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Atomic Mass

General Chemistry • Atoms

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Topic launch

Atomic mass is an average built from isotopes.

The mass shown on the periodic table is not usually the mass of one atom. It represents a weighted average of the naturally occurring isotopes of that element.

Learning target

Explain atomic mass, distinguish it from mass number, calculate weighted average atomic mass, and connect isotope abundance to periodic table values.

Isotope A lighter large abundance Isotope B heavier small abundance Periodic table 35.45 average Atomic mass depends on both isotope mass and isotope abundance.
Mass number: one isotope Atomic mass: weighted average Unit: atomic mass unit, amu

Why it matters

Atomic mass connects atoms to laboratory measurements.

Chemists use atomic mass to convert between particles and measurable mass. Without average atomic mass, formulas, molar masses, and quantitative chemistry would not match real samples.

Molar mass

The atomic mass of an element becomes its molar mass in g/mol when working with macroscopic samples.

Isotope evidence

Different isotope masses explain why many periodic table values are decimals instead of whole numbers.

Real samples

A natural sample contains many atoms, so the measured mass reflects isotope abundances, not just one isotope.

Isotopes different masses Weighted average uses abundance Molar mass mass of 1 mole Atomic mass is the bridge from atomic-scale isotope data to lab-scale calculations.

Core concept

The average is pulled toward the most abundant isotope.

If one isotope is much more common than another, the periodic table atomic mass will be closer to the mass of the common isotope.

Cl-35 about 75.8% Cl-37 about 24.2% Average atomic mass: about 35.45 amu Closer to 35 than 37 because Cl-35 is more abundant.

Model interpretation

  • Isotope mass tells where each isotope sits on the mass scale.
  • Abundance tells how strongly each isotope pulls the average.
  • Average atomic mass is the balance point of all isotope contributions.
A decimal atomic mass does not mean a single atom has a fractional number of protons or neutrons. It means a sample contains a mixture of isotopes.

Vocabulary and variables

Atomic mass problems are weighted-average problems.

The key is to keep the meaning of each number clear: isotope mass is a mass, abundance is a fraction or percent, and mass number is a particle count.

Term Meaning Typical unit or form Important note
Mass number, \(A\) Total protons plus neutrons in one isotope. Whole number Example: carbon-12 has \(A = 12\).
Isotope mass Measured mass of one isotope. amu Usually close to, but not exactly equal to, mass number.
Percent abundance Percent of atoms that are a given isotope in a natural sample. % Must be converted to a decimal fraction in calculations.
Average atomic mass Weighted average mass of naturally occurring isotopes. amu This is the value shown on the periodic table.

Atomic mass unit

One atomic mass unit, amu, is a very small mass unit used for atoms and isotopes.

Fractional abundance

For calculation, 75.77% becomes 0.7577, not 75.77.

Natural sample

The periodic table value assumes the natural isotope mixture for that element.

Main relationship

Average atomic mass is a weighted sum.

Each isotope contributes according to both its mass and how common it is.

\[ \text{average atomic mass} = \sum(\text{isotope mass})(\text{fractional abundance}) \]

Use fractional abundance, not percent abundance, inside the formula.

Two-isotope version

For two isotopes, use \( \bar{m} = m_1f_1 + m_2f_2 \), where \(f_1 + f_2 = 1\).

Interpretation

If \(f_1\) is large, isotope 1 has more influence. If \(f_2\) is small, isotope 2 pulls the average only slightly.

Mass amu for isotope × Fraction decimal abundance = Contribution to average add all isotope contributions The weighted average is not just the simple average unless abundances are equal.

Interactive isotope mixer

Change abundance and watch the average move.

This model uses chlorine-like isotopes. Move the slider to change how much of the sample is lighter isotope. The heavier isotope automatically fills the rest.

34.969 amu 36.966 amu Average: 35.45 amu Cl-35 75.8% Cl-37 24.2% The average shifts toward the isotope with greater abundance.
Light isotope 75.8%
Heavy isotope 24.2%
Average mass 35.452 amu
The average is closer to Cl-35 because the lighter isotope is more abundant.

