10.1. The Mole Concept http://www.ck12.org
way, and a very time consuming one, would be to count all of the individual grains of sugar. The amount of matter
can be measured in three basic ways: mass, volume, and number of particles. In order to fully understand and
manipulate chemical reactions, chemists must be able to understand these three ways of measuring matter and the
interconnections between them.
Names for Numbers
How many bananas is a dozen bananas (Figure10.1)? How many elephants is a dozen elephants? How many
asteroids is a dozen asteroids? For all of these questions, the answer is obviously twelve. There is nothing that we
need to know about the bananas or the elephants or the asteroids in order to answer the question. The term dozen is
always used to refer to twelve of something; it is a name that is given to an amount. Other amounts are given special
names as well. For example, a pair is always two, and a gross of something is a dozen dozens, which would be 144.
FIGURE 10.1
Bananas can be sold by mass or by
count.We can use a conversion factor and dimensional analysis to convert back and forth between the number of items and
the name given to a certain number. For example, if you wanted to know how many bananas there are in 8 dozens,
you could perform the following calculation:
8 dozen bananas× 1 dozen bananas^12 bananas =96 bananasThe conversion factor of 12 items = 1 dozen items is true regardless of the identity of the item. Alternatively, you
could find out how many dozens of asteroids are in a collection of 1242 asteroids.
1242 asteroids×^1 dozen asteroids 12 asteroids = 103 .5 dozen asteroidsThe conversion factor is simply inverted in this case so that the units cancel correctly.
Conversion factors can also be used to relate the amount of something to its mass. Suppose that you have a small
bunch of bananas consisting of five bananas. You place them on a balance and find that the five bananas have a mass
of 850 g. Assuming each banana has the same mass, what would be the mass of 3 dozen bananas? We can employ
two conversion factors to find the answer.
3 dozen bananas× 1 dozen bananas^12 bananas × 5 bananas^850 g =6120 g=6100 g