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

Question

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

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: Understand Plaster of Paris

Plaster of Paris is a common name for a gypsum product used in construction and craft. It is chemically known as calcium sulfate hemihydrate.

Step 2: Identify Characteristics

The defining characteristic of Plaster of Paris is that it is a hemihydrate, which means it has half a molecule of water per molecule of calcium sulfate.

Step 3: Examine Each Option

Look at each option: (a) has 2 full water molecules per calcium sulfate, which is a dihydrate. (b) has one water molecule for two calcium sulfates, making it a hemihydrate. (c) has two water molecules for two calcium sulfates, which is not a hemihydrate. (d) has three water molecules per calcium sulfate, classifying it as a trihydrate.

Step 4: Select the Correct Option

Since Plaster of Paris is calcium sulfate hemihydrate, the correct formula must be a hemihydrate. Option (b) fits this description: it contains one water molecule for every two calcium sulfate molecules, given as: \(2 \mathrm{CaSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\).

Key Concepts

Calcium sulfate hemihydrate

Plaster of Paris is popularly known by its chemical name, calcium sulfate hemihydrate. This compound is derived from gypsum, a naturally occurring mineral. The name "hemihydrate" indicates that for every two calcium sulfate molecules, there is one molecule of water involved. This is represented by the chemical formula \(2 \mathrm{CaSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\).

The term "hemihydrate" is crucial in differentiating Plaster of Paris from other forms of calcium sulfate, such as the dihydrate or trihydrate forms. In water, Plaster of Paris rehydrates back to gypsum, making it useful in applications such as molds and casts. Its reactivity with water determines its functionality, especially in construction and art.

Gypsum products

Gypsum products are essential in numerous industries, and the most familiar among them is Plaster of Paris. Gypsum is a soft mineral composed of calcium sulfate dihydrate \(\mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O}\). When gypsum is heated, it loses water and becomes Plaster of Paris, which is the hemihydrate form.

This transformation makes gypsum products incredibly versatile. They are widely used in drywall, cement, and even in agriculture as a soil conditioner. Plaster of Paris's easy shaping and setting attributes make it ideal for creating sculptures, ornaments, and architectural decorations. The product's ability to be molded and its subsequent hardness upon drying are key to its extensive use in different sectors.

Chemical formula interpretation

Understanding chemical formulas is critical in chemistry. A chemical formula gives us a snapshot of a molecule's composition by showing the types and numbers of atoms present. For instance, the formula \(2 \mathrm{CaSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\) tells us a lot about Plaster of Paris.

Here's how to interpret it:

• \(2\) before \(\mathrm{CaSO}_{4}\) suggests two calcium sulfate units.
• The dot \(\cdot\) before \(\mathrm{H}_{2} \mathrm{O}\) signifies that water is not chemically bonded but rather incorporated in the crystal structure, as a "hydrated" part.
• \(\mathrm{H}_{2} \mathrm{O}\) indicates that water is a part of the compound in a specific ratio.

Each component of the formula provides insight into the compound's molecular structure and its chemical behavior.

Molecular formulas in chemistry

In chemistry, molecular formulas play a vital role in describing molecules according to the number and type of atoms. They are like a chemical dictionary, helping us to understand the molecules' properties and reactions.

When we read a molecular formula, such as \(\mathrm{CaSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\), each element symbol inside represents one atom type, and the subscript next to it indicates the number of those atoms in the molecule. For example, \(\mathrm{H}_{2}\) means two hydrogen atoms.

Molecular formulas help not only in identifying the substance but also in understanding how it will react chemically with other substances. This knowledge is crucial in both scientific studies and practical applications, such as industrial processes and product formulations. By learning molecular formulas, we can predict how compounds will behave, which leads to innovations and efficiency improvements across various fields.