the bonding atoms. This is referred to as head-on overlap of atomic orbitals. For \( p \) orbitals, a sigma bond forms when these orbitals align along the internuclear axis, lending to a stable configuration.

• The overlap is extensive, which makes sigma bonds much stronger.
• Found typically in single bonds, sigma bonds allow for the free rotation of bonded atoms, as their electron density is cylindrically symmetrical around the internuclear axis.
• This type of overlap is also common when bonding involves \( s \) orbitals, either alone or with combination of \( p \) orbitals.

By having such robust electron shielding between the two nuclei, sigma bonds provide the crucial backbone stability to molecular structures.

Pi Bond

Pi (\( \pi \)) bonds arise from the side-by-side overlap of atomic \( p \) orbitals. Unlike sigma bonds, the \( \pi \) bonds are not aligned on the internuclear axis. This type of bonding creates two distinct regions of electron density above and below the plane of the nuclei. Because of its unique configuration, pi bonds do not approach the strength of sigma bonds.

• Pi bonds contribute to the double or triple bonds in conjunction with sigma bonds. For example, in a double bond, one is a sigma bond, and the other is a pi bond.
• Due to their side-to-side nature, pi bonds restrict the rotation about the bond axis, adding rigidity to the molecule.
• The electron density is more dispersed and not centrally located, resulting in weaker bonds and increased reactive characteristics.

As a result, molecules with \( \pi \) bonds often engage more readily in chemical reactions compared to those with only \( \sigma \) bonds.

Orbital Overlapping

Orbital overlapping is a fundamental concept in understanding chemical bonding. The method in which atomic orbitals interact determines the type and strength of the resulting bond.

• Head-on overlap results in sigma bonds, maximizing electron density between the atoms.
• Side-by-side overlap produces pi bonds, which have electron densities above and below the bonding atoms.
• Effective overlapping requires compatible energy levels and spatial orientations of atomic orbitals.

Understanding how orbitals overlap helps explain why certain bonds are stronger or weaker and predicts the shapes and rotations within molecules. It becomes particularly useful when discussing bond angles and the overall geometry of molecules.

P Orbitals

P orbitals are crucial in chemistry for forming both sigma and pi bonds. A \( p \) orbital is dumbbell-shaped and oriented around one of three axes: \( x \), \( y \), or \( z \). This orientation gives the \( p \) orbital unique properties that differentiate it from other orbitals like \( s \) or \( d \).

• P orbitals can form sigma bonds through end-to-end overlap, aligning on the same axis as the nuclei.
• They create pi bonds by overlapping side-by-side with other \( p \) orbitals across different atoms.
• The ability to form multiple overlapping zones is pivotal in creating delocalized electron systems, contributing to complex bonding scenarios like those in aromatic compounds.

The versatility of \( p \) orbitals in bonding makes them instrumental in building a wide range of molecular structures from simple to intricate.