Chapter 4 · Atoms and Elements
4.9Atomic Mass: The Average Mass of an Element's Atoms
12 min · two checks
Predict
If chlorine were half ³⁵Cl and half ³⁷Cl, what would the average atomic mass be, roughly?
The idea
- Compute a weighted average atomic mass from isotope masses and abundances.
- Explain why the table does not list a whole number.
The atomic mass on the periodic table is a weighted average over the naturally occurring isotopes, measured in atomic mass units (u). Multiply each isotope’s mass by its fractional abundance and add. If ⁷⁵% of atoms have mass 20.0 u and 25% have mass 22.0 u, the average is 0.75 × 20.0 + 0.25 × 22.0 = 20.5 u. The more abundant isotope pulls the average toward itself.
Percent abundances must be turned into fractions (divide by 100) before you multiply, unless you divide the whole sum by 100 at the end. Do not average the mass numbers and ignore abundances. Do not round the average back to a whole number; the decimal is the data. This average, in grams per mole, will become the molar mass in Chapter 6. Same number, different unit job.
Keep these
- Atomic mass = Σ (fractional abundance × isotope mass).
- The abundant isotope dominates the average.
- Convert percent to a fraction before multiplying.
Worked path
Boron is 19.9% ¹⁰B (10.013 u) and 80.1% ¹¹B (11.009 u). Estimate the atomic mass.
Observe
Two isotopes with percent abundances.