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 \(2 \mathrm{CaSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\).

Step 1: Identify the Component of Plaster of Paris

Plaster of Paris is primarily made from gypsum. When gypsum is heated to about 150°C, it loses water molecules and forms Plaster of Paris. It is essentially the hemihydrate form of calcium sulfate.

Step 2: Understand the Hemihydrate Concept

The term 'hemihydrate' refers to the fact that every two molecules of calcium sulfate lose 1.5 molecules of water. In chemical terms, this means the formation of Plaster of Paris involves the removal of water so that the formula reflects a loss of water.

Step 3: Analyze Each Option

- Option (a), \(\mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O}\), corresponds to fully hydrated gypsum.- Option (b), \(2 \mathrm{CaSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\), reflects the hemihydrate form: a plausible candidate for plaster.- Option (c), \(2 \mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O}\), implies more water content than hemihydrate, hence incorrect for plaster.- Option (d), \(\mathrm{CaSO}_{4} \cdot 3 \mathrm{H}_{2} \mathrm{O}\), suggests an even higher degree of hydration, which is not typical for plaster.

Step 4: Select the Correct Formula

Based on the chemistry of Plaster of Paris as a hemihydrate, option (b), \(2 \mathrm{CaSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\), correctly represents the molecular formula of Plaster of Paris.

Key Concepts

Hemihydrate Calcium Sulfate

Plaster of Paris is known for its unique chemical identity as hemihydrate calcium sulfate. This means that for every two molecules of calcium sulfate, there is only one molecule of water attached. The formula for Plaster of Paris is traditionally represented as \(2 \mathrm{CaSO}_4 \cdot \mathrm{H}_2\mathrm{O}\). This formula indicates the partial hydration state which is less than that of its parent compound, gypsum.
This transformation to hemihydrate is crucial because it gives Plaster of Paris its characteristic ability to set and harden when mixed with water. Upon mixing, it reabsorbs the lost water turning back into gypsum which forms a solid structure.
To sum up, the term "hemihydrate" marks a distinct chemical state, which is strategically important for applications like casting molds and making sculptures.

Gypsum Dehydration

The process of forming Plaster of Paris from gypsum revolves around the loss of water through heating. Gypsum, chemically known as \(\mathrm{CaSO}_4 \cdot 2\mathrm{H}_2\mathrm{O}\), contains two molecules of water. When this compound is heated to approximately 150°C, it loses about one and a half molecules of water through a process called calcination.
This removal of water from gypsum creates what we call Plaster of Paris, a dry powder that is easy to mold and carve. Upon rehydration by mixing with water, it hardens, making it essential for creating casts, sculptures, and even medical splints.

• Heating facilitates the transition from a fully hydrated to a partially dehydrated state.
• Rehydrating Plaster of Paris leads it to revert to its original gypsum form, explaining its easy setting property.

The dehydration process is hence a critical aspect of converting gypsum into a versatile material like Plaster of Paris.

Chemical Formulas

Chemical formulas act as succinct representations of chemical compounds, showcasing both their elements and the ratios of atoms within them. For Plaster of Paris, the formula \(2 \mathrm{CaSO}_4 \cdot \mathrm{H}_2\mathrm{O}\) succinctly categorizes a hemihydrate by indicating two calcium sulfate units bound to one water molecule.
The chemical formula provides a straightforward way to convey complex information. Here's what you should know:

• Formulas help convey the type and quantity of atoms or molecules within a compound.
• A good understanding of these formulas is essential for predicting chemical reactions and understanding material properties.

This level of descriptive clarity aids chemists and students in understanding how different substances form and behave.