Question

How many moles of gold atoms do 3.45 * 1024 gold atoms constitute?

Short answer

There are approximately 5.73 moles of gold atoms in 3.45 x 10^24 gold atoms.

Step-by-step solution

Understand Avogadro's Number

Avogadro's number is a constant that represents the number of atoms in one mole of a substance. It is approximately equal to 6.022 x 10^23 atoms per mole.

Calculate the Number of Moles

To calculate the number of moles from the number of atoms, use the formula: Number of moles = Number of atoms / Avogadro's number. In this exercise, you have 3.45 x 10^24 gold atoms.

Perform the Division

Divide the number of gold atoms (3.45 x 10^24) by Avogadro's number (6.022 x 10^23) to find the number of moles. The calculation is as follows: \( \frac{3.45 \times 10^{24}}{6.022 \times 10^{23}} \approx 5.73 \) moles.

Key concepts

Moles Calculation

Understanding how to calculate moles is a foundational skill in chemistry that allows students to relate the mass of a substance to the number of molecules or atoms it contains. The mole is a standard SI unit for measuring the amount of substance, and it's defined as the number of atoms found in exactly 12 grams of carbon-12.

When you are given the number of particles of a substance (like atoms or molecules), you can calculate the number of moles by dividing that number by Avogadro's number. Avogadro's number, approximately \( 6.022 \times 10^{23}\), is the bridge between the macroscopic world we can measure and the microscopic world of atoms and molecules.

For example, to determine how many moles of gold atoms are in \(3.45 \times 10^{24}\) gold atoms, divide that number by Avogadro's number: \[ \text{Number of moles} = \frac{\text{Number of atoms}}{\text{Avogadro's number}} = \frac{3.45 \times 10^{24}}{6.022 \times 10^{23}} \approx 5.73 \text{ moles}.\]

This calculation shows that there are approximately 5.73 moles of gold atoms in \(3.45 \times 10^{24}\) gold atoms.

Atomic Structure

The concept of atomic structure is integral to understanding the chemical behavior of elements. An atom consists of a nucleus made up of protons and neutrons, with electrons orbiting around the nucleus. The number of protons in the nucleus, known as the atomic number, defines the identity of an element. Gold, for instance, has an atomic number of 79, meaning there are 79 protons in the nucleus of each gold atom.

Atoms are incredibly small, and their masses are correspondingly minuscule, which is why chemists use the mole concept to work with understandable quantities at a macroscopic scale. By utilizing Avogadro's number, chemists can quantify atoms in a way that correlates with the material's bulk properties, such as mass. Remember that while individual atoms can seem abstract, they are the building blocks of the tangible world, and knowing their structure is vital for exploring and understanding material properties.

Chemical Quantification

Chemical quantification involves measuring and describing the amount of substance present in a sample. It's a critical process in the field of chemistry as it allows scientists to prepare solutions with precise concentrations, reactants in accurate ratios, and to predict the yield of products from a reaction.

To quantify chemicals, scientists primarily use the mole concept along with molar mass, a measure of the mass of one mole of a given substance. For instance, the molar mass of gold is \(197 g/mol\), signifying that one mole of gold atoms weighs 197 grams. If a reaction requires a specific amount of gold, chemists can calculate the required mass by using the molar mass and the number of moles needed.

Through moles and molar mass, we can convert between the mass of a substance and the number of atoms or molecules it contains. Therefore, understanding the mole concept is crucial for accurate chemical quantification, enabling the precise calculation of reactants and products in chemical reactions.