Lecture Notes: Calculating Percentage Abundance from Two Isotopes

Topic: Percentage Abundance Calculation

• Objective: Determine the percentage abundance of copper isotopes, Cu 63 and Cu 65.
• Given: Average relative atomic mass of copper is 63.55.

Concept Overview

• Isotopes in Focus:
  • Cu 63
  • Cu 65
• Key Principle:
  • The percentage abundance of the isotopes must add up to 100%.

Problem Statement

• Question: Given the average relative atomic mass of copper is 63.55, calculate the percentage abundance of Cu 63 and Cu 65.

Solving the Problem

Assumptions

• Let x be the percentage abundance of Cu 63.
• Then the percentage abundance of Cu 65 will be 100 - x.

Equation Setup

• Use the formula for average atomic mass:

  [\frac{x}{100} \times 63 + \frac{100 - x}{100} \times 65 = 63.55]

Solving the Mathematics

1. Eliminate Denominator:

   • Multiply the entire equation by 100:

     [63x + 65(100 - x) = 6355]

2. Simplification:

   • Expand the equation:

     [63x + 6500 - 65x = 6355]

3. Combine Like Terms:

   • Rearrange terms to isolate x:

     [-2x = -145]

4. Solve for x:

   • [x = 72.5]

5. Calculate Cu 65:

   • 100 - 72.5 = 27.5

Answer

• Cu 63 Percentage Abundance: 72.5%
• Cu 65 Percentage Abundance: 27.5%

Conclusion

• The percentages add up to 100%, confirming the solution is correct.
• Key Insight: The calculation is primarily mathematical once the chemical principles are established.

Summary

• Methodology: Establish assumptions, set up and simplify the equation, solve for unknowns.
• Result: Cu 63 = 72.5%, Cu 65 = 27.5%.