Problem 7 - A Complete Resource Book in Chemistry for JEE Main

Question

The compound in which \(\mathrm{C}\) uses only its \(\mathrm{sp}^{3}\) hybrid orbitals for bond formation is (a) \(\mathrm{HCOOH}\) (b) \(\left(\mathrm{NH}_{2}\right)_{2} \mathrm{CO}\) (c) \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{COH}\) (d) \(\mathrm{CH}_{3} \mathrm{CHO}\)

Step-by-Step Solution

Answer

The compound (c) \((CH_3)_3COH\) uses sp³ hybrid orbitals for carbon.

Step 1: Understanding sp³ Hybridization

In sp³ hybridization, one s orbital and three p orbitals from a carbon atom combine to form four equivalent sp³ hybrid orbitals. Each of these orbitals forms a sigma bond with an atom, arranging themselves in a tetrahedral geometry. For a carbon to be sp³ hybridized, it must form four single bonds.

Step 2: Identifying Each Compound's Carbon Hybridization

Examine each compound option:(a) \mathrm{HCOOH}\: The carbon forms two single bonds (with \(OH\) and \(H\)), one double bond (with \(O\)). The presence of a double bond indicates sp² hybridization.(b) \left(\mathrm{NH}_2\right)_2 \mathrm{CO}\: The carbon forms two single bonds (with \(NH_2\)) and one double bond (with \(O\)), indicating sp² hybridization.(c) \left(\mathrm{CH}_3\right)_3 \mathrm{COH}\: The carbon connects using four single bonds (three with \(CH_3\) and one with \(OH\)), indicating sp³ hybridization.(d) \mathrm{CH}_3 \mathrm{CHO}\: The carbon forms three single bonds (with \(H\), another \(C\), and \(CH_3\)) and one double bond (with \(O\)), indicating sp² hybridization.

Step 3: Conclusion Based on Hybridization

Only option (c) \(\left(\mathrm{CH}_3\right)_3 \mathrm{COH}\) has carbon using sp³ hybrid orbitals as it forms four single bonds, perfectly fitting the sp³ hybridization model.

Key Concepts

Hybridization

Hybridization is a fundamental concept in chemistry that explains how atomic orbitals mix to form new hybrid orbitals. These hybrid orbitals have different energies and shapes compared to the original atomic orbitals.
Understanding hybridization helps us predict molecule shapes and bond formation.
The type of hybridization depends on the number and type of bonds around a given atom, most often seen in atoms like carbon. Let’s break down some types:

• sp Hybridization: Mixes one s and one p orbital, forming two equivalent sp orbitals. It has a linear shape.
• sp² Hybridization: Involves one s and two p orbitals, creating three equivalent sp² orbitals, resulting in trigonal planar geometry.
• sp³ Hybridization: Combines one s and three p orbitals to form four sp³ orbitals, adopting a tetrahedral shape.

Hydrogen can form bonds through overlapping with these hybrid orbitals, crucial for constructing organic molecules.

Sigma Bonds

Sigma bonds (\(\sigma\)-bonds) are the strongest type of covalent chemical bond, formed by the direct overlap of atomic orbitals.
These occur when the electron density is concentrated along the axis connecting two nuclei.
Sigma bonds are pivotal in determining the structural framework of a molecule.In any hybridization state:

• sp hybridization can form two sigma bonds, one each with hydrogen or another atom.
• sp² hybridization forms three sigma bonds, accommodating additional bonding like pi bonds (which are not sigma).
• sp³ hybridization results in four sigma bonds, allowing maximum single bond connections.

When forming these bonds, each sp³ hybridized carbon atom will form a sigma bond with other atoms such as hydrogen or another carbon, defining stable compound structures like those in alkanes.

sp3 Hybrid Orbitals

The concept of sp³ hybrid orbitals arises from the need to explain carbon’s tetrahedral bonding in molecules like methane.
In an sp³ hybridized carbon, one s and three p orbitals merge to produce four equivalent orbitals.
These orbitals orient themselves as far as possible from each other, leading to a tetrahedral shape with bond angles of approximately 109.5°.When considering molecules:

• Each sp³ orbital can form a sigma bond with adjacent atoms, resulting in strong, stable single bonds.
• Molecules that use sp³ hybridization are generally non-polar, as the tetrahedral shape allows for symmetrical distribution of charge.
• The presence of sp³ hybridization in compounds often indicates that each carbon atom is bonded exclusively via single sigma bonds.

For example, in \((CH_3)_3COH\), the central carbon uses its sp³ hybrid orbitals to connect with three methyl groups and one hydroxyl group, perfectly fitting the mold of sp³ hybridization.