Understanding Atoms and Calculating Their Numbers in Objects

Key Concepts

• Atoms are extremely tiny.
• Calculating the number of atoms in macroscopic objects involves the mass of a substance and its molar mass.

Example: Helium Balloon

• Scenario: Calculating the number of helium atoms in a balloon.
• Given:
  • 0.3 grams of helium in the balloon.
  • Molar mass of helium: 4 grams/mole.
• Steps to Calculate Number of Helium Atoms:
  1. Convert mass to moles:
     • Formula: ( \text{moles of helium} = \frac{0.3\text{g}}{4\text{g/mol}} )
     • Result: 0.078 moles of helium.
  2. Use Avogadro's number ((6.022 \times 10^{23})) to find the number of atoms:
     • (0.078\text{moles} \times 6.022 \times 10^{23} = 4.7 \times 10^{22}) helium atoms.
  • The balloon contains approximately 50 billion trillion helium atoms.

Example: Xenon Balloon

• Scenario: Calculate the mass of a balloon with 3.2 (\times 10^{21}) xenon atoms.
• Steps to Calculate:
  1. Convert number of atoms to moles:
     • Formula: ( \text{moles of xenon} = \frac{3.2 \times 10^{21}}{6.022 \times 10^{23}} )
     • Result: 0.0053 moles of xenon.
  2. Calculate mass using xenon's molar mass (131.35 g/mol):
     • (0.0053\text{moles} \times 131.35\text{g/mol} )
     • Result: Mass is more than twice that of the helium balloon.

Conclusion

• Even though there are fewer xenon atoms, the mass of xenon is greater due to its higher molar mass.
• Understanding and converting between mass and number of particles can help determine the amount of a substance at an atomic level.