Download The Mole—A Chemist`s “Dozen”

Table 1 Counting Units
Unit
Example
1 dozen
12 golf balls
1 six-pack
6 cans of soft drink
1 ream
500 sheets of paper
1h
60 min
The Mole—A Chemist’s “Dozen”
A dozen is a common counting unit. A counting unit is a convenient number that
makes it easier to count objects. We often count doughnuts and eggs by dozens.
Similarly, we count shoes and gloves in pairs. Table 1 gives examples of common
counting units. Chemists, however, do not work with macroscopic (visible) objects
like shoes and doughnuts. Instead, chemists are interested in microscopic entities:
atoms and molecules. Since these entities are so small, chemists established their
own practical counting unit called the mole.
What Is a Mole?
mole a unit of amount; the amount of
substance containing 6.02 1023 entities;
unit symbol mol
Avogadro’s constant (NA) the number of
entities in 1 mol of a substance
The mole (symbol: mol) is the SI base unit for the amount of a substance. One mole
of a substance contains 602 000 000 000 000 000 000 000 or 6.02 1023 entities of
the substance. These entities could be anything from electrons and atoms to stars.
However, for practical purposes, the mole is used to count microscopic entities: atoms,
ions, molecules, and subatomic particles such as electrons. The value 6.02 1023 is
sometimes called Avogadro’s constant (NA) in honour of the Italian physicist Amadeo
Avogadro (1776–1856). Avogadro’s constant is determined experimentally. As experimental methods improve, the value of the constant becomes more precise. Currently,
NA 6.022 141 99 1023 entities. However, for convenience, we mostly use the value
6.02 1023.
You may wonder why chemists did not choose a more convenient number for their
counting unit. A trillion, for example, would have been easier to remember. There is a logical reason for their choice. Like other SI base units (such as the metre and the kilogram),
the mole is defined against a known standard. The standard chosen to define the mole
is the number of atoms in exactly 12 g of carbon—to be more precise, in the carbon-12
isotope. Scientists have experimentally determined that exactly 12 g of carbon-12
contains 6.02 1023 atoms of carbon.
Remember that a mole is a counting unit just like a dozen. However, instead of
counting atoms by the dozen, chemists count them by the mole. For example, Figure 4
shows equal amounts of carbon atoms and sulfur atoms: 1 mole of each. Both samples
contain 6.02 1023 atoms. The sulfur sample has a larger volume and a greater mass
because sulfur atoms are larger and heavier than carbon atoms. Similarly, a dozen
tennis balls occupy a larger volume than a dozen golf balls.
1 mol of carbon
6.02 1023 atoms
12.01 g
1 mol of sulfur
6.02 1023 atoms
32.06 g
Figure 4 One mole of carbon and one mole of sulfur; both samples contain the same number of
atoms. Since the atoms are different, the mass and volume of each sample are also different. The
amounts of the two substances, however, are the same.
amount (n ) the quantity of a substance,
measured in moles
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Note that, just as the volume of a substance is measured in litres, the amount (n) of
a substance is measured in moles. Scientists use moles to communicate the amount
of tiny entities such as subatomic particles, atoms, formula units, and molecules.
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For example, Figure 5 shows equal amounts of three common substances: a molecular compound, an ionic compound, and an element.
How Big Is a Mole?
It is difficult to comprehend the magnitude of huge numbers like Avogadro’s constant. The following analogy may help.
THE GREEN PEA ANALOGY
The values in Table 2 were determined using the following reasoning. One hundred
green peas fill an average teacup of a known volume. If the volume of a refrigerator
is known, the number of green peas that would fit in the refrigerator can be calculated without actually having to fill the refrigerator with a lot of peas and then
count them all.
Table 2 Representing Quantities of Green Peas
Number of green peas
Object that holds this number of peas
100 or 102 (one hundred)
teacup
1 000 000 or 106 (one million)
refrigerator
9
10 (one billion)
an average three-bedroom home
1012 (one trillion)
all the homes in a small town
1015 (one quadrillion)
all the homes in a large city such as Hamilton
1018 (one quintillion)
one-half of Ontario covered 1 m deep in peas
1021 (one sextillion)
all the continents covered 1 m deep in peas
1
1023 ; of 1 mol<
6
250 planets like Earth covered 1 m deep in peas
Figure 5 Samples of 1 mole each of
sucrose, sodium chloride, and carbon.
All three samples contain the same
number of entities.
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In the sections that follow, you will be performing calculations involving numbers
expressed in scientific notation. Let’s first review the multiplication and division of
numbers in scientific notation. Recall that a number expressed in scientific notation is
written in the form a 10x , where the absolute value of a is 1 or greater but less than
10. For example, the number 1.6 102 is in scientific notation.
Sample Problem 1: Multiplying Numbers Expressed In Scientific Notation
Calculate the product of 2 105 and 7 108.
To multiply numbers in scientific notation, multiply the coefficients and then add the
exponents. Note that the final answer must also be in scientific notation.
2 105 7 108 14 105 8
14 103 [not in scientific notation]
1.4 102 [in scientific notation]
Remember that the coefficient of a number written in scientific notation can only have a
single digit to the left of the decimal point.
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Sample Problem 2: Dividing Numbers Expressed In Scientific Notation
Divide 9 104 by 3 106.
To divide numbers in scientific notation, divide the coefficients and subtract the exponents.
9 104
3 104 6
3 106
3 1010
Practice
1. Perform the following calculations: K/U
(a) 2 104 3 1010 [ans: 6 1014]
(b) 5.0 102 2.4 103
(c)
1.95 102
1.3 105
(d)
1.05 1023
2.5 1025
[ans: 1.2]
[ans: 1.5 107]
[ans: 4.2 101]
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t "WPHBESPTDPOTUBOUNA, is defined as the number of atoms in exactly 12 g of
the carbon-12 isotope.
t 0OFNPMFPGBTVCTUBODFDPOUBJOT 1023 entities (atoms, ions, molecules,
or formula units).
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1. Why are familiar objects such as pens and paper clips not
commonly counted in moles? K/U
(b)
4.6 1022
2
2. Nails are usually sold by mass rather than by number, or
count. Describe how you could determine the number of
nails in a 500 g box. T/I
(c)
6.02 1024
9.0 1021
3. A chemist pours 1 mol of zinc granules into one beaker and
1 mol of zinc chloride powder into another beaker. T/I
(a) What do the two samples have in common?
(b) Which sample has the greater mass? Why?
4. What is the standard that Avogadro’s constant is based
on? K/U
5. (a) Calculate the number of doughnuts in 4 dozen
doughnuts.
(b) Use the same logic used in (a) to calculate the number
of molecules in 4.0 mol of carbon dioxide.
(c) Describe how to calculate the number of entities in a
given amount (number of moles) of a substance. T/I
6. Calculate the following:
T/I
6.02 10
3.01 1025
23
(a)
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7. A table of astronomical data gives the average distance from
Earth to Pluto as 5.7 billion km. The average thickness of a
sheet of notepaper is 1.2 104 m. Approximately how
many sheets of paper would you need to make a pile reaching
from Earth to Pluto? Give your answer in mol. T/I A
8. If you won a mole of dollars in a lottery, and were paid
in $100 bills, how long would it take you to count your
winnings? You will have to estimate how fast you can
count. T/I A
9. Suppose everybody in the world could count 100 objects
in a minute, 24 hours per day, 7 days a week, without
stopping. Use current data on the world’s population to
calculate approximately how long it would take for us all to
T/I
count 1 mol of objects.
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