Unit 1 Atomic Structure and Properties

AP Chemistry Average Atomic Mass

What atomic mass means, how to calculate the weighted average from isotope data, and how to work backward to an unknown abundance, in four worked examples.

The atomic mass under each element on the periodic table is not the mass of any single atom. It is an average over the element's isotopes, and the AP exam asks for it in two forms: calculate it from masses and abundances, or use it to find an abundance. The calculation is the same whether the data come from a table or from a mass spectrum. The spectrum version is in mass spectrometry practice problems; this page starts from the definitions and a table of abundances, and uses isotope notation to keep the terms straight.

Atomic Number, Mass Number, and Atomic Mass: What Each One Means

Atomic number (Z): the number of protons. It identifies the element.
Mass number (A): protons plus neutrons in one isotope. It is a whole number, such as 35 for chlorine-35.
Isotope mass: the measured mass of one isotope in atomic mass units (amu), close to its mass number but not equal, for example 34.969 amu for chlorine-35.
Average atomic mass: the abundance-weighted average of all of an element's isotope masses, the value printed on the periodic table.

Average atomic mass = Σ (isotope mass × fractional abundance). The fractional abundance is the percent divided by 100, and the fractions must add to 1. The chart shows three elements: the average always falls between the lightest and heaviest isotope, nearer the more abundant one.

Fig. 1 · The average sits near the more abundant isotope

Worked Example 1: Calculating the Average Atomic Mass of Chlorine

Chlorine has two isotopes: chlorine-35 (34.969 amu, 75.77%) and chlorine-37 (36.966 amu, 24.23%). Calculate the average atomic mass.

Fractions: 75.77% = 0.7577 and 24.23% = 0.2423.
Products: 0.7577 × 34.969 = 26.50 and 0.2423 × 36.966 = 8.957.
Sum: 26.50 + 8.957 = 35.45 amu.

The answer matches the periodic table, and it sits near 35 because the lighter isotope is three times as abundant. If a problem gives only the mass numbers 35 and 37, the same method gives 0.7577(35) + 0.2423(37) = 35.48, which is acceptable when the isotope masses are not provided. Keep the significant figures consistent with the data.

Worked Example 2: Finding an Unknown Isotope Abundance for Boron

Boron's average atomic mass is 10.81 amu. Its two isotopes are boron-10 (10.013 amu) and boron-11 (11.009 amu). Find the percent abundance of each.

Let x be the fractional abundance of boron-10, so boron-11 is 1 − x.
Equation: 10.013x + 11.009(1 − x) = 10.81.
Solve: 11.009 − 0.996x = 10.81, so x = 0.199/0.996 = 0.200.
Answer: boron-10 is 20.0% and boron-11 is 80.0%.

The sum of abundances equals 1, which supplies the second equation. A sensible check is that the average, 10.81, is much closer to 11.009 than to 10.013, so most boron should be the heavier isotope, as the result shows.

Worked Example 3: Estimating Which Isotope Is More Abundant Without Calculating

Lithium has isotopes of mass number 6 and 7, and its average atomic mass is 6.94. Bromine has isotopes of mass number 79 and 81, and its average is 79.90. Which isotope is more abundant in each?

Lithium: 6.94 is almost at 7, so lithium-7 is far more abundant. The average falls about 94% of the way from 6 to 7, so lithium-7 is about 94% abundant (the actual value is 92.4%).
Bromine: 79.90 is almost exactly halfway between 79 and 81, so the two isotopes are about equally abundant.

For two isotopes, the position of the average between them is roughly the abundance of the heavier isotope. This is a fast way to check a calculated answer or to answer a conceptual question about a spectrum, such as which peak should be taller. It uses the same reasoning as any mass number comparison.

Worked Example 4: Averaging Three Isotopes of Magnesium

Magnesium-24 (23.985 amu) is 78.99%, magnesium-25 (24.986 amu) is 10.00%, and magnesium-26 (25.983 amu) is 11.01%. Find the average atomic mass.

Mg-24: 0.7899 × 23.985 = 18.95
Mg-25: 0.1000 × 24.986 = 2.499
Mg-26: 0.1101 × 25.983 = 2.861
Sum: 18.95 + 2.499 + 2.861 = 24.31 amu.

The method extends to any number of isotopes: one product per isotope, then add. The average, 24.31, sits just above the lightest isotope because that isotope is nearly 80% of the total. The result is also the atomic mass used when you find the molar mass of a compound containing magnesium.

Five Average Atomic Mass Practice Questions With Answers

Gallium has gallium-69 (68.926 amu, 60.11%) and gallium-71 (70.925 amu, 39.89%). Find the average atomic mass.
Show answer
0.6011(68.926) + 0.3989(70.925) = 41.43 + 28.29 = 69.72 amu.
Pretend an element has only two isotopes, with mass numbers 20 and 22, and an average atomic mass of 20.18. Estimate the percent abundance of the heavier isotope.
Show answer
The average is (20.18 − 20)/(22 − 20) = 0.09 of the way from 20 to 22, so the heavier isotope is about 9% and the lighter one about 91%.
An element has isotopes of mass number 63 and 65 and an average atomic mass of 63.55. Which isotope is more abundant, and how do you know?
Show answer
The isotope of mass number 63, because 63.55 is closer to 63 than to 65.
Silicon has isotopes at 27.977 amu (92.23%), 28.976 amu (4.68%), and 29.974 amu (3.09%). Find the average atomic mass.
Show answer
0.9223(27.977) + 0.0468(28.976) + 0.0309(29.974) = 25.80 + 1.356 + 0.926 = 28.09 amu.
Why is the atomic mass on the periodic table usually not a whole number?
Show answer
It is a weighted average over isotopes with different mass numbers, and each isotope's actual mass is also slightly different from its whole-number mass number.

Common Average Atomic Mass Mistakes

Taking a plain average of the isotope masses. It must be weighted by abundance.
Using percent instead of a fraction. Divide each percent by 100 first, or divide the final sum by 100.
Abundances that do not add to 1. In a reverse problem, write the second isotope as 1 − x.
Confusing mass number and atomic mass. The mass number is a whole number of particles; atomic mass is a measured mass in amu.
Reporting an average outside the range of the isotopes. The result must lie between the lightest and heaviest isotope.
Rounding the isotope masses too early. Round only the final answer.

Average atomic mass questions are short, and the checks above catch most errors. To see how a stronger Unit 1 would shift your overall estimate, the AP Chem Score Calculator turns section scores into a 1–5 range.

Frequently Asked Questions

What is average atomic mass?

Average atomic mass is the weighted average of the masses of an element's naturally occurring isotopes, weighted by their relative abundances. It is the number printed under each element's symbol on the periodic table, in atomic mass units (amu).

How do you calculate average atomic mass?

Convert each percent abundance to a decimal, multiply it by that isotope's mass, and add the results: average atomic mass = Σ(mass × fractional abundance).

What is the difference between mass number and atomic mass?

The mass number is a whole number, the count of protons plus neutrons in one isotope. Atomic mass is the actual mass of an atom in amu, and the average atomic mass on the periodic table is a weighted average over all the isotopes, which is why it is usually not a whole number.

Why is the atomic mass on the periodic table not a whole number?

Because it averages several isotopes with different mass numbers, weighted by abundance, and because an isotope's actual mass is slightly different from its mass number.

How can you tell which isotope is more abundant from the average atomic mass?

The average lies closer to the mass of the more abundant isotope. If an element's average is 35.45 and its isotopes are about 35 and 37, the lighter isotope is the more abundant one.

This page is not affiliated with or endorsed by College Board. AP® is a trademark registered by the College Board.