Problem 79 - Chemistry: An Atoms-Focused Approach

Question

Aluminum, silicon, and oxygen form minerals known as aluminosilicates. How many moles of aluminum are in 1.50 moles of the following? a. pyrophyllite,\(\mathrm{Al}_{2} \mathrm{Si}_{4} \mathrm{O}_{10}(\mathrm{OH})_{2}\) b. \(\operatorname{mica}, \mathrm{KAl}_{3} \mathrm{Si}_{3} \mathrm{O}_{10}(\mathrm{OH})_{2}\) c. albite, \(\mathrm{Na} \mathrm{AlSi}_{3} \mathrm{O}_{8}\)

Step-by-Step Solution

Answer

a. Pyrophyllite, \(\mathrm{Al}_{2} \mathrm{Si}_{4}\mathrm{O}_{10}(\mathrm{OH})_{2}\). b. Mica, \(\mathrm{KAl}_{3} \mathrm{Si}_{3}\mathrm{O}_{10}(\mathrm{OH})_{2}\). c. Albite, \(\mathrm{Na} \mathrm{AlSi}_{3} \mathrm{O}_{8}\). Answer: a. 3.00 moles of \(\mathrm{Al}\) b. 4.50 moles of \(\mathrm{Al}\) c. 1.50 moles of \(\mathrm{Al}\)

Step 1: Find the Moles of Aluminum in One Mole of Pyrophyllite

In one mole of pyrophyllite, there are 2 moles of aluminum, as given by the formula \(\mathrm{Al}_{2} \mathrm{Si}_{4}\mathrm{O}_{10}(\mathrm{OH})_{2}\).

Step 2: Calculate the Moles of Aluminum in Given Moles of Pyrophyllite

Now, we need to find out how many moles of aluminum are present in 1.50 moles of pyrophyllite. To do this, multiply the moles of pyrophyllite (1.50) by the moles of aluminum in one mole of pyrophyllite (2): (1.50 moles) * (2 moles of \(\mathrm{Al}\)) = 3.00 moles of \(\mathrm{Al}\) #b. mica, \(\mathrm{KAl}_{3} \mathrm{Si}_{3}\mathrm{O}_{10}(\mathrm{OH})_{2}\)#

Step 1: Find the Moles of Aluminum in One Mole of Mica

In one mole of mica, there are 3 moles of aluminum, as given by the formula \(\mathrm{KAl}_{3} \mathrm{Si}_{3}\mathrm{O}_{10}(\mathrm{OH})_{2}\).

Step 2: Calculate the Moles of Aluminum in Given Moles of Mica

Now, we need to find out how many moles of aluminum are present in 1.50 moles of mica. To do this, multiply the moles of mica (1.50) by the moles of aluminum in one mole of mica (3): (1.50 moles) * (3 moles of \(\mathrm{Al}\)) = 4.50 moles of \(\mathrm{Al}\) #c. albite, \(\mathrm{Na} \mathrm{AlSi}_{3} \mathrm{O}_{8}\)#

Step 1: Find the Moles of Aluminum in One Mole of Albite

In one mole of albite, there is 1 mole of aluminum, as given by the formula \(\mathrm{Na} \mathrm{AlSi}_{3} \mathrm{O}_{8}\).

Step 2: Calculate the Moles of Aluminum in Given Moles of Albite

Now, we need to find out how many moles of aluminum are present in 1.50 moles of albite. To do this, multiply the moles of albite (1.50) by the moles of aluminum in one mole of albite (1): (1.50 moles) * (1 mole of \(\mathrm{Al}\)) = 1.50 moles of \(\mathrm{Al}\)

Key Concepts

Understanding Aluminosilicates

Aluminosilicates are fascinating compounds formed by the combination of aluminum (Al), silicon (Si), and oxygen (O), often with additional elements. These minerals are significant in geology and material sciences due to their unique properties and abundance in the Earth's crust.
Aluminosilicates include a variety of minerals, each with a distinct chemical composition. These minerals form crystalline structures like clays, feldspars, and zeolites. They play key roles in soil fertility and industrial applications.
For example, in the exercise given, we are looking at specific aluminosilicates: pyrophyllite, mica, and albite. Each of these minerals contains a different number of aluminum atoms, which can be determined by analyzing their chemical formulas. Thus, understanding these chemical structures is crucial for identifying and calculating the number of moles of elements present.

Deciphering Chemical Formulas

A chemical formula represents the types and numbers of atoms in a substance. It's akin to a "recipe" that tells us what elements are in a compound and how they are arranged. By reading and interpreting these formulas, we can deduce important information such as the number of specific atoms present.
In aluminosilicates, for example, each formula informs us about the arrangement of aluminum, silicon, and oxygen atoms. Let's take pyrophyllite, which is written as \(\mathrm{Al}_{2} \mathrm{Si}_{4} \mathrm{O}_{10}(\mathrm{OH})_{2}\). This tells us that each molecule contains two aluminum atoms, resulting in two moles of aluminum per mole of the mineral.
Understanding chemical formulas allows us to extract such details, aiding calculations in chemical reactions, material processing, and even everyday applications. Mastery of chemical formulas is foundational for navigating subjects like stoichiometry and beyond.

Grasping Stoichiometry

Stoichiometry is a section of chemistry focused on calculating the quantities of reactants and products in chemical reactions. It offers a quantitative insight into the relationships between substances in a chemical equation.
Through stoichiometry, we learn how to use balanced chemical equations to determine the precise amounts such as moles, masses, and volumes required or produced. For instance, in the exercise, stoichiometry helps us calculate the moles of aluminum in each mineral by using their given formulas.
In practical applications, stoichiometry ensures the correct proportions in chemical processes. It is a vital skill that helps in fields ranging from pharmaceuticals to environmental science, ensuring efficiency and precision. By mastering stoichiometry, students can bridge the gap between theoretical chemistry and practical usage, equipping them with the analytical skills needed in various scientific domains.