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 o!en 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?"e 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. "ese 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. "e 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 experi-mental 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. "ere is a log-ical reason for their choice. Like other SI base units (such as the metre and the kilogram), the mole is de#ned against a known standard. "e standard chosen to de#ne 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. "e 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 sulfur6.02 1023 atoms

32.06 g

1 mol of carbon 6.02 1023 atoms

12.01 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.

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.

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

1 h 60 min

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

amount (n ) the quantity of a substance,

measured in moles

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For example, Figure 5 shows equal amounts of three common substances: a molec-ular compound, an ionic compound, and an element.

How Big Is a Mole?It is di$cult to comprehend the magnitude of huge numbers like Avogadro’s con-stant. "e following analogy may help.

THE GREEN PEA ANALOGY

"e values in Table 2 were determined using the following reasoning. One hundred green peas #ll an average teacup of a known volume. If the volume of a refrigerator is known, the number of green peas that would #t in the refrigerator can be cal-culated without actually having to #ll 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

109 (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

1023 1

6 of 1 mol

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.

1

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 10 2 is in scientific notation.

Sample Problem 1: Multiplying Numbers Expressed In Scientific NotationCalculate the product of 2 105 and 7 10 8.

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 10 8 14 105 8

14 10 3 [not in scientific notation]

1.4 10 2 [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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NA, is de#ned as the number of atoms in exactly 12 g of the carbon-12 isotope.

1023 entities (atoms, ions, molecules, or formula units).

Sample Problem 2: Dividing Numbers Expressed In Scientific Notation

Divide 9 104 by 3 10 6.

To divide numbers in scientific notation, divide the coefficients and subtract the exponents.

9 104

3 10 63 104 6

3 1010

Practice

1. Perform the following calculations: K/U

(a) 2 10 4 3 10 10 [ans: 6 10 14]

(b) 5.0 102 2.4 10 3 [ans: 1.2]

(c) 1.95 102

1.3 10 5 [ans: 1.5 107]

(d) 1.05 10 23

2.5 10 25 [ans: 4.2 101]

1. Why are familiar objects such as pens and paper clips not

commonly counted in moles? K/U

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

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

(a) 6.02 1023

3.01 1025

(b) 4.6 1022

2

(c) 6.02 10 24

9.0 10 21

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 10 4 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

count 1 mol of objects. T/I

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