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) thiocyanate ion, \(\mathrm{NCS}^{-}\) : (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

(a) For \(\mathrm{CO}_{2}\), there are 2 \(\sigma\) bonds and 2 \(\pi\) bonds. (b) For thiocyanate ion, \(\mathrm{NCS}^{-}\), there are 3 \(\sigma\) bonds and 2 \(\pi\) bonds. (c) For formaldehyde, \(\mathrm{H}_{2} \mathrm{CO}\), there are 3 \(\sigma\) bonds and 1 \(\pi\) bond. (d) For formic acid, \(\mathrm{HCOOH}\), there are 4 \(\sigma\) bonds and 1 \(\pi\) bond.

Step-by-step solution

Draw Lewis structures for each molecule/ion

The first step is to draw the Lewis structure of each molecule/ion. You can draw these structures by following Lewis dot structure rules. Here are their Lewis structures:

(a) \(\mathrm{CO}_{2}\)

Carbon has 4 valence electrons, and oxygen has 6 valence electrons each. To achieve stable octet configuration, the carbon atom forms two double bonds with the two oxygen atoms, which looks like this: \[\mathrm{O=C=O}\]

(b) Thiocyanate ion, \(\mathrm{NCS}^{-}\)

Nitrogen has 5 valence electrons, carbon has 4 valence electrons, and sulfur has 6 valence electrons. The thiocyanate ion has an extra electron due to the negative charge, making a total of 16 valence electrons for this ion. The Lewis structure for thiocyanate ion is: \[\mathrm{N=C=S^{-}}\]

(c) Formaldehyde, \(\mathrm{H}_{2}\mathrm{CO}\)

Carbon has 4 valence electrons, oxygen has 6 valence electrons, and hydrogen has 1 valence electron each. The Lewis structure for formaldehyde is: \[\mathrm{H-C=O}\] \[\mathrm{|\label{formaldehyde-H_2CO}}\]

(d) Formic acid, \(\mathrm{HCOOH}\)

Carbon has 4 valence electrons, the two oxygen atoms have 6 valence electrons each, and the two hydrogen atoms have 1 valence electron each. The Lewis structure for formic acid is: \[\mathrm{H-C-O-H}\] \[\mathrm{| |\label{Formic}\(\mathrm{=O}\)\]

Identify the single, double, and triple bonds

Now, we'll identify single, double, and triple bonds present in these structures: (a) In \(\mathrm{CO}_{2}\), there are two double bonds (C=O). (b) In thiocyanate ion, \(\mathrm{NCS}^{-}\), there is one triple bond (N≡C) and one single bond (C-S). (c) In formaldehyde, \(\mathrm{H}_{2} \mathrm{CO}\), there is one double bond (C=O) and two single bonds (C-H). (d) In formic acid, \(\mathrm{HCOOH}\), there is one double bond (C=O), one single bond (C-O), and two single bonds (O-H and C-H).

Calculate the total number of \(\sigma\) and \(\pi\) bonds in each molecule/ion

Finally, we'll use the single, double, and triple bond information to find the number of \(\sigma\) and \(\pi\) bonds: (a) \(\mathrm{CO}_{2}\): Two double bonds (C=O), with 2 \(\sigma\) bonds and 2 \(\pi\) bonds. (b) Thiocyanate ion, \(\mathrm{NCS}^{-}\): One triple bond (N≡C) and one single bond (C-S), with 3 \(\sigma\) bonds and 2 \(\pi\) bonds. (c) Formaldehyde, \(\mathrm{H}_{2} \mathrm{CO}\): One double bond (C=O) and two single bonds (C-H), with 3 \(\sigma\) bonds and 1 \(\pi\) bond. (d) Formic acid, \(\mathrm{HCOOH}\): One double bond (C=O), one single bond (C-O), and two single bonds (O-H and C-H), with 4 \(\sigma\) bonds and 1 \(\pi\) bond.

Key concepts

sigma and pi bonds

In chemistry, understanding sigma (σ) and pi (π) bonds is crucial for deciphering molecular structures and reactions. Sigma bonds are the first bonds formed between two atoms, resulting from the head-on overlap of atomic orbitals. These bonds are strong and provide significant stability to molecules.

• Sigma bonds can occur between s-s, s-p, or p-p orbitals.
• They are characterized by a cylindrical symmetry around the bond axis.

Pi bonds, on the other hand, are formed after sigma bonds and occur by the side-by-side overlap of p-orbitals.

• Pi bonds are present in double and triple bonds alongside sigma bonds.
• They offer less stability and are weaker than sigma bonds due to the lateral overlap.

Understanding the presence of sigma and pi bonds helps in determining how molecules interact under various conditions. For instance, molecules with more pi bonds can participate in more reactive and complex reactions like electrophilic additions.

valence electrons

Valence electrons are the outermost electrons of an atom that participate in chemical bonding. These electrons determine the atom's ability to form bonds and are critical for understanding the structure of molecules.

• They are often represented in Lewis structures, which depict all valence electrons around the atoms in a molecule.
• The number of valence electrons can be found using an element's group number in the periodic table. For example, carbon, in group 14, has 4 valence electrons.

Valence electrons guide the formation of both covalent and ionic bonds by enabling atoms to achieve more stable electronic configurations through sharing, donating, or accepting electrons. By knowing how many valence electrons are available, you can predict the types of bonds that will form, whether single, double, or triple, and even infer the molecule's geometry.

molecular geometry

Molecular geometry refers to the three-dimensional arrangement of atoms in a molecule. This concept is essential because the shape of a molecule influences its physical and chemical properties.

• The VSEPR (Valence Shell Electron Pair Repulsion) theory is often used to predict molecular geometry.
• This theory asserts that electron pairs around a central atom arrange themselves to minimize repulsion, adopting specific geometrical shapes like linear, trigonal planar, tetrahedral, etc.

For example, in carbon dioxide ( CO_2 ), the molecule adopts a linear geometry because there are no lone pairs and the double bonds oppose each other at 180 degrees.
Similarly, understanding a molecule's geometry can provide insights into its reactivity, polarity, and interactions with other molecules. This knowledge is crucial when predicting molecular behavior in chemical reactions.

covalent bonding

Covalent bonding occurs when atoms share pairs of electrons to achieve stable electronic configurations, like the noble gases. This type of bond is prevalent in organic molecules and is one of the strongest forms of chemical bonding.

• In a covalent bond, each atom contributes one or more electrons from its valence shell.
• Covalent bonds can form between atoms of the same element or different elements.

The resulting molecules can vary in complexity, from simple diatomic molecules like oxygen ( O_2 ) to more complex organic compounds like formaldehyde ( H_2CO ).
Covalent bonds lead to the formation of discrete molecules rather than a lattice structure, which is typical in ionic compounds. Understanding covalent bonding not only reveals how molecules are formed but also predicts properties such as boiling and melting points, electrical conductivity, and solubility in various solvents. Studying these interactions helps chemists synthesize new materials and understand biological processes.