Problem 15 - Chemistry The Molecular Science

Question

A crystal of fluorite (a mineral that contains calcium and fluorine) has a mass of \(2.83 \mathrm{~g}\). What is this mass in kilograms? Give the symbols for the elements in this crystal.

Step-by-Step Solution

Answer

The mass is 0.00283 kg, with elements Ca and F.

Step 1: Understanding Conversion

To convert the mass from grams to kilograms, you need to know the conversion factor between these two units. Specifically, 1 kilogram is equal to 1000 grams.

Step 2: Setting up the Conversion

To convert grams to kilograms, use the conversion ratio: \(1 ext{ kg} = 1000 ext{ g}\). Thus, dividing the number of grams by 1000 will give you the mass in kilograms.

Step 3: Performing the Calculation

Divide the mass of the crystal by 1000 to convert it to kilograms: \(\frac{2.83 ext{ g}}{1000} = 0.00283 ext{ kg}\).

Step 4: Identifying Elements in Fluorite

Fluorite is a mineral composed of calcium and fluorine. The chemical formula for fluorite is \(\text{CaF}_2\). Hence, the symbols for the elements present in the crystal are Calcium (Ca) and Fluorine (F).

Key Concepts

Mass Conversion

Mass conversion is a fundamental concept in chemistry and an everyday occurrence in scientific calculations. It involves changing the units of mass to another form depending on the context or specific requirement. Unit conversions are essential for understanding and communicating scientific data consistently.

In the problem provided, we have a sample mass of fluorite given in grams, specifically 2.83 grams. Often, we need to convert this mass into kilograms for various reasons, such as aligning with standard international units used in scientific documentation.

• Start with knowing your conversion factor: 1 kilogram is equivalent to 1000 grams.
• Use the conversion ratio which reflects this relationship: \[ \text{1 kg} = \text{1000 g} \]
• Convert grams to kilograms by dividing the quantity in grams by the conversion factor (1000 for grams to kilograms): \[ \frac{2.83 \, \text{g}}{1000} = 0.00283 \, \text{kg} \]

Remember, correctly performing unit conversions helps avoid misinterpretations and ensures accurate scientific calculations.

Fluorite Composition

Fluorite, also known as fluorspar, is a naturally occurring mineral composed primarily of calcium fluoride, with the chemical formula \( \text{CaF}_2 \). This mineral is significant in various industrial applications due to its rich calcium and fluoride content.

Fluorite's composition is quite simple but essential, as each formula unit consists of one calcium ion \( \text{Ca}^{2+} \) and two fluoride ions \( \text{F}^{-} \). This gives a stoichiometric balance to the mineral and defines its crystalline structure:

• Calcium (Ca) forms the positive ions in the structure.
• Fluorine (F) forms the negative ions, stabilizing the crystal.

Understanding the composition of fluorite is crucial not only for chemistry students but also for industries using fluorite in applications like metallurgy, manufacturing of high-performance optics, and the production of hydrofluoric acid by fluoride release.

Chemical Symbols

Chemical symbols are shorthand representations of elements in a chemical formula or equation. They are crucial in both writing and interpreting chemical compositions and reactions.

Each symbol corresponds to one element from the periodic table, often derived from its English or Latin name. These symbols make it efficient to convey detailed chemical information without using lengthy names.

• The chemical symbol for **Calcium** is \( \text{Ca} \). Calcium, a metal, is vital in the formation of bones and the functioning of cells.
• The chemical symbol for **Fluorine** is \( \text{F} \). Fluorine is a highly reactive, pale yellow gas known for its role in tooth health and industrial applications.

In the crystal of fluorite discussed, recognizing these symbols, \( \text{Ca} \) for calcium and \( \text{F} \) for fluorine, helps in quickly identifying the component elements and understanding their interactions within the mineral.