20. Average Atomic Mass: Working with Isotope Abundance

Lesson 2 taught you to read the atomic mass in an element's box. Here's where that number actually comes from: it's not the mass of one atom — it's a weighted average across every naturally occurring isotope of that element.

• Every isotope of an element contributes to the average in proportion to how common it is in nature — that's what "weighted" means. An isotope that makes up 90% of natural samples counts far more than one that makes up 1%.
• Worked example — chlorine: about 75.77% of natural chlorine is chlorine-35 (mass ≈ 34.97), and about 24.23% is chlorine-37 (mass ≈ 36.97).
• (0.7577 × 34.97) + (0.2423 × 36.97) ≈ 26.50 + 8.96 ≈ 35.45
• That matches the 35.45 you'd read directly off the periodic table for chlorine.
• Because it's a weighted average, the result is almost always closer to the more abundant isotope's mass — chlorine's average (35.45) sits much closer to chlorine-35's mass (34.97) than to chlorine-37's (36.97), because chlorine-35 is roughly three times more common.

This is also why atomic mass is rarely a clean whole number on the periodic table: it's an average across a natural mixture, not a count of particles in one atom.

⚠️ Common misconception: a listed atomic mass like 35.45 does not mean any single chlorine atom has 35.45 nucleons — every individual atom has a whole number of protons and neutrons. The decimal only appears because it's an average across many atoms of different isotopes.

💡 Tip: weighted average = (fraction₁ × mass₁) + (fraction₂ × mass₂) + …, and the answer always lands closest to whichever isotope is most abundant.

📚 Sources: OpenStax Chemistry 2e; IUPAC Periodic Table (standard atomic weights); CK-12 Physical Science.