Overview
This lecture covers the calculation of average atomic mass using isotopic masses and abundances, with worked examples for Gallium, Rubidium, and Magnesium.
Calculating Average Atomic Mass
- Average atomic mass is the weighted average of an element's isotopes based on their relative abundances.
- Formula: (mass₁ × abundance₁) + (mass₂ × abundance₂) + ... for all isotopes.
- Abundance must be expressed as a decimal (percent divided by 100).
Example: Gallium
- Gallium has two isotopes: Gallium-69 (68.926 amu, 60.11%) and Gallium-71 (70.925 amu, 39.89%).
- Calculation: (68.926 × 0.6011) + (70.925 × 0.3989) = 69.72 amu.
- The average atomic mass is closer to Gallium-69 due to its higher abundance.
Example: Rubidium
- Rubidium has two isotopes: Rubidium-85 (84.911 amu) and Rubidium-87 (86.909 amu).
- Atomic mass from the periodic table is 85.47 amu.
- Since 85.47 is closer to 85, Rubidium-85 is more abundant than Rubidium-87.
Example: Magnesium
- Magnesium has three isotopes: Magnesium-24 (23.985 amu, 78.99%), Magnesium-25 (24.9586 amu, 10.00%), Magnesium-26 (25.983 amu, 11.0%).
- Calculation: (23.985 × 0.7899) + (24.9586 × 0.1000) + (25.983 × 0.110) = 24.31 amu.
Key Terms & Definitions
- Isotope — atoms of the same element with different numbers of neutrons and masses.
- Abundance — the relative proportion of an isotope found in nature, usually given as a percentage.
- Average atomic mass — the weighted mean of all isotopic masses of an element, based on their abundances.
- Respectively — in the same order as previously mentioned items.
Action Items / Next Steps
- Practice calculating average atomic mass for elements with given isotopic data.
- Review the periodic table to check reported average atomic masses.