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?

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: \[ \text{C}_8\text{H}_6\text{N}_2\text{O}_2 \]

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.

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.