Overview
This lecture explains how to calculate the average (weighted) atomic mass of elements using isotope abundances and masses, with worked examples for carbon, lead, and uranium.
Atomic Mass and Isotopes
- The atomic mass shown on the periodic table is a weighted average of all naturally occurring isotopes of that element.
- Weighted average means isotopes contribute to the atomic mass in proportion to their natural abundance.
- Isotopes are atoms of the same element with different numbers of neutrons.
Formula for Average Atomic Mass
- The formula: Atomic mass = Σ (abundance × mass) for all isotopes.
- Abundance must be expressed as a decimal (not percent); convert by moving the decimal two places left.
- Known as fractional or standard abundance.
Example 1: Carbon
- Only consider stable isotopes: carbon-12 and carbon-13.
- Convert abundances from percent: 98.93% → 0.9893; 1.07% → 0.0107.
- Calculation: (0.9893 × 12.0000) + (0.0107 × 13.0033) = 12.01 (rounded to correct sig figs).
- Check answer against periodic table value (~12.011).
Example 2: Lead
- Lead has four stable isotopes; convert all given abundances to decimals.
- Add each isotope’s (abundance × mass) result.
- Apply correct sig fig rules for multiplication and addition.
- Sum to get average atomic mass for lead: ~207 amu (atomic mass units).
Example 3: Uranium
- Abundances provided as decimals; no conversion needed.
- Three main isotopes considered: uranium-234, -235, -238.
- Multiply each abundance by its mass, add results.
- Round according to significant figures for a final atomic mass close to 238.
Atomic Mass Unit (AMU)
- 1 amu = 1/12 the mass of a carbon-12 atom.
- AMU is nearly the mass of a proton or a neutron.
- Used for convenience in expressing atomic and isotopic masses.
Mass Defect
- Slight difference between the isotope’s mass number and actual atomic mass is called mass defect.
- Mass defect arises because binding energy (strong nuclear force) affects nuclear mass.
- For basic chemistry, always use measured atomic masses, not whole number mass numbers.
Key Terms & Definitions
- Isotope — Atoms of the same element with different numbers of neutrons.
- Abundance — Fraction of an element’s atoms that are a particular isotope.
- Weighted Average — Average that accounts for the relative abundances of isotopes.
- Atomic Mass Unit (AMU) — A unit equal to 1/12 the mass of a carbon-12 atom.
- Mass Defect — The small difference between an isotope’s mass number and its actual atomic mass due to nuclear binding energy.
- Strong Nuclear Force — The force that holds protons and neutrons together in the nucleus.
Action Items / Next Steps
- Practice converting isotope abundance percentages to decimals.
- Calculate average atomic mass for elements given isotope data.
- Review and memorize key terms and the atomic mass formula.