Overview
This lecture explains isotopes, how to calculate average atomic mass using percent abundance, and how to determine the percent composition of isotopes in an element.
Isotopes: Key Concepts
- Isotopes are different versions of the same element with the same number of protons but different numbers of neutrons.
- Isotopes have the same atomic number but different masses.
- The atomic mass shown on the periodic table is the weighted average of all isotopes of an element.
Calculating Average Atomic Mass
- Convert percent abundance values to decimals by dividing by 100 (or moving the decimal left two places).
- Use the formula: average atomic mass = Σ (isotope fraction × isotope mass) for all isotopes.
- Add all the products together to get the average atomic mass.
- Round the final result to match the significant figures given in the percentages or masses.
Example Calculation: Average Atomic Mass
- For four isotopes: multiply each decimal abundance by its mass and add the results.
- Example: 0.005600 × 83.91343 + ... = 87.616626; rounded to 87.62 amu.
Determining Percent Abundance When Average Atomic Mass is Known
- Let the unknown percentage of one isotope be x; the other isotope is (1 − x).
- Set up the equation: average atomic mass = (x × mass₁) + [(1 − x) × mass₂].
- Distribute and solve for x through algebraic manipulation.
- Convert x and (1 − x) to percentages by multiplying by 100.
Example Calculation: Percent Abundance
- For copper isotopes: let x be percent abundance for Cu-63, (1 − x) for Cu-65.
- Solve the equation to find x = 0.6915 (69.15%) for Cu-63, and 1 − x = 0.3085 (30.85%) for Cu-65.
Key Terms & Definitions
- Isotope — Atoms of the same element with the same number of protons but different numbers of neutrons.
- Atomic Mass — The weighted average mass of all naturally occurring isotopes of an element.
- Percent Abundance — The percentage of a specific isotope present in a sample of an element.
Action Items / Next Steps
- Practice similar isotope abundance and average atomic mass problems to prepare for exams.
- Review calculation steps and ensure comfort with setting up and solving equations for percent abundance.