123 123Calculator

Average Atomic Mass Calculator

No chlorine atom weighs 35.45 — three quarters weigh 35 and a quarter weigh 37.

Clear
Average atomic mass35.45293weighted by natural abundance. THIS is why atomic weights are not whole numbers
Isotope 1 contributes26.492434.96885 × 75.76%
Isotope 2 contributes8.9605336.9659 × 24.24%
Abundances entered100%which sums to 100, as it should
Nearest whole number35the average sits 0.4529 from it. For elements with one dominant isotope the gap is tiny; for chlorine or bromine it is large
The chlorine example75.76% of 34.969 + 24.24% of 36.966 = 35.45no chlorine atom weighs 35.45. Three quarters weigh 35 and a quarter weigh 37, and the average is what you get when you weigh a bottle of it
Why the weights driftisotope ratios vary by sourceIUPAC now gives intervals rather than single values for a dozen elements, because terrestrial samples genuinely differ. Lithium varies enough to matter in careful work

The formula

average = Σ (isotope mass × abundance) ÷ Σ abundance

Nobody's chlorine weighs 35.45

Roughly three quarters of natural chlorine is chlorine-35 and a quarter is chlorine-37.

The weighted mean is 35.45, and it describes a bottle rather than an atom. Every individual atom weighs close to 35 or close to 37 and none weighs the average.

Some weights are now intervals

IUPAC publishes ranges rather than single values for about a dozen elements, because the isotope ratio genuinely varies with the source.

Lithium from different deposits differs enough that the standard weight is given as an interval, and precise work has to specify where the material came from.

Ideal behaviour is an approximation

The colligative and gas relations here assume dilute solutions and ideal gases, which real systems approach and do not reach.

At high concentration or high pressure the deviations become large, and the corrections are substance-specific. These figures are right where the assumptions hold and approximate where they do not.