Question

Total possible acyclic hydrocarbon alkane with minimum number of carbon which have all \(1^{\circ}, 2^{\circ}, 3^{\circ}\) and \(4^{\circ}\) carbon is (A) 1 (B) 2 (C) 3 (D) 5

Short answer

In the smallest acyclic alkane containing carbon atoms with all types of hybridization (primary, secondary, tertiary, and quaternary), there are a total of 3 carbon atoms. The structure is: ``` C / C-C-C \ C ``` with a 4° carbon in the center, flanked by two 3° carbons, and the top and bottom carbons being 2° and 1°, respectively. Answer: \( \boxed{3} \).

Step-by-step solution

Find a carbon atom with 4° hybridization

To form a 4° (quaternary) carbon, it must be connected to four other carbon atoms. Since this is an alkane, the connections are single bonds. So, we start by drawing a carbon atom surrounded by four other carbon atoms as shown below: ``` C / | \ C-C | C \ | / C ``` The central carbon atom is 4°.

Find carbon atoms with 3°, 2°, and 1° hybridization

Now, we should connect the other carbon atoms in such a way that we have at least one 3°, one 2°, and one 1° carbon atom. Following the rules for hybridization, let's connect the carbon atoms: ``` C / C-C-C C \ C ``` Here is the hybridization for each carbon atom: - Central carbon (C2): 4° - Carbon to the left (C1) and right (C3) of the central carbon: 3° - Top carbon (C4): 2° - Bottom carbon (C5): 1° Thus, we have now found a single structure (C) that has one carbon atom of each hybridization degree (1°, 2°, 3°, and 4°). Answer: (C) 3

Key concepts

Carbon Hybridization

In organic chemistry, the concept of carbon hybridization refers to the mixing of atomic orbitals within carbon atoms to form new hybrid orbitals. These orbitals determine the molecular geometry and bonding properties of the carbon atoms. A carbon atom can form single, double, or triple bonds, depending on its hybridization state. For alkanes, single bonds are formed which are described by the sp³ hybridization.
sp³ hybridization means that one s orbital mixes with three p orbitals to create four equivalent sp³ hybrid orbitals. These orbitals are oriented in a tetrahedral shape, allowing alkanes to form stable and versatile structures.
Carbon atoms with different hybridization states hold differing roles in molecular structures, which is impactful in determining the chemical and physical properties of the compounds.

Quaternary Carbon

A quaternary carbon is a carbon atom that is bonded to four other carbon atoms. In alkanes, a quaternary carbon holds a special position where it serves as a connector for multiple carbon chains or rings, playing a central role in branching.

• It's often responsible for creating complex structures as it allows for a significant amount of branching in organic molecules.
• The ability of carbon to attach to four other carbons gives rise to diversity in organic compounds. This makes quaternary carbons especially important in forming highly branched or compact structures.

Its role can lead to special features in molecules, influencing the physical properties like boiling and melting points.

Carbon Connectivity

Carbon connectivity describes how carbon atoms are linked to each other within a molecule. This connectivity is crucial in defining the skeleton or backbone of organic compounds, such as alkanes.
Carbon atoms can be categorized based on their connectivity:

• Primary (1°) carbon is attached to only one other carbon atom.
• Secondary (2°) carbon is connected to two other carbon atoms.
• Tertiary (3°) carbon is attached to three other carbons.
• Quaternary (4°) carbon, as discussed, connects to four other carbon atoms.

For alkanes to possess varied types of carbon hybridization, they need a complex web of connectivity to include primary, secondary, tertiary, and quaternary carbons.

Organic Chemistry Problems

When faced with organic chemistry problems, students often need to visualize complex molecular structures and deduce connectivity. Problems like creating specific alkanes that exhibit multiple types of carbon provide practice in understanding molecular geometry and hybridization.
These exercises commonly involve:

• Identifying and drawing molecular structures.
• Determining hybridization states for each carbon atom.
• Recognizing connectivity and functional roles of different carbon atoms in a molecule.

Understanding these problems enhances problem-solving skills and deepens comprehension of organic chemistry fundamentals by challenging students to apply concepts learned in theoretical sessions.