Question

Plaster of Paris is (1) \(\mathrm{CaSO}_{4} \cdot \frac{1}{2} \mathrm{H}_{2} \mathrm{O}\) (2) hemihydrate (3) formed by partial dehydration of gypsum (4) all of these

Short answer

The answer is (4) all of these.

Step-by-step solution

Identify Plaster of Paris

Plaster of Paris is a chemical compound commonly used in building materials and medical casts. It is known for its ability to form a hard, solid structure once it is mixed with water and allowed to dry.

Check Chemical Formula

The chemical formula for Plaster of Paris is \(\text{CaSO}_{4} \cdot \frac{1}{2} \text{H}_{2} \text{O}\). This indicates it is calcium sulfate hemihydrate.

Validate the Hemihydrate Aspect

The term 'hemihydrate' means that the compound has half a mole of water per mole of calcium sulfate. This is true for the formula \(\text{CaSO}_{4} \cdot \frac{1}{2} \text{H}_{2} \text{O}\).

Formation Process

Plaster of Paris is formed by the partial dehydration of gypsum (which has the formula \(\text{CaSO}_{4} \cdot 2 \text{H}_{2} \text{O}\)). This process involves heating gypsum to around 150 degrees Celsius to remove some of the water content, resulting in the hemihydrate form.

Conclusion

Since Plaster of Paris fits the given criteria: \(1\) \(\text{CaSO}_{4} \cdot \frac{1}{2} \text{H}_{2} \text{O}\), \(2\) hemihydrate, \(3\) formed by partial dehydration of gypsum, the answer must be \(4\) all of these.

Key concepts

Hemihydrate

The term 'hemihydrate' indicates that the compound includes half a mole of water per mole of calcium sulfate. In the case of Plaster of Paris, this half-mole of water is crucial for its ability to rehydrate and harden when mixed with more water. When Plaster of Paris is mixed with water, it undergoes a chemical reaction that binds water molecules into a new crystal structure, creating a hard, durable solid. This process is known as setting, and it highlights the importance of the hemihydrate nature of Plaster of Paris. If you were working with a dihydrate (\(\text{CaSO}_{4} \cdot 2 \text{H}_{2} \text{O}\)), which is gypsum, the setting process and properties would be different. Recognizing the 'hemi' (half) in 'hemihydrate' helps us understand the precise water content and behavior of the compound during its transition from a powder to a solid structure.

Gypsum Dehydration

The formation of Plaster of Paris from gypsum involves a process known as partial dehydration. Gypsum, or calcium sulfate dihydrate (\(\text{CaSO}_{4} \cdot 2 \text{H}_{2} \text{O}\)), contains two moles of water for every mole of calcium sulfate. To create Plaster of Paris, gypsum is heated to approximately 150 degrees Celsius. This heating process drives off 1.5 moles of water, leaving behind calcium sulfate hemihydrate (\(\text{CaSO}_{4} \cdot \frac{1}{2} \text{H}_{2} \text{O}\)). This partial dehydration is critical because it transforms gypsum into a material capable of setting quickly when mixed with water again. The dehydration process changes the structure but retains the essential properties needed to form a hard, solid mass when water is reintroduced. This is why understanding the dehydration process is vital for comprehending how Plaster of Paris works and why it is so widely used for casting and construction.