Problem 37 - A Complete Resource Book in Chemistry for JEE Main

Question

The general formula of an ionic compound crystallizing in zinc blende structure is (a) \(\mathrm{AB}_{3}\) (b) \(\mathrm{AB}_{2}\) (c) \(\mathrm{A}_{2} \mathrm{~B}_{2}\) (d) \(\mathrm{AB}\)

Step-by-Step Solution

Answer

The correct formula for the zinc blende structure is (d) \(\mathrm{AB}\).

Step 1: Understanding the Zinc Blende Structure

The zinc blende structure is also known as the cubic close-packed (fcc) structure. In this structure, zinc cations and sulfur anions alternate positions in a face-centered cubic lattice.

Step 2: Ionic Formula Composition

The composition of a compound crystallizing in the zinc blende structure typically consists of an equal ratio of cations to anions. This implies a 1:1 ratio, consistent with simple binary compounds.

Step 3: Identifying the Correct Formula

Given that the zinc blende structure involves a 1:1 ratio between its cations and anions, it corresponds to a compound where the formula is \( ext{AB}\) where A represents the cation and B represents the anion.

Step 4: Evaluating Options

Among the provided options, option (d) \(\text{AB}\) fits the description of a zinc blende structure. Thus, the general formula of an ionic compound crystallizing in the zinc blende structure is \(\text{AB}\).

Key Concepts

Ionic Compounds

Ionic compounds are formed when atoms transfer electrons from one to another, resulting in the formation of charged ions. The atom that loses electrons becomes a positively charged cation, while the atom that gains electrons becomes a negatively charged anion. In nature, opposite charges attract, and these cations and anions arrange themselves to form neutral ionic compounds.

These compounds are known for their high melting and boiling points due to the strong electrostatic forces holding the ions together. Additionally, ionic compounds typically form crystalline solids at room temperature and often dissolve in water to create conductive solutions.

In the zinc blende structure, an ionic compound is formed by an equal number of cations and anions. This results in a simple binary form, denoted by the formula \(\text{AB}\), where A is typically a metal and B is a nonmetal.

Cubic Close-Packed Structure

The cubic close-packed structure is an exceptionally efficient way to pack spheres, such as atoms, in a crystalline lattice. It's also known as face-centered cubic (fcc) structure. In this arrangement, each sphere (or atom) is surrounded by 12 others, maximizing contact and minimizing empty space.

• Each layer in the cubic close-packed structure follows a sequence, often referred to as ABC stacking. This means that no two layers are directly on top of one another, contributing to the high density of the arrangement.
• In the context of ionic compounds like those in the zinc blende structure, the Anions form the fcc lattice while the Cations fill the tetrahedral holes.

The cubic close-packed arrangement is critical in determining how ions distribute in a crystal lattice, impacting its chemical and physical properties.

Crystal Lattice Structures

Crystal lattice structures provide the foundation for the arrangement of atoms, ions, or molecules in a crystalline material. They define not only the geometric arrangement but also the symmetry of the crystals.

In a crystal lattice, the repeating pattern of a unit cell occurs throughout the solid. The unit cell is the smallest component that, through repetition, builds the entire structure.

• Common types of crystal lattice structures include simple cubic, body-centered cubic, and face-centered cubic, corresponding to how layers stack in the crystal.
• The zinc blende structure is a specific type of face-centered cubic lattice that perfectly describes how compounds like zinc sulfide arrange themselves in solid form.

Understanding the type of crystal lattice is fundamental to predicting the behavior and reactivity of a material, as well as its interaction with other substances.