Problem 45 - A Complete Resource Book in Chemistry for JEE Main

Question

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

Step-by-Step Solution

Answer

The molecular formula of plaster of Paris is (b) \(2 \mathrm{CaSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\).

Step 1: Identifying the Compound

Plaster of Paris is known chemically as calcium sulfate hemihydrate. It is represented as \( ext{CaSO}_4 imes rac{1}{2} ext{H}_2O\). This indicates that half a molecule of water is associated with calcium sulfate.

Step 2: Understanding the Options

The options given are hydrated forms of calcium sulfate. We need to determine which of these options represents calcium sulfate hemihydrate.

Step 3: Analyzing Each Option

Let's evaluate the options:(a) \( ext{CaSO}_4 imes 2 ext{H}_2O\) equates to calcium sulfate dihydrate, which is known as gypsum, not plaster of Paris.(b) \(2 ext{CaSO}_4 imes ext{H}_2O\) simplifies to \( ext{CaSO}_4 imes rac{1}{2} ext{H}_2O\) per calcium sulfate molecule, which matches plaster of Paris.(c) \(2 ext{CaSO}_4 imes 2 ext{H}_2O\) represents one water molecule per two calcium sulfate molecules, not a hemihydrate.(d) \( ext{CaSO}_4 imes 3 ext{H}_2O\) is incorrect for plaster of Paris as it does not represent a hemihydrate.

Step 4: Selecting the Correct Answer

Based on the analysis, option (b) \(2 ext{CaSO}_4 imes ext{H}_2O\) simplifies to the formula of calcium sulfate hemihydrate or plaster of Paris.

Key Concepts

Chemical formula

The chemical formula of a substance is a way to represent its chemical composition. It shows the number of atoms of each element in a molecule. For plaster of Paris, the chemical formula is related to its composition as calcium sulfate hemihydrate. In essence, this formula reflects the ratio of calcium, sulfur, oxygen, and water molecules in the compound.
Plaster of Paris is identified by the simplified formula \( \mathrm{CaSO}_{4} \cdot \frac{1}{2} \mathrm{H}_{2} \mathrm{O} \). This indicates that there is one molecule of calcium sulfate for every half molecule of water. It can also be represented as \( 2 \mathrm{CaSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O} \) to show that per two units of calcium sulfate, there is one water molecule.
Using the chemical formula helps us understand how plaster of Paris behaves in chemical reactions, how we can produce it, and how it interacts with other substances.

Hydrates

Hydrates are compounds that include water molecules within their structure. These water molecules are known as "water of crystallization" and are integrally connected to the compound. The general notation for a hydrate is \( MX \cdot n \mathrm{H}_2\mathrm{O} \), where \( n \) represents the number of water molecules.
In the case of plaster of Paris, the compound is a special type of hydrate known as a "hemihydrate," meaning there is half a water molecule associated with each formula unit of calcium sulfate. This unique relationship is crucial, as it defines the physical and chemical properties of the compound.
When plaster of Paris is mixed with water, it reabsorbs the water becoming gypsum—a dihydrate. This reaction, where the water is reintroduced, causes it to harden, which is why it's commonly used in casting and construction applications.

Calcium sulfate hemihydrate

Calcium sulfate hemihydrate is the chemical name for plaster of Paris. It is formed when gypsum, which is calcium sulfate dihydrate, is heated to remove some of its water content. By losing water, the dihydrate turns into a hemihydrate, making it the versatile plaster of Paris.
When we say "hemihydrate," we refer to the presence of half a molecule of water in relation to the calcium sulfate. This precise transformation is crucial as it retains sufficient hydration to revert to a solid form when combined with liquid water post-production.

• It plays a significant role in various fields such as construction, art, and medicine due to its capacity to solidify quickly.
• The properties of calcium sulfate hemihydrate allow it to create smooth finishes and durable casts.

Understanding calcium sulfate hemihydrate’s role in plaster of Paris gives us insights into its practical uses and its reactions with other substances.