Dynamic relationship

Abundance controls the position of the average.

The graph shows the average atomic mass as the abundance of the lighter isotope increases from 0% to 100%.

When light isotope abundance is 0%

The sample is entirely the heavier isotope, so the average is the heavier isotope mass.

When light isotope abundance is 100%

The sample is entirely the lighter isotope, so the average is the lighter isotope mass.

The relationship is linear because the average is a weighted sum: changing abundance changes the weights directly.

Worked example

Calculate the average atomic mass of chlorine.

Use two naturally occurring chlorine isotopes: Cl-35 with mass 34.969 amu and abundance 75.77%, and Cl-37 with mass 36.966 amu and abundance 24.23%.

Convert percentages to fractions. \(75.77\% = 0.7577\) and \(24.23\% = 0.2423\).

Multiply each mass by its fractional abundance. \(34.969(0.7577)\) and \(36.966(0.2423)\).

Add the isotope contributions. \(34.969(0.7577) + 36.966(0.2423) = 35.453\ \text{amu}\).

Interpret the result. The value is closer to 35 than 37 because Cl-35 is more abundant.

\[ \bar{m} = 34.969(0.7577) + 36.966(0.2423) = 35.453\ \text{amu} \]

This is why chlorine appears near 35.45 amu on the periodic table.

Common mistake

Do not average isotope masses equally unless the abundances are equal.

A simple average ignores how common each isotope is. Atomic mass is a weighted average, not always a halfway point.

Incorrect reasoning

“Chlorine has isotopes near 35 and 37, so its average must be exactly 36.”

Correct reasoning

Because Cl-35 is much more abundant than Cl-37, the average is pulled closer to 35, giving about 35.45 amu.

Method Calculation idea When valid?
Simple average Add masses and divide by number of isotopes. Only when all isotopes have equal abundance.
Weighted average Multiply each mass by fractional abundance, then add. Used for real periodic table atomic masses.
Another common mistake is using 75.77 instead of 0.7577. Percent values must be converted to fractions before multiplying.

Practice check

Try a weighted average.

An element has two isotopes. Isotope X has mass 10.01 amu and abundance 19.9%. Isotope Y has mass 11.01 amu and abundance 80.1%. Calculate the average atomic mass.

Before opening the answer

  • Convert each percent abundance to a decimal fraction.
  • Multiply each isotope mass by its fraction.
  • Add the two contributions.
\[ \bar{m} = m_1f_1 + m_2f_2 \]

The final value should be closer to 11.01 amu because isotope Y is more abundant.

Show answer

Convert abundances: \(19.9\% = 0.199\) and \(80.1\% = 0.801\). Then calculate \(10.01(0.199) + 11.01(0.801) = 1.992 + 8.819 = 10.811\ \text{amu}\). The average atomic mass is about 10.81 amu.

Continue learning

Apply atomic mass to isotope and periodic table problems.

Use atomic mass calculations to explain why periodic table values are decimals and to connect isotope abundance with measured sample masses.

Atomic Mass Calculator

Calculate weighted average atomic mass from isotope masses and abundances.

Atomic Mass Questions

Practice isotope abundance, average atomic mass, and periodic table interpretation.
List isotopes mass and abundance Weight values use fractions Interpret average compare to isotopes

Summary

Atomic mass is a weighted isotope average.

Mass number is not atomic mass

Mass number is a whole-number count of protons plus neutrons for one isotope.

Abundance matters

The most abundant isotope pulls the average atomic mass closest to its isotope mass.

Use fractions

Percent abundance must be converted to fractional abundance before calculating.

\[ \text{average atomic mass} = \sum(\text{isotope mass})(\text{fractional abundance}) \]

This relationship explains why periodic table atomic masses are often decimal values.

Final check: isotope mass tells “how heavy,” abundance tells “how common,” and atomic mass combines both.