ChemGem

How to Calculate Average Atomic Mass (Step-by-Step, with Practice)

Most elements are a mix of isotopes. The periodic-table mass is their weighted average (the average atomic mass), so the more common isotope counts more.

Spot it, solve it, practice it: 4 steps, 1 worked example, 4 practice problems. Free, no account.

ChemGemUpdated Section 1.4

The route · 4 steps

  1. Turn each percentage into a decimal fraction.
  2. Multiply each isotope mass by its fraction.
  3. Add the contributions.
  4. Check: the answer lies closer to the most common mass.
Try one now See a worked example
Spot it

How to recognize average atomic mass questions

Look for isotope masses with percentages, or atoms with the same protons but different neutrons, and an "average mass" asked for.

Example wording, with the clue words marked:

Two atoms both contain 11 protons. One has 12 neutrons and the other 13. Which classification fits?

Not sure it’s this type? Compare the neighbors:

Step-by-step

Worked example: average atomic mass

The idea

Chlorine-35 and chlorine-37 both have 17 protons, but 18 versus 20 neutrons. A chlorine periodic-table card highlights average atomic mass 35.45.
Isotopes: same protons, different neutrons. The table mass (35.45 u) is an average, not a mass number.
Twelve chlorine-35 atoms at 34.969 u each and four chlorine-37 atoms at 36.966 u each. Add the masses of all atoms and divide by sixteen to find the average mass.
Add the masses of all 16 atoms, then divide by 16. The common isotope pulls the average toward itself.
Weighted average mass
average = (mass1 × fraction1) + (mass2 × fraction2) + …
fraction = percent100
75% = 0.75. The fractions add to 1, the whole sample.
The chlorine pile, as a weighted average
IsotopeProtonsNeutronsIsotope massFraction of pileContribution
Chlorine-35171834.969 u12/16 = 0.7526.23 u
Chlorine-37172036.966 u4/16 = 0.259.24 u
Average1.0035.47 u
Real chlorine (about 75.8% and 24.2%) gives the table’s 35.45 u.

On the periodic table: The decimal on each square is the weighted average atomic mass: chlorine (Cl) shows 35.45, with atomic number 17.

On the periodic table: Isotope masses and abundances are not on the table; the problem supplies them.

Worked example · 4 steps

A fictional element has isotope masses 30 u at 70% and 32 u at 30%. Find the average mass.

Isotope massAbundance
30 u70%
32 u30%
Fictional element: no real square, so use these supplied values.
  1. 1
    Turn percentages into fractions

    Divide each by 100. The fractions add to 1.

    70100 = 0.70    30100 = 0.30
  2. 2
    Weight the first isotope

    It contributes more because it is more common.

    30 u × 0.70 = 21.0 u
  3. 3
    Weight the second isotope

    Include the less common isotope too.

    32 u × 0.30 = 9.6 u
  4. 4
    Add the contributions

    Together they give the average mass.

    21.0 u + 9.6 u = 30.6 u
    30 u31 u32 u70%30%30.6 uweighted averagemidpoint, not the answer
  5. ✓
    Answer

    Average mass = 30.6 u

Your turn

Average atomic mass practice problems

Answer first, then check. Hints open one at a time; the answer and full solution open after you try.

Problem 1 of 4 · warm-up

Two atoms both contain 11 protons. One has 12 neutrons and the other 13. Which classification fits?

Hint 1 · the clue

Proton counts match but neutron counts differ.

Hint 2 · the next move

Same number of protons but different neutrons: that pattern defines isotopes of one element.

Your path:

  1. Same protons → same element
  2. Different neutrons → different mass numbers
  3. So they are isotopes
Answer

Answer: Different isotopes of one element

Full worked solution

What you know: both atoms have 11 protons; one has 12 neutrons and the other 13. What you want: how to classify them.

