Problem 55 - General Chemistry: Principles and Modern Applications

Question

What is the total number of atoms in (a) 15.8 mol \(\mathrm{Fe}\); (b) \(0.000467 \mathrm{mol} \mathrm{Ag} ;\) (c) \(8.5 \times 10^{-11} \mathrm{mol} \mathrm{Na} ?\)

Step-by-Step Solution

Answer

The total number of atoms are: (a) \(9.51 \times 10^{24}\) atoms Fe, (b) \(2.81 \times 10^{20}\) atoms Ag, and (c) \(5.12 \times 10^{13}\) atoms Na.

Step 1: Calculate the total number of Fe atoms

Multiply the given number of Fe moles by Avogadro's number to find the total number of Fe atoms. The calculation will be: \(15.8 \, \text{mol Fe} \times 6.022 \times 10^{23} \text{ atoms/mol} = 9.51 \times 10^{24}\, \text{atoms Fe}\).

Step 2: Calculate the total number of Ag atoms

Multiply the given number of Ag moles by Avogadro's number to find the total number of Ag atoms. The calculation will be: \(0.000467 \, \text{mol Ag} \times 6.022 \times 10^{23}\, \text{ atoms/mol} = 2.81 \times 10^{20}\, \text{atoms Ag}\).

Step 3: Calculate the total number of Na atoms

Multiply the given number of Na moles by Avogadro's number to find the total number of Na atoms. The calculation will be: \(8.5 \times 10^{-11} \, \text{mol Na} \times 6.022 \times 10^{23} \, \text{atoms/mol} = 5.12 \times 10^{13}\, \text{atoms Na}\).

Key Concepts

Avogadro's Number

In chemistry, the Avogadro's number is a fundamental concept that helps scientists link the macroscopic scale we see with the microscopic scale of atoms and molecules. It is the number of atoms or molecules in one mole of a substance. Avogadro's number is a constant with a value of approximately \(6.022 \times 10^{23}\). This large number helps convert atomic measurements to macroscopic quantities and vice versa.

• For example, in the exercise, when we multiply moles of a substance by Avogadro's number, we get the total number of atoms in that number of moles.
• This allows scientists and students to work with quantities that are much easier to use in lab settings.

Understanding this number is crucial for accurately executing calculations involving moles, atoms, and molecules.

Number of Atoms

The number of atoms in a sample links directly to the amount of substance you have, measured in moles. A mole represents \(6.022 \times 10^{23}\) particles, which can be atoms, molecules, ions, etc.When you have a certain amount of a substance in moles, multiplying that number by Avogadro's number gives you the total number of atoms in the sample.

• For instance, with 15.8 moles of iron (Fe), the calculation \(15.8 \, \text{mol Fe} \times 6.022 \times 10^{23} \, \text{atoms/mol}\) results in approximately \(9.51 \times 10^{24} \, \text{atoms of Fe}\).
• Applying this method systematically helps convert the tiny atomic scale to something practical.

This technique is integral for performing detailed quantitative analyses in chemistry.

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships of reactants and products in a chemical reaction. It is based on the conservation of mass, meaning that any chemical equation needs to be balanced. To use stoichiometry effectively, you often convert between moles and atoms, or molecules, using Avogadro’s number as demonstrated in the exercise.

• This approach ensures that chemical reactions are perfectly measured and predictable, which is critical in laboratory and industrial settings.
• Furthermore, stoichiometry enables chemists to predict yields of products and optimize the amounts of reactants needed.

Thus, understanding stoichiometry is essential for those engaged in any form of chemical experimentation or process development.