Question

From their Lewis structures, determine the number of \(\sigma\) and \(\pi\) bonds in each of the following molecules or ions: (a) \(\mathrm{CO}_{2}\); (b) cyanogen, \((\mathrm{CN})_{2} ;\) (c) formaldehyde, \(\mathrm{H}_{2} \mathrm{CO}\); (d) formic acid, \(\mathrm{HCOOH}\), which has one \(\mathrm{H}\) and two \(\mathrm{O}\) atoms attached to \(\mathrm{C}\).

Short answer

The number of \(\sigma\) and \(\pi\) bonds in the given molecules or ions are as follows: (a) \(\mathrm{CO}_{2}\): 2 \(\sigma\) bonds and 2 \(\pi\) bonds (b) Cyanogen, \((\mathrm{CN})_{2}\): 3 \(\sigma\) bonds and 4 \(\pi\) bonds (c) Formaldehyde, \(\mathrm{H}_{2} \mathrm{CO}\): 3 \(\sigma\) bonds and 2 \(\pi\) bonds (d) Formic acid, \(\mathrm{HCOOH}\): 4 \(\sigma\) bonds and 2 \(\pi\) bonds

Step-by-step solution

Draw the Lewis structures of the molecules or ions.

: (a) \(\mathrm{CO}_{2}\): The central atom is C and has two O atoms bonded to it. The Lewis structure will represent a double bond between the central C and each O atom. (b) Cyanogen, \((\mathrm{CN})_{2}\): The cyanogen molecule consists of a carbon atom singly bonded to a nitrogen, which is then triple bonded to another nitrogen, that is singly bonded to another carbon atom. (c) Formaldehyde, \(\mathrm{H}_{2} \mathrm{CO}\): The central atom is C and has an O atom and two H atoms bonded to it. The Lewis structure will represent a double bond between the central C and O atom, and a single bond between the central C and each H atom. (d) Formic acid, \(\mathrm{HCOOH}\): The central atom is C, which has an H, O, and an OH group attached to it. The Lewis structure will represent a double bond between the central C and O atom, a single bond between the central C and the hydroxyl O, and a single bond between C and H.

Count the σ and π bonds in each molecule/ion.

: (a) \(\mathrm{CO}_{2}\): In a double bond, there is one \(\sigma\) bond and one \(\pi\) bond. Therefore, \(\mathrm{CO}_{2}\) has 2 (\(\sigma\) bonds) + 2 (\(\pi\) bonds) = 4 bonds. (b) Cyanogen, \((\mathrm{CN})_{2}\): In a single bond, there is one \(\sigma\) bond, and in a triple bond, there is one \(\sigma\) bond and two \(\pi\) bonds. The cyanogen molecule has 3 (\(\sigma\) bonds) + 4 (\(\pi\) bonds) = 7 total bonds. (c) Formaldehyde, \(\mathrm{H}_{2} \mathrm{CO}\): The Lewis structure of formaldehyde has 3 (\(\sigma\) bonds) + 2 (\(\pi\) bonds) = 5 total bonds. (d) Formic acid, \(\mathrm{HCOOH}\): The Lewis structure of formic acid has 4 (\(\sigma\) bonds) + 2 (\(\pi\) bonds) = 6 total bonds. In summary: (a) \(\mathrm{CO}_{2}\): 2 \(\sigma\) bonds and 2 \(\pi\) bonds (b) Cyanogen, \((\mathrm{CN})_{2}\): 3 \(\sigma\) bonds and 4 \(\pi\) bonds (c) Formaldehyde, \(\mathrm{H}_{2} \mathrm{CO}\): 3 \(\sigma\) bonds and 2 \(\pi\) bonds (d) Formic acid, \(\mathrm{HCOOH}\): 4 \(\sigma\) bonds and 2 \(\pi\) bonds

Key concepts

Sigma Bonds

Sigma bonds, often represented as \( \sigma \) bonds, are a fundamental component to understanding chemical bonding. These bonds form the backbone of molecular structures. A sigma bond is the strongest type of covalent bond and occurs when two atomic orbitals overlap head-on. This overlap can occur between:

• Two s-orbitals
• One s-orbital and one p-orbital
• Two p-orbitals, provided they align end-to-end

Sigma bonds are characterized by this head-on overlap, which allows for free rotation around the bond axis. This is a key distinction from other types of bonds. Every single bond in a molecule is, at its core, a sigma bond. For instance, in molecules like formic acid \( \text{HCOOH} \) or formaldehyde \( \text{H}_2\text{CO} \), each C-H and C-O single bond is a sigma bond. Each initial double or triple bond contains only one sigma bond, the rest are pi bonds.

Pi Bonds

Pi bonds \( \pi \) are another critical type of covalent bond that adds depth to molecular bonding. Unlike sigma bonds, pi bonds result from the side-by-side overlap of p-orbitals. Because this type of overlap occurs above and below the bond axis, pi bonds restrict the rotation around the bond, which can influence the molecular shape and properties.To understand pi bonds, it's essential to see them in the context of double and triple bonds:

• Double bonds consist of one sigma bond and one pi bond.
• Triple bonds include one sigma bond and two pi bonds.

These bonds add additional layers of electron sharing and influence the molecule's reactivity and stability. For example, in carbon dioxide (\( \text{CO}_2 \)), the double bonds between the carbon and oxygen include both a sigma and a pi bond.

Molecular Geometry

Molecular geometry is the three-dimensional arrangement of atoms within a molecule. It plays a crucial role in determining the physical and chemical properties of a substance. The geometry is largely determined by the number of electron pairs around the central atom, both bonding and non-bonding.Common geometries include:

• Linear
• Trigonal planar
• Tetrahedral
• Bent
• Trigonal bipyramidal
• Octahedral

Using the VSEPR (Valence Shell Electron Pair Repulsion) model, you can predict the geometry by considering the electron repulsions. For example, carbon dioxide \( \text{CO}_2 \) is linear due to two double bonds causing minimal electron pair repulsion. In contrast, formaldehyde \( \text{H}_2\text{CO} \) adopts a trigonal planar shape due to the presence of one double bond and two single bonds.

Covalent Bonding

Covalent bonding is essential in the formation of molecules by the sharing of electron pairs between atoms. This type of bonding arises when atoms, usually non-metals, have similar electronegativities, making it energetically favorable for them to share electrons equally.The shared electron pair constitutes the covalent bond, which can be either polar or non-polar depending on the atoms involved:

• Polar covalent bonds occur between atoms with different electronegativities, leading to an unequal sharing of electrons.
• Non-polar covalent bonds occur between atoms with similar electronegativities, leading to equal sharing of electrons.

Understanding covalent bonding is crucial for predicting molecular properties such as melting and boiling points, solubility, and reactivity. For example, in formic acid \( \text{HCOOH} \), the covalent bonds between carbon, hydrogen, and oxygen determine the molecule's acidity and solubility.