  1. Compare protons first. Protons identify the element. Both have 11, so both are the same element.
  2. Compare neutrons next. 12 and 13 differ, so their mass numbers differ: 11 + 12 = 23 and 11 + 13 = 24.
  3. Same protons with different neutrons is the definition of isotopes: Different isotopes of one element.

Why it matters: Isotopes behave almost the same chemically but have different masses, which is why the periodic table lists an average mass.

Watch out: Different neutron counts do not make different elements. Only a different proton count does.

Your route: Compare protons → Compare neutrons

11Na22.99On the periodic table: Sodium (Na) has atomic number 11, the whole number in its box, so both atoms are sodium.

Answer: Different isotopes of one element

Problem 2 of 4

A fictional element has isotopes 28 u (70%) and 30 u (30%). What is the average mass?

Hint 1 · the clue

Masses and abundances appear together.

Hint 2 · the next move

Isotope masses with percentages and "average mass" asked: that signals a weighted average.

Your path:

  1. Change each percent to a decimal
  2. Multiply each mass by its decimal
  3. Add the contributions
Answer

Answer: 28.6 u

Full worked solution

What you know: isotopes of 28 u (70%) and 30 u (30%). What you want: the weighted average mass.

  1. Change each percent to a fraction: 70% = 0.70 and 30% = 0.30. They add to 1.00.
  2. Weight each isotope: 28 u × 0.70 = 19.6 u and 30 u × 0.30 = 9.0 u.
  3. Add the contributions: 19.6 u + 9.0 u = 28.6 u.

Check: The average must sit between 28 and 30, and closer to 28 because that isotope is more common. 28.6 fits.

Watch out: Don't just take the plain middle (29 u). That ignores which isotope is more common.

Your route: Percent to fraction → Multiply each mass → Add

Answer: 28.6 u

Problem 3 of 4

A fictional element has isotopes 50 u (60%) and 52 u (40%). What is the average mass?

Hint 1 · the clue

Masses and abundances appear together.

Hint 2 · the next move

Isotope masses with percentages and "average mass" asked: that signals a weighted average.

Your path:

  1. Change each percent to a decimal
  2. Multiply each mass by its decimal
  3. Add the contributions
Answer

Answer: 50.8 u

Full worked solution

What you know: isotopes of 50 u (60%) and 52 u (40%). What you want: the weighted average mass.

  1. Change each percent to a fraction: 60% = 0.60 and 40% = 0.40. They add to 1.00.
  2. Weight each isotope: 50 u × 0.60 = 30.0 u and 52 u × 0.40 = 20.8 u.
  3. Add the contributions: 30.0 u + 20.8 u = 50.8 u.

Check: The average must sit between 50 and 52, and closer to 50 because that isotope is more common. 50.8 fits.

Watch out: Don't just take the plain middle (51 u). That ignores which isotope is more common.

Your route: Percent to fraction → Multiply each mass → Add

Answer: 50.8 u

Problem 4 of 4

Isotopes of 10 u and 12 u are each 50%. Average?

Hint 1 · the clue

Turn each percentage into a fraction, multiply it by that isotope’s mass, and add the contributions.

Hint 2 · the next move

Isotope masses with percentages and "Average?" asked: that signals a weighted average.

Your path:

  1. Change each percent to a decimal
  2. Multiply each mass by its decimal
  3. Add the contributions
Answer

10(0.50) + 12(0.50) = 11.0 u.

Full worked solution

What you know: isotopes of 10 u and 12 u, each 50%. What you want: the average mass.

  1. Change each percent to a fraction: 50% = 0.50.
  2. Weight each isotope: 10 u × 0.50 = 5.0 u and 12 u × 0.50 = 6.0 u.
  3. Add the contributions: 5.0 u + 6.0 u = 11.0 u.

Check: With equal amounts, the average lands exactly halfway between 10 and 12.

Answer: 10(0.50) + 12(0.50) = 11.0 u.

Watch out

Common average atomic mass mistakes