The Average Atomic Mass Formula
Average atomic mass is a weighted average: each isotope counts in proportion to how common it is. Average atomic mass = Σ (isotope mass × fractional abundance), where each fractional abundance is the percent divided by 100 and all of them add to 1. For chlorine, 34.969 × 0.7578 + 36.966 × 0.2422 = 26.50 + 8.95 = 35.45 amu, the value printed on the AP periodic table. The concept is explained with more worked problems in AP Chemistry average atomic mass, and the notation for individual isotopes in isotope notation.
How to Find Average Atomic Mass From a Mass Spectrum
A mass spectrum of an element has one peak per isotope. The horizontal position of a peak is the isotope’s mass and its height is its relative abundance. Some spectra label heights as percents that add to 100; others scale the tallest peak to 100. Either way, enter the heights as they appear. The calculator divides each by the total, so boron’s peaks at 10.013 (height 24.8) and 11.009 (height 100) become 19.9% and 80.1%, for an average of 10.81 amu. On the AP exam you may also be asked to go the other way and identify an element from its spectrum: compare the average with the periodic table, which the calculator does for you. Practice reading spectra in mass spectrometry practice problems.
How to Find Percent Abundance From Average Atomic Mass
For an element with two isotopes, one unknown is enough. Let x be the fraction of isotope 1, so isotope 2 is 1 − x. Then average = m1x + m2(1 − x), which rearranges to x = (average − m2) ÷ (m1 − m2). Copper’s isotopes have masses 62.930 and 64.928, and its average is 63.55, so x = (63.55 − 64.928) ÷ (62.930 − 64.928) = 0.690: about 69% copper-63 and 31% copper-65. Choose “Find the percent abundances” above to solve these.
How to Check an Average Atomic Mass Answer
- It must lie between the lightest and heaviest isotope. An average outside that range means a calculation error.
- It must be closest to the most abundant isotope. Copper is mostly copper-63, so 63.55 is nearer 63 than 65.
- It should match the periodic table to about two decimal places when you use natural abundances.
Questions like these open the AP Chemistry Unit 1 practice test, and the Unit 1 FRQ practice starts with chlorine’s average atomic mass. Average atomic mass is also the molar mass you use in every mole calculation, which the molar mass calculator applies to whole compounds. To turn practice results into a predicted 1–5 score, use the AP Chem Score Calculator.
Related Resources
- AP Chem Score Calculator
- All AP Chemistry Calculators
- AP Chemistry Average Atomic Mass
- AP Chemistry Mass Spectrometry Practice Problems
- AP Chemistry Isotope Notation
- Molar Mass Calculator
- Unit 1 Review: Atomic Structure and Properties
Frequently Asked Questions
How do you calculate average atomic mass?
Multiply the mass of each isotope by its fractional abundance (the percent divided by 100), then add the products. For chlorine, (34.969)(0.7578) + (36.966)(0.2422) = 35.45 amu, the value on the periodic table.
How do you find average atomic mass from a mass spectrum?
Each peak gives an isotope mass (its position) and a relative abundance (its height). If the heights do not already add to 100, divide each height by their sum to get its fraction, then take the weighted average. This calculator does the conversion when you enter the peak heights directly.
How do you find percent abundance from average atomic mass?
For an element with two isotopes, let x be the fraction of the first. Then average = (mass 1)x + (mass 2)(1 - x), so x = (average - mass 2) / (mass 1 - mass 2). For copper, (63.55 - 64.928) / (62.930 - 64.928) = 0.690, so copper-63 is about 69%.
Why is average atomic mass not a whole number?
It is a weighted average of the isotopes found in nature, and each isotope's mass is itself close to, but not exactly, a whole number. Chlorine is about three-quarters chlorine-35 and one-quarter chlorine-37, so its average, 35.45, falls between them and closer to 35.
Is average atomic mass the same as molar mass?
Numerically, yes. An average atomic mass of 35.45 amu per atom means a molar mass of 35.45 grams per mole of atoms, which is why the periodic table value is used in mole calculations.
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