The Foundations of Chemistry

and

Solution

_?_ Fe atoms2.451 mol Fe atoms
1.476
 1024 Fe atoms

We expected the number of atoms in more than two moles of atoms to be a very
large number. Written in nonscientific notation, the answer to this example is:
1,476,000,000,000,000,000,000,000.

You should now work Exercise 42.

If we know the atomic weight of an element on the carbon-12 scale, we can use the
mole concept and Avogadro’s number to calculate the averagemass of one atom of that
element in grams (or any other mass unit we choose).

6.022
 1023 Fe atoms



1 mol Fe atoms

1 mol atoms



6.022
 1023 atoms

6.022
 1023 atoms



1 mol atoms

Try to name this number with its

many zeroes.

2-6 The Mole 61

CC The Development of Science

HEMISTRY IN USE

Avogadro’s Number

If you think that the value of Avogadro’s number, 6
 1023 ,

is too large to be useful to anyone but chemists, look up into

the sky on a clear night. You may be able to see about 3000

stars with the naked eye, but the total number of stars swirling

around you in the known universe is approximately equal to

Avogadro’s number. Just think, the known universe contains

approximately one mole of stars! You don’t have to leave earth

to encounter such large numbers. The water in the Pacific

Ocean has a volume of about 6
 1023 mL and a mass of

about 6
 1023 g.

Avogadro’s number is almost incomprehensibly large. For

example, if one mole of dollars given away at the rate of a

million per second beginning when the earth first formed

some 4.5 billion years ago, would any remain today? Surpris-

ingly, about three fourths of the original mole of dollars

would be left today; it would take about 14,500,000,000 more

years to give away the remaining money at $1 million per

second.

Computers can be used to provide another illustration

of the magnitude of Avogadro’s number. If a computer can

count up to one billion in one second, it would take that

computer about 20 million years to count up to 6
 1023. In

contrast, recorded human history goes back only a few thou-

sand years.

The impressively large size of Avogadro’s number can give

us very important insights into the very small sizes of indi-

vidual molecules. Suppose one drop of water evaporates in

one hour. There are about 20 drops in one milliliter of wa-

ter, which weighs one gram. So one drop of water is about

0.05 g of water. How many H 2 O molecules evaporate per

second?



 5 
 1017 H 2 O molecules/s

5 
 1017 H 2 O molecules evaporating per second is five hun-

dred million billion H 2 O molecules evaporating per second

—a number that is beyond our comprehension! This calcu-

lation helps us to recognize that water molecules are incred-

ibly small. There are approximately 1.7
 1021 water mole-

cules in a single drop of water.

By gaining some appreciation of the vastness of Avogadro’s

number, we gain a greater appreciation of the extremely tiny

volumes occupied by individual atoms, molecules, and ions.

Ronald DeLorenzo

Middle Georgia College

Original concept by Larry Nordell

1 min



60 s

1 h



60 min

6 
 1023 H 2 O molecules



1 mol H 2 O

1 mol H 2 O



18 g H 2 O

0.05 g H 2 O



1 h

_?_ H 2 O molecules



1 s