Average Atomic Mass from Abundances

No single chlorine atom weighs 35.45 amu. Every chlorine atom is either Cl-35 or Cl-37, each with its own whole-number-ish mass. The 35.45 on the periodic table is a population average: if you grabbed a huge sample of natural chlorine atoms and averaged their masses, 35.45 is what you'd get, because Cl-35 shows up far more often than Cl-37.

The calculation is a weighted average, not a plain average. You multiply each isotope's mass by its fractional abundance (percent divided by 100), then add the results. Because the more abundant isotope gets multiplied by a bigger fraction, it pulls the final answer closer to itself. That's why chlorine's average, 35.45 amu, sits much closer to 35 than to 37: roughly three-quarters of all chlorine atoms are the lighter isotope, so the lighter mass dominates the sum.

This idea connects directly to the mole concept that follows. Average atomic mass is what lets a single number on the periodic table stand in for a real mixture of isotopes, so that grams of an element can be converted to moles of atoms without tracking every isotope separately. It also sets up isotope abundance problems where the mass is known and you solve backward for the missing percentages, using algebra on the same weighted-average equation.