Understanding Relative Atomic Mass and Weighted Average

Introduction

• Discussion on the concept of relative atomic mass and atomic weight.
• Use of a thought question involving the average weight of pickup trucks.

Example Scenario: Rodeo Pickup Trucks

• Two types of Rodeo pickup trucks:
  • Rodeo Clown: Weighs 5,000 lb.
  • Rodeo Cowboy: Weighs 20,000 lb.
• Initial approach to find average weight:
  • Add weights: 5,000 lb + 20,000 lb.
  • Divide by two: ((5,000 + 20,000) / 2 = 12,500) lb.
  • This calculation assumes equal numbers of both types.

Real-World Consideration

• Usage statistics:
  • 20% of Rodeo pickups are Rodeo Clown.
  • 80% of Rodeo pickups are Rodeo Cowboy.
• This changes the average calculation as it does not assume equal distribution.

Weighted Average Calculation

• Importance of calculating a weighted average:
  • Reflects the actual distribution of the trucks.
  • Account for the larger number of Rodeo Cowboys on the road.
• Calculation steps:
  • Multiply the weight of each truck by its respective percentage:
    • Rodeo Clown: 5,000 lb (\times) 0.20
    • Rodeo Cowboy: 20,000 lb (\times) 0.80
  • Sum these values to find the weighted average.
• Result:
  • Weighted average is closer to the weight of the Rodeo Cowboy due to greater prevalence.

Conclusion

• Utilizing a weighted average gives a more accurate representation of the average truck weight on the road.
• This concept parallels the calculation of relative atomic mass, where isotopic abundance is considered.