Chemistry / Unit 2 Chem 0241 worked example, 60 to 90 seconds
Calculating Isotopic Abundance from Average Atomic Mass
The idea
Calculating isotopic abundance from an element's average atomic mass means setting one isotope's unknown fraction as x, writing the other as 1 minus x, and solving the weighted-average equation for x.
In practice
Chlorine's average mass is 35.453 u from two isotopes, chlorine-35 at 34.96885 u and chlorine-37 at 36.96590 u. Letting x be the fraction of chlorine-35, the equation 34.96885x + 36.96590(1 − x) = 35.453 solves to x ≈ 0.7576. So chlorine is about 75.76% chlorine-35 and, by subtracting from 1.00, about 24.24% chlorine-37. Checking the result by substituting back, 0.7576 × 34.96885 plus 0.2424 × 36.96590 gives approximately 35.453 u, confirming the abundances found.
Where people slip
Plugging the two isotope masses into the equation in the wrong order flips which percentage belongs to which isotope, even though the final average still checks out arithmetically.
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