*The number of copper atoms in 13.2 mol of copper is 7.94×1024 atoms. This is determined by using the molar mass of copper (63.55 g/mol) to convert moles to grams, and then using Avogadro’s number (6.022×1023 atoms/mol) to convert from grams to atoms.*

## Introduction

Copper is an abundant metallic chemical element that has been used for centuries in a wide array of applications, from decorative architecture to electrical wiring. It has an atomic number of 29, meaning each copper atom contains 29 protons. The mass of a single copper atom is 63.55 atomic mass units.

In chemistry, we can use the mole concept to relate an easily measured quantity like mass to the atomic scale. The mole allows us to work with manageable macroscopic amounts of substances while still tracking the number of individual atoms involved in quantitative chemical calculations.

In this blog post, we’ll go through the steps to determine the number of copper atoms present in a sample of 13.2 moles of copper. We’ll use fundamental chemical concepts like molar mass and Avogadro’s number to bridge the scale from laboratory measurements to the atomic level.

## Defining the Mole

The mole is a standard unit in chemistry defined as the amount of a substance containing 6.022×1023 constituent particles, which may be atoms, molecules, ions, or electrons. This number 6.022×1023 is known as Avogadro’s constant.

For atomic and molecular substances, counting out individual atoms or molecules is an impractical task. But the mole gives chemists a way to relate a measurable property like mass to the number of particles in the sample. Using the mole, macroscopic masses can be easily converted into numbers of atoms and molecules.

## Molar Mass

The molar mass of an element or compound gives the mass in grams of one mole of that substance. It provides the conversion between mass and amount in moles. For copper, the molar mass can be calculated from its atomic mass:

Atomic mass of copper = 63.55 amu 1 amu = 1 g/mol Therefore, molar mass of copper = 63.55 g/mol

So the mass of one mole of copper atoms is 63.55 grams. The molar mass allows us to convert back and forth between mass in grams and amount in moles.

## Avogadro’s Number

As mentioned earlier, the number 6.022×1023 particles per mole is called Avogadro’s constant or Avogadro’s number, after Amedeo Avogadro. Since one mole contains 6.022×1023 entities, Avogadro’s number links amount in moles to number of particles.

Some comparisons provide perspective on just how large Avogadro’s number really is:

- There are roughly 7.5 billion people on Earth. Avogadro’s number is equivalent to 800 billion Earth populations.
- A single mole contains as many particles as there are stars in 3000 Milky Way galaxies.
- If you could count one atom per second, it would take about 19 billion years to count to Avogadro’s number.

Avogadro’s number provides an essential connection between macroscopic measurements and the microscopic world of atoms and molecules.

## Calculating Atoms from Moles

Now we can put together the mole concepts to determine the number of copper atoms present in 13.2 mol of copper.

Step 1) Use molar mass to convert moles of Cu to mass in grams: 13.2 mol Cu x (63.55 g Cu/mol) = 838.86 g Cu

Step 2) Use Avogadro’s number to convert from grams Cu to number of Cu atoms: 838.86 g Cu x (6.022×1023 atoms Cu/mol) = 5.06×1025 atoms Cu

Therefore, 13.2 mol of copper contains 5.06×1025 copper atoms. That’s over 500 billion trillion individual copper atoms! By leveraging the mole and Avogadro’s number, we can easily relate macroscopic amounts of substances to the underlying atomic world.

## Conclusion

The mole provides chemists with a convenient way to work with massive numbers of atoms and molecules using easily measured laboratory quantities like mass. By combining molar mass and Avogadro’s constant, we can convert between the mass of a sample and the number of constituent particles it contains. These fundamental concepts are essential for quantitative work and calculations in chemistry. Understanding mole calculations allows us to toggle between the real-world measurements and the atomic-scale properties of matter.

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