A 7.8 gram copper coin contains approximately 7.39 × 10^22 atoms. This astonishingly large number highlights the microscopic scale of individual atoms.
Understanding the Calculation
To determine the number of atoms in a given mass of a substance, chemists use fundamental constants and properties specific to that material. The calculation involves three key pieces of information:
- Mass of the Substance: The total mass of the object in question.
- Molar Mass: The mass of one mole of a substance, expressed in grams per mole (g/mol). This value is unique for each element or compound. For copper, its atomic weight on the periodic table directly corresponds to its molar mass.
- Avogadro's Number: A fundamental constant representing the number of particles (atoms, molecules, ions, etc.) in one mole of any substance. It's a bridge between the macroscopic world (grams) and the microscopic world (atoms).
Key Data for a Copper Coin
Here's a breakdown of the values used in calculating the number of atoms in a 7.8-gram copper coin:
| Property | Value | Source |
|---|---|---|
| Mass of Copper Coin | 7.8 grams (g) | Specific example |
| Molar Mass of Copper | 63.5 grams per mole (g/mol) | PubChem |
| Avogadro's Number | 6.022 × 10^23 atoms per mole (atoms/mol) | National Institute of Standards and Technology (NIST) |
Step-by-Step Calculation
The process to find the number of atoms in the coin involves two main steps:
-
Calculate the Number of Moles:
- The number of moles (
n) is found by dividing the mass of the coin (m) by the molar mass of copper (M). - Formula:
n = m / M - Calculation:
n = 7.8 g / 63.5 g/mol ≈ 0.1228 moles
- The number of moles (
-
Calculate the Total Number of Atoms:
- Once the number of moles is known, multiply it by Avogadro's number (
N_A) to get the total number of atoms. - Formula:
Total Atoms = n × N_A - Calculation:
Total Atoms = 0.1228 mol × (6.022 × 10^23 atoms/mol) ≈ 7.39 × 10^22 atoms
- Once the number of moles is known, multiply it by Avogadro's number (
This calculation reveals that even a small, everyday object like a coin contains an unfathomably vast quantity of atoms, underscoring the minuscule size of individual atomic particles.
