Problem 12 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

In allene \(\left(\mathrm{C}_{3} \mathrm{H}_{4}\right)\), the type(s) of hybridization of the carbon atoms is (are): (a) \(s p\) and \(s p^{3}\) (b) \(s p^{2}\) and \(s p\) (c) only \(s p^{2}\) (d) \(s p^{2}\) and \(s p^{3}\)

Step-by-Step Solution

Answer

(b) \(sp^2\) and \(sp\)

Step 1: Understand the Structure of Allene

Allene, represented as \(\text{C}_3\text{H}_4\), has a linear arrangement due to the involvement of multiple bonds. It has a central carbon atom double bonded to each of the two terminal carbon atoms.

Step 2: Analyze the Hybridization of Terminal Carbon Atoms

The terminal carbon atoms in allene are each bonded to the central carbon and to two hydrogen atoms. For these carbons, since there are three regions of electron density (one double bond and two single bonds), the hybridization is \(sp^2\).

Step 3: Determine the Hybridization of the Central Carbon Atom

The central carbon in allene is bonded to both terminal carbons via double bonds. This creates two regions of electron density (two double bonds). Hence, the central carbon atom exhibits a linear geometry and \(sp\) hybridization.

Step 4: Conclude the Hybridization Types Present in Allene

The terminal carbon atoms are \(sp^2\) hybridized, and the central carbon is \(sp\) hybridized. Thus, the hybridizations present in allene are \(sp^2\) and \(sp\).

Key Concepts

Allene Structure

Allene, represented by the molecular formula \( \text{C}_3\text{H}_4 \), is a unique organic compound. It consists of three carbon atoms and four hydrogen atoms. To understand allene's structure, it's important to note that it has a central carbon atom that forms double bonds with each of the two terminal carbon atoms. This creates a linear arrangement for the central carbon.
The terminal carbon atoms each form two additional single bonds with hydrogen atoms, leading to a unique spatial configuration. This connectivity results in a fascinating structure where the terminal carbon atoms lie in different planes, giving allene a twisted shape. It's this configuration that leads to the distinct hybridization seen in allene's carbon atoms.

sp Hybridization

Hybridization is a concept used to describe how atomic orbitals mix to form new hybrid orbitals, enabling atoms in molecules to form certain geometries. In allene, the central carbon atom undergoes \( sp \) hybridization. This occurs when one \(s\) orbital and one \(p\) orbital mix to form two equivalent \( sp \) hybrid orbitals.
The \( sp \) hybridized carbon forms two pi bonds with the terminal carbons in allene, each using a different \( p \) orbital. This arrangement results in a linear geometry around the central carbon atom, as the two \( sp \) hybrid orbitals are oriented 180 degrees apart.
Key characteristics of \( sp \) hybridized carbon include:

• Linear electron pair geometry.
• Formation of two pi bonds in allene.
• Utilization of one \(s\) and one \(p\) atomic orbital for hybridization.

Understanding this hybridization is crucial for predicting how molecules like allene behave and interact.

sp2 Hybridization

The two terminal carbon atoms in allene each exhibit \( sp^2 \) hybridization. This hybridization occurs when one \(s\) orbital mixes with two \(p\) orbitals to form three \( sp^2 \) hybrid orbitals. These three orbitals arrange themselves in a trigonal planar geometry around the carbon atom.
In allene, each terminal carbon uses its \( sp^2 \) hybrid orbitals to form:

• One sigma bond with the central carbon atom via a double bond.
• Two sigma bonds with hydrogen atoms.

The remaining unhybridized \( p \) orbital perpendicular to the plane of the \( sp^2 \) orbitals forms a pi bond with the central atom. This arrangement allows for the unique geometry of allene, where each terminal carbon's plane is perpendicular to the other's. Such features are essential to understanding chemical reactivity and molecular interactions in allenes.