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## 2.5 Atomic Masses

### Learning Objective

1. 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 unitOne-twelfth the mass of a 12C atom. (abbreviated u, although amu is also used) is defined as 1/12 of the mass of a 12C atom:

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 massA weighted average of the masses of all the element’s naturally occurring isotopes. (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.

The table in Chapter 21 "Appendix: Periodic Table of the Elements" also lists the atomic masses of the elements.

### Example 6

What is the average mass of a carbon atom in grams?

Solution

This is a simple one-step conversion, similar to conversions we did in Chapter 1 "Chemistry, Matter, and Measurement". We use the fact that 1 u = 1.661 × 10−24 g:

This is an extremely small mass, which illustrates just how small individual atoms are.

### Skill-Building Exercise

1. What is the average mass of a tin atom in grams? The atomic mass of tin is 118.71 u.

### Concept Review Exercises

1. Define atomic mass. Why is it considered a weighted average?

2. What is an atomic mass unit?

1. 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.

2. An atomic mass unit is 1/12th of the mass of a 12C atom.

### Key Takeaway

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

### Exercises

1. What is the atomic mass of zinc in atomic mass units?

2. What is the atomic mass of barium in atomic mass units?

3. What is the average mass of a single magnesium atom in grams?

4. What is the average mass of a single calcium atom in grams?

5. What is the mass of 1.00 × 1024 aluminum atoms in grams?

6. What is the mass of 5.00 × 1023 carbon atoms in grams?

7. Which has more mass—1 tungsten atom or 11 oxygen atoms?

8. Which has more mass—1 magnesium atom or 6 helium atoms?