Question

Formula of plaster of Paris is (a) \(\mathrm{CaSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\) (b) \(3 \mathrm{CaSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\) (c) \(\mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O}\) (d) \(\mathrm{CaSO}_{4} \cdot 1 / 2 \mathrm{H}_{2} \mathrm{O}\)

Short answer

a) CaSO4.H2O b) 3CaSO4.H2O c) CaSO4.2H2O d) CaSO4.1/2H2O Answer: d) CaSO4.1/2H2O

Step-by-step solution

Understand the formation and properties of plaster of Paris

Plaster of Paris is obtained by heating gypsum (calcium sulfate dihydrate) at 373 K (100°C). The water of crystallization is partially removed to get a hemihydrate form. Plaster of Paris sets to a hard mass on mixing with water due to the formation of interlocking crystals which incorporate water.

Compare the given options with our understanding of plaster of Paris

Now that we know plaster of Paris is a hemihydrate of calcium sulfate, we can find the option representing this property. (a) \(\mathrm{CaSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\): Calcium sulfate monohydrate (b) \(3 \mathrm{CaSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\): An incorrect formula for plaster of Paris (c) \(\mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O}\): Calcium sulfate dihydrate, which is gypsum (d) \(\mathrm{CaSO}_{4} \cdot 1 / 2 \mathrm{H}_{2} \mathrm{O}\): Calcium sulfate hemihydrate

Select the correct formula based on our comparison

From the above comparison, we can conclude that option (d) \(\mathrm{CaSO}_{4} \cdot 1 / 2 \mathrm{H}_{2} \mathrm{O}\) is the correct formula for plaster of Paris, as it represents the calcium sulfate hemihydrate.

Key concepts

Calcium Sulfate Hemihydrate

Calcium sulfate hemihydrate, the scientific backbone behind the common material 'plaster of Paris', is a fascinating compound used extensively in construction and medical applications. Its chemical formula is represented as \(\mathrm{CaSO}_4 \cdot \frac{1}{2} \mathrm{H}_2 \mathrm{O}\). This signifies the compound is comprised of one molecule of calcium sulfate bonded to half a molecule of water, or water of crystallization.

When gypsum, \(\mathrm{CaSO}_4 \cdot 2\mathrm{H}_2 \mathrm{O}\), is heated to about 373 K (100°C), part of the water content is removed, resulting in the hemihydrate form. It's in the process of losing this water that we get plaster of Paris—a material that can be molded when wet and sets into a hard structure. This unique property is due to the hemihydrate form rehydrating to form interlocking crystals of gypsum during the setting process.

Properties of Plaster of Paris

Plaster of Paris is widely recognized for its quick-setting characteristics and versatility. One of its most important properties is its ability to set into a hard, solid form when mixed with water. It exhibits this property because the hemihydrate form reverts to the dihydrate form, forming a matrix of interlocking gypsum crystals.

Key Properties

• Quick Setting: One of the primary reasons it’s so valued in both medical and craft applications is its ability to set rapidly once it's mixed with water.
• Fire Resistance: Plaster of Paris does not burn easily and is hence used in fireproofing.
• Molding Ability: Before setting, it's malleable and hence can take on any shape, making it great for casts and molds.
• Surface Finish: Once set, it creates a smooth surface which can be painted or decorated as desired.

It's the balance between ease of use and structural integrity that makes plaster of Paris a material of choice for artisans, builders, and medical professionals alike.

Water of Crystallization

Water of crystallization is a term used in chemistry to describe water molecules that are an integral part of the structure of a crystalline compound. These water molecules are not just trapped; they help maintain the crystal's stability and structure.

In the context of plaster of Paris, water of crystallization plays a critical role. The gypsum we start with, \(\mathrm{CaSO}_4 \cdot 2\mathrm{H}_2 \mathrm{O}\), has two water molecules per calcium sulfate unit — this is referred to as 'dihydrate'. When gypsum is heated, some of the water is driven off, and the substance becomes 'hemihydrate', losing one and a half molecules of water per molecule of calcium sulfate.

However, when plaster of Paris is mixed with water, it reabsorbs water and turns back into the dihydrate form. It is during this rehydration process that it hardens and forms a stable, solid mass. This process illustrates the critical importance of the water of crystallization in the transformation and setting of plaster of Paris.