Question

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

Short answer

The molecular formula of gypsum is (a) \( \mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O} \).

Step-by-step solution

Analyze the options

Read through the given options (a, b, c, d) to understand what each molecular formula represents. They each show a version of calcium sulfate (CaSO₄) combined with a certain amount of water (H₂O). This means we are looking at different hydrates of calcium sulfate.

Understand what gypsum is

Research or recall that gypsum is a naturally occurring mineral. It is primarily composed of calcium sulfate dihydrate, which gives it its definitive structure.

Identify the dihydrate form

A dihydrate compound means there are two molecules of water attached to one formula unit of the salt. Hence, the chemical formula for gypsum will have two water molecules associated with the calcium sulfate.

Match formula with options

Look for the option where calcium sulfate is combined with two molecules of water. Option (a) shows \( \mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O} \), which matches the description of a dihydrate.

Key concepts

Calcium sulfate dihydrate

Calcium sulfate dihydrate, often known as gypsum, is a naturally occurring mineral. In its simplest terms, the term "dihydrate" refers to the fact that this compound comprises calcium sulfate and two water molecules. This structure is expressed in the chemical formula \[ \mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O} \]. This formula reveals how a single calcium sulfate unit associates with two water molecules, bonding to form this mineral.

Gypsum is widely used in construction, notably for creating plasterboard and cement. Its ability to hold water makes it valuable in agriculture for soil treatment. Another interesting use of gypsum is in medicine, where it serves as a casting material.

Understanding the importance of its dihydrate structure can provide insight into why it's favored in these applications. The presence of water molecules within its structure contributes to its binding property, essential in many of its uses.

Hydrates

Hydrates are compounds that include water molecules integrated into their structure. In the chemical formula of a hydrate, such as calcium sulfate dihydrate, the water content is represented as an integral part of the compound, separated by a dot.

The water molecules in a hydrate are referred to as "water of crystallization". They occupy specific positions within the crystal lattice of the compound. In the case of gypsum, two molecules of water are associated with each calcium sulfate unit.

Recognizing hydrates is crucial because they differ from anhydrous compounds, which lack water in their structure. Changes in temperature or humidity conditions can lead to dehydration, altering the compound's properties significantly. Hydrates are essential in many scientific and industrial applications where moisture content is a critical factor.

Molecular formula identification

Identifying a molecular formula involves examining the components and ratios within a compound. For gypsum (calcium sulfate dihydrate), the molecular formula \[ \mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O} \] clearly indicates that there is one calcium sulfate molecule linked with two water molecules.

To determine the correct formula, it's important to understand the basic components:

• Calcium (Ca): a metal element
• Sulfate (SO₄): a polyatomic ion
• Water (H₂O): hydrogen and oxygen compound

Correct identification ensures precision in communicating and understanding chemical compounds. Misidentification can result in significant errors, especially in chemical reactions where proportions are critical. This is why learning to efficiently read and decipher chemical formulas is vital.

Inorganic compounds

Inorganic compounds usually originate from mineral sources and largely do not contain carbon-hydrogen (C-H) bonds, unlike organic compounds. For example, gypsum, with the molecular formula \[ \mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O} \], falls into this category.

Inorganic compounds include salts, minerals, metals, and bases. These are typically characterized by ionic or covalent bonds. They often demonstrate high melting points and can conduct electricity when dissolved in water.

Understanding inorganic compounds' roles can illuminate their uses—from building materials to industrial processing and chemical reactions. Gypsum specifically demonstrates practical applications due to its ability to solidify upon losing water molecules, a feature that underscores its inorganic nature. Broadly, the study of inorganic chemistry helps explain the behavior and utility of mineral-derived substances in our everyday environment.