For each of the following line-angle drawings, 
(i) give the number of carbons, 
(ii) label the carbons, 
(iii) tell how many hydrogens are on each carbon, and 
(iv) draw the hybrid structural formula.
(d)

Verified step by step guidance

1. Step 1: Count the number of carbons in the molecule. Each vertex in the line-angle drawing represents a carbon atom, and each line represents a bond. Include all carbons in the main chain and any branching groups.
2. Step 2: Label each carbon atom sequentially, starting from one end of the molecule. Assign numbers to each carbon in the main chain and label branching carbons accordingly.
3. Step 3: Determine the number of hydrogens attached to each carbon. Recall that carbon forms four bonds total, so subtract the number of bonds to other atoms (including double or triple bonds) from four to find the number of hydrogens.
4. Step 4: Draw the hybrid structural formula. Replace the line-angle drawing with explicit representations of all carbons, hydrogens, and bonds. Show all single, double, and triple bonds clearly.
5. Step 5: Double-check your work to ensure all carbons and hydrogens are accounted for, and the hybrid structural formula matches the original line-angle drawing.

Key Concepts

Line-Angle Drawings

Line-angle drawings, also known as skeletal structures, are a simplified way to represent organic molecules. In these drawings, vertices represent carbon atoms, and lines represent bonds between them. Hydrogen atoms attached to carbons are usually omitted for clarity, as they are implied by the tetravalency of carbon. Understanding how to interpret these drawings is essential for identifying the structure and composition of organic compounds.

Hybridization

Hybridization is the concept that describes the mixing of atomic orbitals to form new hybrid orbitals, which can explain the geometry of molecular bonding. In organic chemistry, common types include sp3, sp2, and sp hybridization, corresponding to different bonding scenarios and molecular shapes. Recognizing the hybridization of carbon atoms helps in determining the number of hydrogen atoms attached to each carbon and the overall structure of the molecule.

Valency and Hydrogen Count

Valency refers to the ability of an atom to bond with other atoms, which is particularly important for carbon, as it typically forms four bonds. The number of hydrogen atoms attached to each carbon atom can be deduced from its valency and the number of bonds it forms with other atoms. For example, a carbon with four single bonds (sp3 hybridized) will have no hydrogen atoms attached, while a carbon with three single bonds will have one hydrogen atom.