The Foundations of Chemistry

EXAMPLE 2-5 Masses of Atoms

Calculate the average mass of one iron atom in grams.

Plan

We expect that the mass of a single atom in grams would be a verysmall number. We know

that one mole of Fe atoms has a mass of 55.85 g and contains 6.022
 1023 Fe atoms. We use

this information to generate unit factors to carry out the desired conversion.

Solution


9.274
 10 ^23 g Fe/Fe atom

Thus, we see that the average mass of one Fe atom is only 9.274
 10 ^23 g, that is,

0.00000000000000000000009274 g.

Example 2-5 demonstrates how small atoms are and why it is necessary to use large

numbers of atoms in practical work. The next example will help you to realize how large

Avogadro’s number is.

EXAMPLE 2-6 Avogadro’s Number

A stack of 500 sheets of typing paper is 1.9 inches thick. Calculate the thickness, in inches and

in miles, of a stack of typing paper that contains one mole (Avogadro’s number) of sheets.

Plan

We construct unit factors from the data given, from conversion factors in Table 1-7, and from

Avogadro’s number.

Solution

_?_ in1 mol sheets

2.3
 1021 in.

_?_ mi2.3
 1021 in.

3.6
 1016 mi

By comparison, the sun is about 93 million miles from the earth. This stack of paper would

make 390 million stacks that reach from the earth to the sun.

1 mi



5280 ft

1 ft



12 in.

1.9 in.



500 sheets

6.022
 1023 sheets



1 mol sheets

1 mol Fe atoms



6.022
 1023 Fe atoms

55.85 g Fe



1 mol Fe atoms

_?_ g Fe



Fe atom

To gain some appreciation of how little
this is, write 9.274
10 ^23 gram as a
decimal fraction, and try to name the
fraction.

62 CHAPTER 2: Chemical Formulas and Composition Stoichiometry

Problem-Solving Tip:When Do We Round?

Even though the number 1.9 has two significant figures, we carry the other numbers in

Example 2-6 to more significant figures. Then we round at the end to the appropriate

number of significant figures. The numbers in the distance conversions are exact num-

bers.

Imagine the number of trees required
to make this much paper!