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,\((\mathrm{CN})_{2} ;(\mathbf{c})\) formaldehyde, \(\mathrm{H}_{2} \mathrm{CO}\) (d) formic acid, HCOOH, which has one H and two O atoms attached to \(\mathrm{C}\) .

Short answer

(a) CO2: σ bonds = 2 π bonds = 2 (b) (CN)2: σ bonds = 3 π bonds = 4 (c) H2CO: σ bonds = 3 π bonds = 1 (d) HCOOH: σ bonds = 4 π bonds = 1

Step-by-step solution

(a) CO2 (Carbon dioxide)

: In CO2, carbon has 4 valence electrons and each oxygen atom has 6 valence electrons. 1. Draw the Lewis structure: Carbon is in the center with a double bond to each oxygen atom. 2. Identify the σ and π bonds: Each double bond contains one σ bond and one π bond. There are two double bonds in total. σ bonds = 2 π bonds = 2

(b) (CN)2 (Cyanogen)

: In (CN)2, each carbon has 4 valence electrons, and each nitrogen atom has 5 valence electrons. 1. Draw the Lewis structure: Each carbon atom is triple-bonded to a nitrogen atom, and the two cyanide units are connected by a single bond. 2. Identify the σ and π bonds: - In each triple bond, there is one σ bond and two π bonds. There are two triple bonds in total. - One single bond between the cyanide units is considered a σ bond. σ bonds = 1 (single bond) + 2 (triple bonds) = 3 π bonds = 4 (from the triple bonds)

(c) H2CO (Formaldehyde)

: In H2CO, carbon has 4 valence electrons, oxygen has 6 valence electrons, and each hydrogen atom has 1 valence electron. 1. Draw the Lewis structure: The carbon atom is in the center, double bonded to the oxygen atom and single bonded to two hydrogen atoms. 2. Identify the σ and π bonds: - In the double bond between carbon and oxygen, there is one σ bond and one π bond. - Both hydrogen atoms are bonded to the carbon atom by a single bond - two σ bonds. σ bonds = 2 (from hydrogen atoms) + 1 (from the double bond) = 3 π bonds = 1 (from the double bond)

(d) HCOOH (Formic acid)

: In HCOOH, carbon has 4 valence electrons, oxygen has 6 valence electrons, and hydrogen has 1 valence electron. 1. Draw the Lewis structure: The carbon atom is in the center, double bonded to one oxygen atom, single bonded to another oxygen atom, and single bonded to a hydrogen atom. The single bonded oxygen atom is also bonded to another hydrogen atom. 2. Identify the σ and π bonds: - In the double bond between carbon and oxygen, there is one σ bond and one π bond. - For the single bonds (C-O, C-H, and O-H), there are 3 σ bonds. σ bonds = 3 (from single bonds) + 1 (from the double bond) = 4 π bonds = 1 (from the double bond)

Key concepts

Sigma Bonds

Sigma (\( \sigma \)) bonds are the strongest type of covalent bonds. They form when two atomic orbitals overlap directly between bonding atoms. This type of bonding allows for the greatest overlap, which makes the \( \sigma \) bond very stable. In molecular structures, every single bond is a \( \sigma \) bond. Additionally, in multiple bonds like double or triple bonds, one of the components is always a \( \sigma \) bond. Here are some key features of \( \sigma \) bonds:

• They involve head-on overlapping of orbitals.
• They allow free rotation of the bonded atoms around the bond axis, which influences molecular shapes.
• Present in any type of bond (single, double, triple).

Understanding \( \sigma \) bonds is crucial for predicting how molecules will interact, their shape, and properties.

Pi Bonds

Pi (\( \pi \)) bonds occur when two orbitals overlap sideways. This type of bond is typically found in double and triple bonds, in addition to a \( \sigma \) bond. Unlike \( \sigma \) bonds, \( \pi \) bonds do not allow free rotation of the atoms involved. Here are some core aspects of \( \pi \) bonds:

• They involve lateral or side-to-side overlapping of orbitals.
• They do not permit free rotation around the bond axis, resulting in fixed structures.
• Each double bond consists of one \( \pi \) bond, and each triple bond consists of two \( \pi \) bonds.

Pi bonds contribute to the reactivity and rigidity of molecules because of their structure. They are essential for understanding organic reactions and the strengths of various chemical bonds.

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms in a molecule. It is determined by the number and arrangement of \( \sigma \) and \( \pi \) bonds, as well as lone pairs of electrons. Here's why molecular geometry is so significant:

• It affects the physical and chemical properties of the molecule, including polarity and reactivity.
• Molecular geometry can influence the molecule's boiling and melting points, solubility, and other physical properties.
• VSEPR (Valence Shell Electron Pair Repulsion) theory is often used to predict molecular geometry. It states that electron pairs will arrange themselves as far apart as possible to minimize repulsion.

Grasping molecular geometry helps predict how a molecule will behave in a given environment, which is vital for chemistry students.

Valence Electrons

Valence electrons are the outermost electrons in an atom. They play a key role in bond formation and define an atom's chemical properties. When constructing a Lewis structure, knowing the number of valence electrons helps in predicting molecule stability and behavior. Key points about valence electrons include:

• They determine how atoms bond with each other.
• Atoms seek to have complete outer shells, hence they gain, lose, or share electrons to achieve this condition.
• The number of valence electrons can usually be determined by an element's group number on the periodic table.

A good understanding of valence electrons paves the way for predicting how atoms will interact and the types of bonds they will form, which is essential for creating accurate Lewis structures and understanding chemical reactions.