Calculating Isotopic Abundance from Average Atomic Mass

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.

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.