Understanding Isotopes and Percent Abundance

Introduction

• Lecture by Melissa Maribel on isotopes and calculating percent abundance.
• Goal: To help students understand concepts for easier learning and faster graduation.

Isotopes

• Definition:
  • Isotopes are different versions of the same element.
  • Example: Different weights of the same person over the years.
• Chemistry Context:
  • Gold (Au) has isotopes with different atomic masses: 196 AMU, 197 AMU, and 198 AMU.
  • All isotopes have the same atomic number (protons, electrons) but different masses (varying neutrons).

Average Atomic Mass Calculation

• Example Element X with four isotopes:
  1. 0.5600% - mass: 83.91343 AMU
  2. 9.860% - mass: 85.90927 AMU
  3. 7.000% - mass: 86.90890 AMU
  4. 82.58% - mass: 87.90562 AMU
• Percent Abundance: The percentage of each isotope in the sample.
• Steps for Calculation:

  1. Convert percentages to decimals by dividing by 100 or moving the decimal two places left.

  2. Use the percent abundance formula:

     [ \text{Atomic Mass} = (\text{Percent in Decimal}) \times (\text{Mass of Isotope}) ]

  3. Multiply and sum for all isotopes.

Example Calculation

• For the first isotope:
  • [ 0.005600 \times 83.91343 = 0.4699915 ]
• Repeat for all isotopes.
• Sum of Atomic Masses:
  • Result: 87.616626 AMU
• Rounding:
  • Round to four significant figures based on initial data.
  • Final atomic mass: 87.62 AMU.

Percent Composition of Copper

• Isotopes of Copper:
  • Copper-63: 62.9296 AMU
  • Copper-65: 64.9278 AMU
• Given average atomic mass: 63.546 AMU.
• Finding Percent Abundance:
  1. Set equation using unknown percentage (X) for Copper-63.
  2. Use the formula for average atomic mass considering both isotopes:
     • Copper-63:
       [ X \times 62.9296 ]
     • Copper-65:
       [ (1-X) \times 64.9278 ]
  3. Simplify and solve for X.

Example Calculation

• Set up the equation:
  • [ 63.546 = (X \times 62.9296) + ((1-X) \times 64.9278) ]
• Rearrange and simplify to find value for X (Copper-63):
  • Result: 0.6915 (or 69.15%)
• For Copper-65:
  • Result: 0.3085 (or 30.85%)

Conclusion

• Practice problems are key for exam preparation.
• Melissa encourages students to practice to solidify concepts.
• Reminder to seek tutoring if needed and to check for available sessions.
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