Question

Asbestos, a known cancer-causing agent, has a typical formula of \(\mathrm{Ca}_{3} \mathrm{Mg}_{5}\left(\mathrm{Si}_{4} \mathrm{O}_{11}\right)_{2}(\mathrm{OH})_{2} .\) How many atoms of each element are given in this formula?

Short answer

The asbestos formula contains 3 Calcium atoms, 5 Magnesium atoms, 8 Silicon atoms, 24 Oxygen atoms, and 2 Hydrogen atoms.

Step-by-step solution

Identify Elements

List all the elements present in the asbestos formula: Calcium (Ca), Magnesium (Mg), Silicon (Si), Oxygen (O), and Hydrogen (H).

Count Atoms of Each Element

Count the number of atoms for each element in the formula by multiplying the subscript (number) after each element or group of elements by any outside subscript. Calcium: 3 atoms, Magnesium: 5 atoms, Silicon: 4 atoms inside the parentheses multiplied by 2 outside, giving 8 atoms, Oxygen: 11 atoms inside the parentheses multiplied by 2 outside, plus 2 atoms from the hydroxide (OH) groups, giving a total of 24 atoms, Hydrogen: 2 atoms from the two hydroxide (OH) groups.

Compile Atom Count

Combine the individual counts to state the total number of atoms for each element: Calcium (Ca): 3, Magnesium (Mg): 5, Silicon (Si): 8, Oxygen (O): 24, Hydrogen (H): 2.

Key concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the amounts of reactants and products in a chemical reaction. It is a foundational concept for balancing chemical equations, determining reaction yields, and calculating the quantities of chemicals needed or produced. Stoichiometry requires a thorough understanding of the chemical formulae of the substances involved.

For instance, interpreting the stoichiometry of asbestos, given by the formula \(\mathrm{Ca}_{3} \mathrm{Mg}_{5}\left(\mathrm{Si}_{4} \mathrm{O}_{11}\right)_{2}(\mathrm{OH})_{2} \) involves identifying that the compound is composed of calcium (Ca), magnesium (Mg), silicon (Si), oxygen (O), and hydrogen (H), and then determining the number of atoms of each element. Knowing stoichiometry does not only assist in the understanding of a compound's quantitative aspects but is also essential in real-world applications, such as calculating the mass of a product formed from a given mass of reactant, which is crucial in industrial chemical processes.

Chemical Nomenclature

Chemical nomenclature is the systematic naming of chemical compounds. It provides a uniform way to refer to chemical substances and is governed by rules and conventions established by the International Union of Pure and Applied Chemistry (IUPAC). Understanding nomenclature is vital for clear communication in science, especially in the instruction and study of chemistry.

In the asbestos formula, chemical nomenclature helps in identifying the chemical structure and types of atoms involved. For example, the notation \(\mathrm{OH})_{2} \) at the end of the asbestos chemical formula indicates the presence of hydroxide groups. Properly interpreting these symbols is crucial for understanding the compound's properties. Chemical nomenclature also guides us on how to construct and read formulas and teaches us about the types of bonds and the arrangement of atoms within a molecule, which has a direct impact on the molecule's function and reactivity.

Molecular Composition

Molecular composition refers to the types and numbers of atoms that comprise a molecule. It reveals the molecule's chemical identity, impacts its physical properties, and dictates how it will behave in a chemical reaction.

The molecular composition of asbestos, as indicated by its formula, \(\mathrm{Ca}_{3} \mathrm{Mg}_{5}\left(\mathrm{Si}_{4} \mathrm{O}_{11}\right)_{2}(\mathrm{OH})_{2} \), specifies that asbestos is made up of a specific number of calcium, magnesium, silicon, oxygen, and hydrogen atoms. The subscripts in the formula denote the count of each type of atom within a molecule. For example, the presence of \(\mathrm{Si}_{4}\) inside the parentheses followed by a subscript 2 outside indicates that there are a total of 8 silicon atoms in each molecule of asbestos. This kind of detailed understanding of molecular composition is essential for predicting how the substance will interact with other chemicals and for determining its suitability for various applications, including its mechanical strength, resistance to heat, and unfortunately, its potential health hazards.