Problem 4 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

When gypsum is heated to \(393 \mathrm{~K}\), it forms: (a) Anhydrous \(\mathrm{CaSO}_{4}\) (b) \(\mathrm{CaSO}_{4}{\underline{\phantom{xx}}}^{\sim} 5 \mathrm{H}_{2} \mathrm{O}\) (c) \(\mathrm{CaSO}_{4}^{-} 0.5 \mathrm{H}_{2} \mathrm{O}\) (d) Dead burnt plaster

Step-by-Step Solution

Answer

When gypsum is heated to 393 K, it forms \( \text{CaSO}_4 \, \cdot \, 0.5\text{H}_2\text{O} \) (option c).

Step 1: Understanding the Question

The problem asks us to determine what compound is formed when gypsum is heated to 393 K. Gypsum, known chemically as calcium sulfate dihydrate, has the formula \( \text{CaSO}_4 \, \cdot \, 2\text{H}_2\text{O} \). When heated, it loses some of this water, forming different substances depending on the temperature range.

Step 2: Identifying Gypsum Dehydration

Gypsum \( (\text{CaSO}_4 \, \cdot \, 2\text{H}_2\text{O}) \) loses its water molecules sequentially when heated. At around 373 K to 393 K, gypsum typically loses 1.5 water molecules to form hemihydrate calcium sulfate, commonly known as Plaster of Paris, with the chemical representation \( \text{CaSO}_4 \, \cdot \, 0.5\text{H}_2\text{O} \).

Step 3: Reviewing the Options

Given the options: (a) Anhydrous \( \text{CaSO}_4 \) (b) \( \text{CaSO}_4 \, \cdot \, 5\text{H}_2\text{O} \) (c) \( \text{CaSO}_4 \, \cdot \, 0.5\text{H}_2\text{O} \) (d) Dead burnt plaster The formula \( \text{CaSO}_4 \, \cdot \, 0.5\text{H}_2\text{O} \), corresponding to option (c), matches the product formed from heating gypsum to 393 K.

Step 4: Concluding the Solution

Based on the heating process of gypsum and the given options, when gypsum is heated to 393 K, it forms \( \text{CaSO}_4 \, \cdot \, 0.5\text{H}_2\text{O} \), also known as Plaster of Paris. This corresponds to option (c).

Key Concepts

Calcium Sulfate Dihydrate

Calcium sulfate dihydrate is more commonly known by its mineral name, gypsum. It is an abundant natural mineral with the chemical formula \( \text{CaSO}_4 \cdot 2\text{H}_2\text{O} \). This means it consists of calcium sulfate combined with two molecules of water, making it a hydrated form of calcium sulfate.
Gypsum is found in a crystal lattice structure where the water molecules are integrated into the mineral framework. When expressed, the water of crystallization plays a crucial role in its chemical and physical properties.

• Physical State: Gypsum is usually found in a fine powder or crystal form.
• Uses: It is widely used in building materials, like drywall or plasterboard.

The transformation of gypsum when heated is an essential aspect of its versatility in different applications, especially in construction.

Plaster of Paris

Plaster of Paris is a well-known product that results from the partial dehydration of gypsum. Specifically, when gypsum \( (\text{CaSO}_4 \cdot 2\text{H}_2\text{O}) \) is heated to approximately 373 K to 393 K, it loses part of its water content, transitioning to a substance called calcium sulfate hemihydrate, with the formula \( \text{CaSO}_4 \cdot 0.5\text{H}_2\text{O} \).
Plaster of Paris is widely used due to its ability to be easily shaped and molded, and it hardens upon cooling and exposure to moisture.

• Fast-setting: Once mixed with water, it sets rapidly, allowing for quick application and turn-around.
• Versatility: Used for making sculptures, casts, and building materials.

This property makes Plaster of Paris invaluable in artistic and medical applications, where molds and casts are frequently needed.

Chemical Reactions

Chemical reactions are processes where substances, called reactants, are transformed into different substances, known as products. In the context of gypsum dehydration, the reaction involves the application of heat to calcium sulfate dihydrate, resulting in the formation of different compounds as water molecules are removed.
The dehydration of gypsum follows a specific pathway:

• Initially, gypsum loses part of its water molecule content between 373 K and 393 K, forming Plaster of Paris \( (\text{CaSO}_4 \cdot 0.5\text{H}_2\text{O}) \).
• If further heated, it can eventually lead to anhydrous calcium sulfate \( (\text{CaSO}_4) \).

This controlled dehydration process highlights the dependency of product formation on the temperature range, which is crucial for manufacturing and industrial applications where specific forms of calcium sulfate are required.