Problem 89 - Chemistry: The Central Science in SI Units, Global Edition

Question

When aluminum replaces up to half of the silicon atoms in \(\mathrm{SiO}_{2}\), a mineral class called feldspars result. The feldspars are the most abundant rock-forming minerals, comprising about \(50 \%\) of the minerals in Earth's crust. Orthoclase is a feldspar in which Al replaces one-fourth of the Si atoms of \(\mathrm{SiO}_{2},\) and charge balance is completed by \(\mathrm{K}^{+}\) ions. Determine the chemical formula for orthoclase.

Step-by-Step Solution

Answer

The chemical formula for orthoclase is \(\mathrm{K}_{1}\mathrm{Al}\mathrm{Si}_{3}\mathrm{O}_{8}\).

Step 1: Determine the number of Al and Si atoms in orthoclase

Let's first determine the fraction of Al atoms in orthoclase. Since Al replaces one-fourth of the Si atoms, the fraction of Al atoms in orthoclase will be \(1/4\). The remaining fraction, \(3/4\), will comprise Si atoms.

Step 2: Set up the orthoclase formula with Al and Si fractions

With the fractions determined in step 1, we can now represent the orthoclase formula as a combination of Si and Al atoms (using x as the number of oxygen atoms): Orthoclase = \(\frac{3}{4}\mathrm{Si} + \frac{1}{4}\mathrm{Al} + x\mathrm {O}\)

Step 3: Determine number of oxygen atoms

Orthoclase is related to \(\mathrm{SiO}_{2}\), which has a 1:2 ratio of Si to O atoms. We can use this information to determine the number of oxygen atoms in relation to Al and Si atoms: \(x = 2(\frac{3}{4}\mathrm{Si} + \frac{1}{4}\mathrm{Al})\) Now we will solve for x: \(x = \frac{3}{2}\mathrm{Si} + \frac{1}{2}\mathrm{Al}\)

Step 4: Write the orthoclase formula without fractions

To simplify the orthoclase formula, we will multiply the equation by 4 to eliminate the fractions: Orthoclase = \(3\mathrm{Si} + \mathrm{Al} + (3\mathrm{Si} + \mathrm{Al})\mathrm{O}\) Orthoclase = \(\mathrm{K}_{1}\mathrm{Al}\mathrm{Si}_{3}\mathrm{O}_{8}\) The chemical formula for orthoclase is \(\mathrm{K}_{1}\mathrm{Al}\mathrm{Si}_{3}\mathrm{O}_{8}\).

Key Concepts

Orthoclase

Orthoclase is a significant member of the feldspar mineral family. It plays a crucial role in geology due to its abundance and the insights it provides into Earth's processes.

It belongs to the potassium feldspar group, characterized by its composition, which includes potassium, aluminum, and silicate. Orthoclase exhibits a monoclinic crystal structure, meaning its crystals have an asymmetrical shape.

This mineral is often found in igneous rocks, such as granite, which is a common rock type within Earth’s crust. Orthoclase is not just a mere component of rocks; it contributes to their color and appearance. Its pink hue often gives granite its distinctive look.

Understanding orthoclase helps us comprehend the physical makeup of our planet and the processes that produce the rocks surrounding us.

Chemical Formula

A key aspect of orthoclase is its chemical formula: \(\mathrm{KAlSi}_3\mathrm{O}_8\). This formula represents its molecular structure, providing us insight into its composition.

Let’s break it down:

• \(\mathrm{K}\): Potassium - Adds charge balance by bonding with aluminum.
• \(\mathrm{Al}\): Aluminum - Substitutes one-fourth of silicon atoms originally present in the structure of \(\mathrm{SiO}_2\), affecting its chemical behavior and physical properties.
• \(\mathrm{Si}\): Silicon - The backbone of the mineral, providing structure.
• \(\mathrm{O}_8\): Oxygen - Binds everything together, helping maintain stability in the crystal lattice.

The formula highlights how different elements come together in a precise way to create a stable and structured mineral. Understanding this formula helps us grasp the complexity and beauty of Earth's minerals.

Aluminum Substitution

Aluminum substitution is a fascinating process within the formation of feldspar minerals. In the case of orthoclase, aluminum replaces one-fourth of the silicon atoms present in the mineral \(\mathrm{SiO}_2\).

This substitution is pivotal because:

• It alters the mineral's physical and chemical properties, including its color and durability.
• It necessitates the presence of \(\mathrm{K}^+\) ions for charge balance, leading to the formation of orthoclase rather than other feldspar varieties.
• It provides insight into geological conditions; the amount of aluminum substitution and presence of potassium can indicate the environmental conditions during the mineral's formation.

This substitution process elucidates the dynamic nature of mineral formation and the intricate changes that can create vastly different minerals from seemingly similar starting materials.

Earth's Crust

The Earth's crust is a complex, rocky shell that forms the outermost layer of our planet. Feldspar minerals, like orthoclase, are incredibly abundant here, forming about 50% of it.

These minerals:

• Are key building blocks of rocks like granite and basalt.
• Help in understanding geological processes, such as volcanic activity and plate tectonics.
• Influence soil formation and, consequently, the life that thrives on Earth’s surface.

Studying mineral composition in Earth's crust helps us appreciate how our planet has evolved over billions of years. The presence of orthoclase and other feldspars tells us not just about the Earth's past but also provides clues about its future. Understanding these minerals gives insight into both the stability and dynamic changes occurring within Earth's crust.