Problem 4 - Advanced Problems in Organic Chemistry for Competitive Examinations

Question

Compare the hybridisation of the central carbon atoms in carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) and allene \(\left(\mathrm{H}_{2} \mathrm{C}=\mathrm{C}=\mathrm{CH}_{2}\right) .\) Which statement is correct? (a) The hybridisation types of these two carbons cannot be compared because of large electronegativity difference between carbon and oxygen in \(\mathrm{CO}_{2}\), that does not exist in allene. (b) The hybridisation of carbon in \(\mathrm{CO}_{2}\) cannot be determined, because the lone electron pairs on oxygen do not allow for angle measurements that are necessary to determine the hybridisation involved. (c) \(\operatorname{In} \mathrm{CO}_{2}\) the carbon is sp \(^{2}\) hybridised, but in allene the central carbon is sp hybridised. (d) In \(\mathrm{CO}_{2}\) the carbon is sp hybridised but in allene the central carbon is sp hybridised.

Step-by-Step Solution

Answer

(d) In CO2, the carbon is sp hybridised; in allene, the central carbon is sp hybridised.

Step 1: Determine Hybridization of Carbon in CO2

In CO2, the central carbon is double-bonded to each of the two oxygen atoms. Each double bond counts as one region of electron density, totaling two regions. Thus, the carbon in CO2 has 2 regions of electron density, indicating sp hybridization (since sp hybridized orbitals can form linear 180-degree angle structures, as seen in CO2).

Step 2: Analyze Hybridization of Central Carbon in Allene

Allene ( ext{H}_2 ext{C}= ext{C}= ext{CH}_2) contains three carbon atoms. The central carbon is double-bonded to the two outer carbons, creating two regions of electron density. In allene, the central carbon needs sp hybrid orbitals for making two sigma bonds and maintaining the linear arrangement of these two double bonds, again indicating sp hybridization.

Step 3: Compare and Conclude Hybridization Types

Both central carbons in CO2 and allene have sp hybridization. Each has two areas of electron density resulting in linear geometries, unlike the other option descriptions which state incorrect hybridization types or irrelevant factors. Therefore, the hybrid states are both sp and comparable, contrary to options a, b, and c.

Key Concepts

sp Hybridization

In organic chemistry, the concept of hybridization helps us understand the shapes and bonding of molecules. Specifically, sp hybridization is a type of chemical bonding where one s orbital and one p orbital from an atom combine to form two equivalent hybrid orbitals. This typically occurs in molecules where the central atom forms linear geometries.
For an atom to be sp hybridized, it generally has two regions of electron density around it. These regions could be double bonds or lone pairs of electrons. In the case of carbon dioxide (\( \text{CO}_2 \)), each carbon is bonded with two oxygen atoms via double bonds. Each double bond accounts for one area of electron density. As a result, there are two regions of electron density around the carbon, necessitating sp hybridization.
On the other hand, consider the molecule allene (\( \text{H}_2\text{C}=\text{C}=\text{CH}_2 \)), where the central carbon atom also forms two double bonds, one with each adjacent carbon. This again indicates the presence of two electron density regions, leading to the conclusion that the central carbon in allene is sp hybridized.

Molecular Geometry

Molecular geometry is key to understanding the spatial arrangement of atoms within a molecule and can affect the molecule’s properties significantly. The geometry of a molecule is primarily determined by the type of hybridization and the number of electron density regions.
In the case of sp hybridization, the resulting molecular geometry is linear. This is because the sp hybrid orbitals are arranged 180 degrees apart, allowing the molecule to assume a straight-line shape. This is observed in both carbon dioxide and allene:

• In \( \text{CO}_2 \), the linear shape is a result of the central carbon atom forming double bonds with two oxygens, aligning the atoms in a straight line.
• Similarly, in allene, the central carbon’s sp hybridization forces the double bonded carbons to align linearly, influencing the overall spatial orientation.

Understanding the linear geometry in these molecules helps predict their physical properties and behavior in chemical reactions.

Electron Density Regions

Electron density regions around a central atom are areas where electrons are most likely to be found. They include bonds (single, double, or triple), as well as lone pairs of electrons. The count and arrangement of these regions help determine the hybridization of the atom, and consequently, the molecular geometry.
In carbon dioxide, the carbon atom forms two double bonds, each representing a single electron density region. Consequently, these two regions require sp hybridization to form the molecule’s linear structure.
Similarly, the central carbon in allene also exhibits two electron density regions due to its double bonds with adjacent carbons. This similarity shows why both central carbons in \( \text{CO}_2 \) and allene lead to the same hybridization type despite the different surrounding elements. Recognizing electron density regions is crucial for understanding how atoms form bonds and arrange themselves in three-dimensional space, impacting how the molecule interacts with other substances.