Understanding Average Atomic Mass and Avogadro's Number

Introduction to Average Atomic Mass

• Concept: Average atomic mass gives an idea of mass at an atomic or molecular level.
• Application: Useful for understanding mass in chemistry labs.

From Atomic Mass to Real-World Masses

• Challenge: Transition from atomic to lab scale where substances are measured in grams.
• Solution: Use Avogadro's number to relate atomic mass to grams.

Avogadro's Number

• Defined as 6.02214076 x 10^23 atoms per mole.
• Allows conversion from atomic mass units to grams.
• Example with Lithium:
  • Average atomic mass = 6.94 unified atomic mass units.
  • If you have Avogadro's number of lithium atoms, the mass will be 6.94 grams.

The Mole Concept

• Definition: A mole is equivalent to Avogadro's number of entities (atoms, molecules).
• Analogy: Similar to a dozen, but much larger (6.022 x 10^23).
• Origin: Named by Wilhelm Ostwald, related to 'molecule'.

Practical Application: Calculating Atoms in a Sample

• Scenario: Calculate atoms in a 15.4 mg sample of Germanium.

Step-by-Step Calculation

1. Convert Milligrams to Grams:

   • 15.4 mg = 0.0154 grams (divide by 1000).

2. Convert Grams to Moles:

   • Germanium's molar mass: 72.63 grams/mole.
   • Calculation: ( \text{moles of germanium} = \frac{0.0154}{72.63} ).

3. Convert Moles to Atoms:

   • Multiply moles by Avogadro's number.
   • Formula: ( \text{atoms} = \text{moles} \times 6.022 \times 10^{23} ).

4. Significant Figures:

   • Result: 1.28 x 10^20 atoms of Germanium (rounded to three significant digits).

Conclusion

• The use of Avogadro's number and the concept of a mole allow chemists to transition between the atomic scale and laboratory measurements efficiently.