Chapter 4, Section 3

Chapter 4, Section 3

Atomic Mass

A glance back at Table 4.1 on page 106 shows that the actual mass of a proton or a neutron is very small (1.67 × 10⁻²⁴ g). The mass of an electron is 9.11 × 10⁻²⁸ g, which is negligible in comparison. Given these values, the mass of even the largest atom is incredibly small. Since the 1920s, it has been possible to determine these tiny masses by using a mass spectrometer. With this instrument, the mass of a fluorine atom was found to be 3.155 × 10⁻²³ g, and the mass of an arsenic atom was found to be 1.244 × 10⁻²² g. Such data about the actual masses of individual atoms can provide useful information, but, in general, these values are inconveniently small and impractical to work with. Instead, it is more useful to compare the relative masses of atoms using a reference isotope as a standard. The isotope chosen is carbon-12. This isotope of carbon was assigned a mass of exactly 12 atomic mass units. An atomic mass unit (amu) is defined as one twelfth of the mass of a carbon-12 atom. Using these units, a helium-4 atom, with a mass of 4.0026 amu, has about one-third the mass of a carbon-12 atom. On the other hand, a nickel-60 atom has about five times the mass of a carbon-12 atom.

A carbon-12 atom has six protons and six neutrons in its nucleus, and its mass is set as 12 amu. The six protons and six neutrons account for nearly all of this mass. Therefore the mass of a single proton or a single neutron is about one-twelfth of 12 amu, or about 1 amu. Because the mass of any single atom depends mainly on the number of protons and neutrons in the nucleus of the atom, you might predict that the atomic mass of an element should be a whole number. However, that is not usually the case.

In nature, most elements occur as a mixture of two or more isotopes. Each isotope of an element has a fixed mass and a natural percent abundance. Consider the three isotopes of hydrogen discussed earlier in this section. According to Table 4.3, almost all naturally occurring hydrogen (99.985%) is hydrogen-1. The other two isotopes are present in trace amounts. Notice that the atomic mass of hydrogen listed in Table 4.3 (1.0079 amu) is very close to the mass of hydrogen-1 (1.0078 amu). The slight difference takes into account the larger masses, but smaller amounts, of the other two isotopes of hydrogen.

Table 4.3: Natural Percent Abundance of Stable Isotopes of Some Elements

Now consider the two stable isotopes of chlorine listed in Table 4.3: chlorine-35 and chlorine-37. If you calculate the arithmetic mean of these two masses ((34.969 amu + 36.966 amu)/2), you get an average atomic mass of 35.968 amu. However, this value is higher than the actual value of 35.453. To explain this difference, you need to know the natural percent abundance of the isotopes of chlorine. Chlorine-35 accounts for 75% of the naturally occurring chlorine atoms; chlorine-37 accounts for only 25%. See Figure 4.10. The atomic mass of an element is a weighted average mass of the atoms in a naturally occurring sample of the element. A weighted average mass reflects both the mass and the relative abundance of the isotopes as they occur in nature.

Figure 4.10

For: Links on Isotopes
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4.3 Using Atomic Mass to Determine the Relative Abundance of Isotopes

Problem-Solving 4.21 Solve Problem 21 with the help of an interactive guided tutorial.

Now that you know that the atomic mass of an element is a weighted average of the masses of its isotopes, you can determine atomic mass based on relative abundance. To do this, you must know three values: the number of stable isotopes of the element, the mass of each isotope, and the natural percent abundance of each isotope.  To calculate the atomic mass of an element, multiply the mass of each isotope by its natural abundance, expressed as a decimal, and then add the products. The resulting sum is the weighted average mass of the atoms of the element as they occur in nature.

You can calculate the atomic masses listed in Table 4.3 based on the given masses and natural abundances of the isotopes for each element. For example, carbon has two stable isotopes: carbon-12, which has a natural abundance of 98.89%, and carbon-13, which has natural abundance of 1.11%. The mass of carbon-12 is 12.000 amu; the mass of carbon-13 is 13.003 amu. The atomic mass is calculated as follows.

Atomic mass of carbon = (12.000 amu × 0.9889) + (13.003 amu × 0.0111) = 12.011 amu

4.2 Calculating Atomic Mass

Problem-Solving 4.24 Solve Problem 24 with the help of an interactive guided tutorial.