Overview
This lecture explains how to calculate the average atomic mass of elements with multiple isotopes and determines isotope abundances using weighted averages.
Calculating Average Atomic Mass
- Multiply each isotope's mass by its percent abundance expressed as a decimal.
- Add the resulting values from all isotopes to get the average atomic mass.
- Example: Gallium 69 (68.926 amu × 0.6011) + Gallium 71 (70.925 amu × 0.3989) = 69.72 amu.
Interpreting Weighted Averages
- The average atomic mass is closer to the isotope with greater abundance.
- For Gallium, the average is closer to Gallium 69 because it is more abundant (60%) than Gallium 71 (40%).
Determining Most Abundant Isotope
- Compare the reported atomic mass to the masses of the isotopes.
- Whichever isotope’s mass the average is closest to is the more abundant isotope.
- Example: Rubidium’s average atomic mass (85.47 amu) is closer to Rubidium 85 (84.911 amu) than Rubidium 87 (86.909 amu), so Rubidium 85 is more abundant.
Calculating with Multiple Isotopes
- Apply the same process for elements with more than two isotopes.
- Example with Magnesium:
- Magnesium 24: 23.985 × 0.7899
- Magnesium 25: 24.9586 × 0.1000
- Magnesium 26: 25.983 × 0.110
- Add results to find average atomic mass (24.31 amu for Magnesium).
Key Terms & Definitions
- Isotope — Atoms of the same element with different numbers of neutrons.
- Atomic mass unit (amu) — Standard unit for atomic masses.
- Percent abundance — The percentage of a specific isotope among all isotopes of an element.
- Weighted average — An average that accounts for the relative abundances of values.
- Atomic mass/atomic weight/relative atomic mass — Terms used interchangeably for the weighted average mass of an element’s isotopes.
Action Items / Next Steps
- Practice calculating average atomic masses using given isotope data.
- Check calculated values against those on the periodic table for verification.