Problem 152 - A Complete Resource Book in Chemistry for JEE Main

Question

Match the following Column-I (a) Diamond (b) Graphite (c) Fullerene (d) Norbide Column-II (p) sp \(^{2}\)-hybridisation (q) sp \(^{3}\)-hybridisation (r) Tetrahedral (s) Carbide

Step-by-Step Solution

Answer

(a) - (q), (b) - (p), (c) - (p), (d) - (s).

Step 1: Understanding the Properties of Diamond

Diamond is a form of carbon where each carbon atom is covalently bonded to four other carbon atoms in a three-dimensional tetrahedral structure. This implies that in diamonds, the carbon atoms use sp\(^{3}\) hybridisation.

Step 2: Understanding the Properties of Graphite

Graphite is composed of layers of carbon atoms arranged in a hexagonal lattice. Each carbon atom is bonded to three others within the plane, using sp\(^{2}\) hybridisation. This allows for the typical layered and planar structure of graphite.

Step 3: Understanding the Properties of Fullerene

Fullerenes, such as C60, have a spherical structure composed of hexagonal and pentagonal arrangements of carbon atoms. These molecules also exhibit sp\(^{2}\) hybridisation due to their planar bonding structure.

Step 4: Understanding the Properties of Norbide

Norbide is typically a compound of boron and carbon, known as boron carbide (B4C). This compound is referred to as a carbide.

Step 5: Matching the Options from the Columns

Now let's map each item from Column-I to Column-II based on the chemical properties:- (a) Diamond corresponds to (q) sp\(^{3}\)-hybridisation.- (b) Graphite corresponds to (p) sp\(^{2}\)-hybridisation.- (c) Fullerene corresponds to (p) sp\(^{2}\)-hybridisation.- (d) Norbide corresponds to (s) Carbide.

Key Concepts

sp3 hybridisation

In chemistry, hybridisation helps explain the shape and bonding of molecules. When considering sp\(^{3}\) hybridisation, we often picture a tetrahedral arrangement. This is where each central atom, like carbon in this instance, bonds with four other atoms, each at the corners of a tetrahedron.
This is commonly seen in molecules such as methane (CH\(_4\)). In this setup, carbon employs sp\(^{3}\) hybrid orbitals that result from combining one s orbital with three p orbitals.
This blend forms four equivalent sp\(^{3}\) orbitals, leading to:

• A three-dimensional structure where bonds have an angle of approximately 109.5°.
• Strong sigma bonds are formed between carbon and hydrogen or any other element bonded to it.

An excellent example found in nature is diamond. Each of its carbon atoms utilizes sp\(^{3}\) hybridisation, bonding with four other carbon atoms. This network forms a sturdy and rigid structure, giving diamond its renowned hardness.

sp2 hybridisation

Another critical form of hybridisation, sp\(^{2}\), is intimately tied to the planar nature of bonding structures. Here, carbon atoms combine one s orbital and two p orbitals to form three equivalent sp\(^{2}\) hybrid orbitals.
This configuration is prominently seen in molecules with trigonal planar geometry. The angles formed between these bonds are roughly 120°.
One standout example is the planar structure of molecules like ethylene (C\(_2\)H\(_4\)), where carbon atoms form a double bond using:

• Three sigma bonds per carbon atom, using sp\(^{2}\) orbitals.
• One pi bond resulting from the side-to-side overlap of remaining unhybridized p orbitals.

Graphite utilizes sp\(^{2}\) hybridisation too. Here, each carbon atom connects with three others, creating sturdy sheets arranged in a hexagonal pattern. This is why graphite can easily break into flakes and is slippery, as layers slide past each other effortlessly. Fullerenes like C\(_{60}\) also employ sp\(^{2}\) hybridisation, shaping its distinctive spherical morphology.

carbon allotropes

Carbon, a versatile element, occurs in several structural forms known as allotropes. Each allotrope exhibits unique properties due to differing arrangements of carbon atoms.
Here are some well-known carbon allotropes:

• Diamond: Distinguished by its sp\(^{3}\) hybridised structure, diamond forms a three-dimensional tetrahedral network. This results in a strong and durable crystalline form.
• Graphite: Famously soft, graphite is made of layers bonded weakly together, showcasing sp\(^{2}\) hybridisation. It conducts electricity, owing to the free-moving electrons along its layers.
• Fullerenes: These spherical, hollow structures, like buckyballs, also use sp\(^{2}\) hybridisation. Their unique geometry contributes to novel properties like electrical conduction and strength.
• Graphene: Essentially a single layer of graphite, graphene is becoming highly significant in material science for its incredible strength and conductivity.

These allotropes show how versatile carbon can be, capable of forming vastly different materials just by rearranging its atomic bonds. This versatility is what makes carbon such an essential element in both natural and engineered materials.