Question

Indigo is the dye used in coloring blue jeans. The term navy blue is derived from the use of indigo to dye British naval uniforms in the eighteenth century. The structure of the indigo molecule is a. How many \(\sigma\) bonds and \(\pi\) bonds exist in the molecule? b. What hybrid orbitals are used by the carbon atoms in the indigo molecule?

Short answer

In the indigo molecule, there are 18 \(\sigma\) bonds and 4 \(\pi\) bonds. The hybrid orbitals used by the carbon atoms in the molecule are \(sp^3\) hybridized for single bonds and \(sp^2\) hybridized for double bonds.

Step-by-step solution

Identify the indigo molecule structure

The structure of the indigo molecule can be found in various sources, like scientific articles, textbooks or online resources. For this exercise, we will assume that the student has access to the indigo molecule structure. If you don't have access to the structure, you can search for it online. The indigo molecule has the following structure: \[ \text{C}_8\text{H}_6\text{N}_2\text{O}_2 \]

Counting sigma (\(\sigma\)) and pi (\(\pi\)) bonds

Now that we have the structure of the indigo molecule, count the total number of single, double, and triple bonds present. In the indigo molecule, there are: - 14 single bonds (C-C, C-H, and C-N) - 4 double bonds (C=C and C=O) - No triple bonds Sigma (\(\sigma\)) bonds are present in all single, double, and triple bonds, while pi (\(\pi\)) bonds are only present in double and triple bonds. There is one \(\pi\) bond in a double bond and two \(\pi\) bonds in a triple bond. The number of sigma (\(\sigma\)) bonds in the indigo molecule is: 14 (single bonds) + 4 (double bonds) = 18 \(\sigma\) bonds The number of pi (\(\pi\)) bonds in the indigo molecule is: 4 (double bonds) = 4 \(\pi\) bonds So, there are 18 \(\sigma\) bonds and 4 \(\pi\) bonds in the indigo molecule.

Identify the hybrid orbitals of the carbon atoms

Next, we need to identify the hybrid orbitals used by the carbon atoms in the indigo molecule. We'll consider each type of bond present in the molecule. 1. Single bonds between carbon atoms (C-C): These carbon atoms are \(sp^3\) hybridized. 2. Double bonds between carbon atoms (C=C): These carbon atoms are \(sp^2\) hybridized. 3. Triple bonds between carbon atoms: There are no triple bonds in the indigo molecule. Summarizing, the hybrid orbitals used by the carbon atoms in the indigo molecule are \(sp^3\) hybridized for single bonds and \(sp^2\) hybridized for double bonds.

Key concepts

Indigo Molecule

The indigo molecule is a famous organic compound widely known for its vibrant blue color. It has been used as a dye for centuries, notably for coloring denim fabric and British naval uniforms in the eighteenth century. The structure of the indigo molecule is represented by the chemical formula \( \text{C}_8\text{H}_6\text{N}_2\text{O}_2 \). This formula indicates that the molecule comprises eight carbon atoms, six hydrogen atoms, two nitrogen atoms, and two oxygen atoms.

Organic chemistry allows us to delve into the detailed structure of indigo to understand its bonding and properties. The molecule consists of a backbone of carbon atoms forming a series of rings. Each ring in the indigo molecule contributes to its stability and color characteristics through a complex arrangement of bonds. These bonds can be classified into sigma and pi types, which is crucial for understanding how molecules behave at an atomic level.

Sigma and Pi Bonds

In organic molecules, such as indigo, the types of bonds between atoms define much of their chemistry. Sigma (\( \sigma \)) bonds are the strongest type of covalent bond and form because of the head-on overlap of atomic orbitals. In the indigo molecule, sigma bonds are present in all types of bonding – single (C-C, C-H, C-N), double (C=C, C=O), and theoretically triple bonds.

There are 18 sigma bonds in the indigo molecule: 14 from the single bonds and 4 from the double bonds. Sigma bonds allow the molecule to maintain its stable structure.

Pi (\( \pi \)) bonds arise from the side-to-side overlap of orbitals and occur in multiple bonds, namely double and triple bonds. In the indigo molecule, pi bonds only appear in its 4 double bonds, adding up to a total of 4 pi bonds. These pi bonds are responsible for the planarity and the colorful properties of the molecule, due to the delocalized electrons they accommodate. These delocalized electrons play a significant role in the molecule's interaction with light, giving indigo its distinctive blue color.

Hybrid Orbitals

Hybrid orbitals are a concept in chemistry that describes the combination of standard atomic orbitals into new hybrid orbitals suitable for the pairing of electrons to form chemical bonds. In the indigo molecule, carbon atoms utilize different hybridizations based on the types of bonds they form.

For single bonds, such as C-C in the molecule, each carbon atom is \( sp^3 \) hybridized. This hybridization involves one s orbital and three p orbitals mixing to form four equivalent \( sp^3 \) orbitals, shaped tetrahedrally.

However, when it comes to double bonds, such as the C=C in the indigo structure, the carbon atoms are \( sp^2 \) hybridized. This involves the mixing of one s orbital and two p orbitals, creating three equivalent \( sp^2 \) orbitals that are typically planar, with one remaining p orbital forming the pi bond.

Understanding these hybridizations helps explain the geometry and properties of organic molecules like indigo, affecting how they interact in chemical reactions and with light.