2.5: Atomic Masses

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Skills to Develop

To define atomic mass and atomic mass unit.

Even though atoms are very tiny pieces of matter, they have mass. Their masses are so small, however, that chemists often use a unit other than grams to express them—the atomic mass unit.

The atomic mass unit (abbreviated u, although amu is also used) is defined as 1/12 of the mass of a ¹²C atom:

\[\mathrm{1\:u=\dfrac{1}{12}\textrm{ the mass of }^{12}C\:atom} \label{Eq1}\]

It is equal to 1.661 × 10⁻²⁴ g.

Masses of other atoms are expressed with respect to the atomic mass unit. For example, the mass of an atom of ¹H is 1.008 u, the mass of an atom of ¹⁶O is 15.995 u, and the mass of an atom of ³²S is 31.97 u. Note, however, that these masses are for particular isotopes of each element. Because most elements exist in nature as a mixture of isotopes, any sample of an element will actually be a mixture of atoms having slightly different masses (because neutrons have a significant effect on an atom’s mass). How, then, do we describe the mass of a given element? By calculating an average of an element’s atomic masses, weighted by the natural abundance of each isotope, we obtain a weighted average mass called the atomic mass (also commonly referred to as the atomic weight) of an element.

For example, boron exists as a mixture that is 19.9% ¹⁰B and 80.1% ¹¹B. The atomic mass of boron would be calculated as (0.199 × 10.0 u) + (0.801 × 11.0 u) = 10.8 u. Similar average atomic masses can be calculated for other elements. Carbon exists on Earth as about 99% ¹²C and about 1% ¹³C, so the weighted average mass of carbon atoms is 12.01 u.

Example \(\PageIndex{1}\): Average Atomic Mass of Isotopes

Use the following information to determine the atomic mass of magnesium. (Do not look at the value on the periodic table.)

Isotope	Exact Mass (atomic mass units)	Relative Abundance (percentage)
²⁴Mg, magnesium-24	23.9850 u	78.99 %
²⁵Mg, magnesium-25	24.9858 u	10.00 %
²⁶Mg, magnesium-26	25.9826 u	11.01 %

SOLUTION

Atomic masses are the average of the naturally occuring isotopes. The fraction of each is the percentage, divided by 100.

= (fraction of ²⁴Mg)(exact mass ²⁴Mg) + (fraction of ²⁵Mg)(exact mass ²⁵Mg) + (fraction of ²⁶Mg)(exact mass ²⁶Mg)

= (78.99/100)(23.9850 u) + (10.00/100)(24.9858 u) + (11.01/100)(25.9826 u)

= (0.7899)(23.9850 u) + (0.1000)(24.9858 u) + (0.1101)(25.9826 u)

= (18.9457515 u) + (2.49858 u) + (2.86068426 u)

= 24.30501576 u = 24.31 u

The digits underlines are not significant. When multiplying, the answers are known to the fewest total significant figures (four). When adding, the answer is known to the fewest decimal places (two).

Concept Review Exercises

Define atomic mass. Why is it considered a weighted average?
What is an atomic mass unit?

Answers

The atomic mass is an average of an element’s atomic masses, weighted by the natural abundance of each isotope of that element. It is a weighted average because different isotopes have different masses.
An atomic mass unit is exactly 1/12th of the mass of a ¹²C atom (and very close to the mass of one proton or one neutron).

Key Takeaway

Atoms have a mass that is based largely on the number of protons and neutrons in their nucleus.

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