Introductory Chemistry: A Foundation - Zumdahl S.S., DeCoste D.J. 2019

Chemical Composition
Atomic Masses: Counting Atoms by Weighing


· To understand atomic mass and its experimental determination.

In Chapter 6 we considered the balanced equation for the reaction of solid carbon and gaseous oxygen to form gaseous carbon dioxide:

Now suppose you have a small pile of solid carbon and want to know how many oxygen molecules are required to convert all of this carbon into carbon dioxide. The balanced equation tells us that one oxygen molecule is required for each carbon atom.

To determine the number of oxygen molecules required, we must know how many carbon atoms are present in the pile of carbon. But individual atoms are far too small to see. We must learn to count atoms by weighing samples containing large numbers of them.

In the last section we saw that we can easily count things like jelly beans and mints by weighing. Exactly the same principles can be applied to counting atoms.

Because atoms are so tiny, the normal units of mass—the gram and the kilogram—are much too large to be convenient. For example, the mass of a single carbon atom is g. To avoid using terms like when describing the mass of an atom, scientists have defined a much smaller unit of mass called the atomic mass unit (amu) . In terms of grams,

Now let’s return to our problem of counting carbon atoms. To count carbon atoms by weighing, we need to know the mass of individual atoms, just as we needed to know the mass of the individual jelly beans. Recall from Chapter 4 that the atoms of a given element exist as isotopes. The isotopes of carbon are , , and . Any sample of carbon contains a mixture of these isotopes, always in the same proportions. Each of these isotopes has a slightly different mass. Therefore, just as with the nonidentical jelly beans, we need to use an average mass for the carbon atoms. The average atomic mass for carbon atoms is amu. This means that any sample of carbon from nature can be treated as though it were composed of identical carbon atoms, each with a mass of amu. Now that we know the average mass of the carbon atom, we can count carbon atoms by weighing samples of natural carbon. For example, what mass of natural carbon must we take to have carbon atoms present? Because amu is the average mass,

Now let’s assume that when we weigh the pile of natural carbon mentioned earlier, the result is amu. How many carbon atoms are present in this sample? We know that an average carbon atom has the mass amu, so we can compute the number of carbon atoms by using the equivalence statement

to construct the appropriate conversion factor,

The calculation is carried out as follows:

The principles we have just discussed for carbon apply to all the other elements as well. All the elements as found in nature typically consist of a mixture of various isotopes. So to count the atoms in a sample of a given element by weighing, we must know the mass of the sample and the average mass for that element. Some average masses for common elements are listed in Table 8.1.

Table 8.1. Average Atomic Mass Values for Some Common Elements


Average Atomic Mass (amu)







Interactive Example 8.1. Calculating Mass Using Atomic Mass Units (amu)

Calculate the mass, in amu, of a sample of aluminum that contains atoms.


To solve this problem we use the average mass for an aluminum atom: amu. We set up the equivalence statement:

It gives the conversion factor we need:

Self-Check: Exercise 8.1

· Calculate the mass of a sample that contains nitrogen atoms.

See Problems 8.5 and 8.8.

The opposite calculation can also be carried out. That is, if we know the mass of a sample, we can determine the number of atoms present. This procedure is illustrated in Example 8.2.

Interactive Example 8.2. Calculating the Number of Atoms from the Mass

Calculate the number of sodium atoms present in a sample that has a mass of amu.


We can solve this problem by using the average atomic mass for sodium (see Table 8.1) of amu. The appropriate equivalence statement is

which gives the conversion factor we need:

Self-Check: Exercise 8.2

· Calculate the number of oxygen atoms in a sample that has a mass of amu.

See Problems 8.6 and 8.7.

To summarize, we have seen that we can count atoms by weighing if we know the average atomic mass for that type of atom. This is one of the fundamental operations in chemistry, as we will see in the next section.

The average atomic mass for each element is listed in tables found inside the front cover of this book. Chemists often call these values the atomic weights for the elements, although this terminology is passing out of use.