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 oen 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 10 23 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 10 23 is sometimes called Avogadro’s constant (N A ) 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, N A 6.022 141 99 10 23 entities. However, for convenience, we mostly use the value 6.02 10 23 . 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 dened against a known standard. e standard chosen to dene 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 10 23 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 10 23 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 sulfur 6.02 10 23 atoms 32.06 g 1 mol of carbon 6.02 10 23 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 10 23 entities; unit symbol mol Avogadro’s constant (N A ) the number of entities in 1 mol of a substance amount (n ) the quantity of a substance, measured in moles 16 NEL
3
Embed
Table 1 Counting Units The Mole—A Chemist’s “Dozen” · 2013-04-07 · tennis balls occupy a larger volume than a dozen golf balls. 1 mol of sulfur 6.02 1023 atoms 32.06 g
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
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
16 NEL
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.
17NEL
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