Problem 48 - A Complete Resource Book in Chemistry for JEE Main

Question

What is the molecular formula of gypsum? (a) \(\mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O}\) (b) \(\mathrm{CaSO}_{4} \cdot 3 \mathrm{H}_{2} \mathrm{O}\) (c) \(\mathrm{CaSO}_{a} \mathrm{H}_{2} \dot{O}\) (d) \(2 \mathrm{CaSO}_{4} \mathrm{H}_{2} \mathrm{O}\)

Step-by-Step Solution

Answer

The molecular formula of gypsum is (a) \( \mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O} \).

Step 1: Understand the Compound

Gypsum is a naturally occurring mineral that is mainly composed of calcium sulfate dihydrate. This means its basic components are calcium sulfate (\( \mathrm{CaSO}_4 \)) and water (\( \mathrm{H}_2\mathrm{O} \)). A dihydrate compound has two molecules of water associated with each molecule of the main substance.

Step 2: Match the Formula

Given the options, identify the formula that represents gypsum with two water molecules per calcium sulfate unit. The compound that matches this description is calcium sulfate dihydrate, which is represented as \( \mathrm{CaSO}_{4} \cdot 2\mathrm{H}_{2} ext{O} \).

Key Concepts

Calcium Sulfate Dihydrate

One of the key components of gypsum is calcium sulfate dihydrate. This term might sound complex, but let's break it down.

• "Calcium sulfate" refers to the combination of calcium, sulfur, and oxygen. Its basic chemical form is \[\mathrm{CaSO}_4\]
• "Dihydrate" means that each molecule of calcium sulfate is associated with two water molecules. The prefix "di" signifies two, indicating the presence of two water molecules.

This combination results in gypsum's molecular formula:\[\mathrm{CaSO}_4 \cdot 2\mathrm{H}_2\mathrm{O}\]The two water molecules are integral parts of the structure, contributing to its physical properties, such as hardness and solubility. Gypsum, with its dihydrate formula, plays a crucial role in various applications including construction and agriculture.
Understanding calcium sulfate dihydrate helps us appreciate the chemical properties and uses of gypsum.

Gypsum Chemical Composition

The chemical composition of gypsum is predominantly calcium sulfate dihydrate. This composition is what defines gypsum’s characteristics and functions. To better understand this, let’s dive into the components:

• The basic building block is calcium sulfate, which is represented by the formula:\[\mathrm{CaSO}_4\]This consists of one calcium ion (\( \mathrm{Ca}^{2+} \)) along with a sulfate ion (\( \mathrm{SO}_4^{2-} \)).
• The water of hydration is two molecules of water (\( 2\mathrm{H}_2\mathrm{O} \)), which accounts for the "dihydrate" in its name.

Together, these components create gypsum's chemical formula \(\mathrm{CaSO}_4 \cdot 2\mathrm{H}_2\mathrm{O}\), determining its properties such as its ability to be molded, which makes it useful in industries like drywall manufacturing and plastering. Knowing the chemical composition helps in comprehending how gypsum is processed and utilized in different sectors.

Molecular Structure of Gypsum

Understanding the molecular structure of gypsum provides insight into its functionality and its wide range of applications. Gypsum's structure comprises layers of calcium sulfate dihydrate.

The Layered Structure

Calcium sulfate and water molecules form two distinct layers that alternate to create this crystalline structure.

• Each calcium ion is coordinated with four oxygen atoms belonging to a sulfate group (\( \mathrm{SO}_4^{2-} \)).
• Water molecules are nestled in between these layers, serving to hold them together through hydrogen bonding and contributing to the mineral's softness and elasticity.

The presence of water within this structure is essential in gypsum’s role as a binding and finishing material in construction. Gypsum's ability to recrystallize after being set makes it highly valuable in creating smooth plaster coats and other textures. This unique molecular arrangement not only dictates the physical properties of gypsum but also its varied use—from wall construction to fertilizers.