Module RW-1
The Mole in Chemistry
How do you determine the number of atoms or
molecules in everyday items?
● How do we determine “quantity” in everyday life?
● How do we generally keep track of items too small
and too numerous to count one-by-one?
● Can we adapt conventional methods to deal with
atoms and molecules?
● What experimental data are necessary to
determine, for example, the number of atoms
present in a paper clip?
Quantitative Concepts and Skills
Unit Conversions
Scientific Notation
Significant figures
Prepared for SSAC by
Rachel Wang – Spokane Falls Community College
© The Washington Center for Improving the Quality of Undergraduate Education. All rights reserved. *YEAR*
1
Overview of Module
Slides 3 & 4
• provide a brief review of atoms, molecules, significant figures and scientific
notation.
Slides 5-7
• connect conventional ways of determining quantity to what we do in chemistry with
atoms and molecules by drawing a parallel between “dozen” (a lump sum of 12)
and “mole” (a lump sum of 6.022 x 1023, called Avogadro’s number) through
exercises in spreadsheet 1* & 2.
Slides 8-11
• examine the origin of Avogadro’s number and how this number facilitates
moles  grams conversions through exercises in spreadsheets 3 & 4.
Slide 12
• presents a composite diagram in spreadsheet 5 summarizing all the conversions:
grams  moles  numbers of atoms or molecules.
Slides 13-15
• address the question “how do you determine the number of atoms or molecules
present in everyday items?” with a sample problem concerning paper clips.
Slides 16
• lists the assignment to hand in.
* An Excel file is inserted in Slide 6. You may activate / download it by
double-clicking the icon in the NORMAL view (view menu).
2
Review: Atoms and Molecules
1.
All matter is composed of small representative units of atoms
and/or molecules. (Atomic Theory)
2.
The mass of an atom (atomic mass) is reported in the atomic
mass unit (amu), which is approximately the mass of a proton.
This is experimentally determined as:
 1 amu = 1.66058 x 10-24 grams
3.
The periodic table displays the average atomic mass of each
element. For example:
 Hydrogen (H) = 1.01 amu, and oxygen (O) = 16.00 amu.
4.
The formula mass of a compound is the sum of all the atomic
masses in the formula. For example:
 mass of H2SO4
= 2 (H) + (S) + 4(O)
= 2(1.01) + (32.06) + 4(16.00)
= 98.08 amu
3
Review: Significant Figures & Scientific Notation
1. An answer derived by multiplication or division should not have
more significant figures than any of the data used to derive it.
2. All non-zero digits in a measurement are significant. A zero digit is
significant if it is a “captive” between two non-zero digits or if it is at the
end of a number behind the decimal point.
Example: The number 0.0035090 has a total of five significant figures,
shown underlined. The zeros in front are NOT significant digits.
3. In scientific notation, the number in front includes all the significant
digits. The power of ten shows magnitude.
For example: 0.0035090 in scientific notation is 3.5090 x 10-3 (which
shows up as: 3.5090E-3 in a spreadsheet cell.)
How to format cells for scientific notation within a spreadsheet:
Left-click the cell  Click Format on toolbar  number  scientific 
decimal places = [Decide based on significant figures.]
Example: To keep the 5 significant figures in this number: 0.0035090, you will select 4 decimal
places to display: 3.5090E-3 in the cell.
4
How we determine quantity: Counting, Weighing or Volume Measurements
We will first consider how people normally keep track of quantity in
everyday life. There are generally three ways to do this:
Counting  by number of units.
Example: oranges priced by number.
If a single unit is too small, we devise a lump sum.
Example: eggs are priced by the dozen, which is a lump sum of
12 units.
(2) Weighing  by weight or mass.
Example: meat is priced by the pound.
(3) Measuring  by volume.
This is easier to use with liquids or gases.
Example: gasoline is priced by the gallon.
(1)
•Is it surprising to you that we employ similar ways in
chemistry to keep track of atoms and molecules as described
above? But, indeed we do.
•The next two slides compare two parallel ways of counting
by number of units: As we count small items by the “dozen”
in everyday life, we count atoms and molecules by the “mole”
in chemistry.
5
Counting by the dozen
B
2
3
4
5
6
7
8
9
lump sum
practice exercise
How many eggs are there in 15
dozens of eggs?
How many donuts are there in 2.6
dozen donuts?
How many atoms are there in 57
dozens of Al atoms?
How many molecules are there in
9.6 dozens of H 2O molecules?
How many dozens of eggs are
10 there in 15 eggs?
How many dozens of donuts are
11 there in 26 donuts?
How many dozens of atoms are
12
there in 1.8x10 5 Fe?
C
D
E
1 dozen = 12
quantity in quantity in
lump sum number
type of
item
1.5E+01
1.8E+02 eggs
2.6E+00
3.1E+01 donuts
1.3E+00
1.5E+01 eggs
2.2E+00
2.6E+01 donuts
How many dozens of molecules
18
13 are there in 4.6x10 CO2?
= given values. Start with these.
Double-Click the Excel
icon in normal view and
complete Sheet 1.
Instructions: Input a cell
equation in D6 using D3 as
absolute reference ($D$3).
Click & drag its anchor to
input similar equations in
subsequent Cells D7-D9.
Follow similar procedures
with C10 and then C11-13.
= answers calculated by cell equations.
Express all numbers in scientific notation and correct number of significant
figures.
6
Counting by the mole
1. Print a hardcopy (or save your work on a disk) of the spreadsheet you
just completed on “counting by the dozen” for submission later.
2. Go to Sheet 2 of your downloaded Excel file and complete the
spreadsheet table on “counting by the mole”. Note that Rows 1
through 13 of Sheet 2 exactly duplicate those of Sheet 1, except that
the word “dozen(s)” is replaced with “mole(s)” everywhere. Note the
dramatic change in your answers when the numerical value of
6.022x1023 is used as the lump sum instead of 12.
14
How many moles of eggs are there in
2.60x1023 eggs?
15
How many moles of atoms are there in
4.60x1024 atoms?
16
How many pennies are there in 0.557
moles of pennies?
17
How many moles are there in 2.60x1023
water molecules?
• These four exercises are added to the
“counting by the moles” worksheet.
• Complete the cells under Columns D,
E, and F with appropriate values, units
or equations.
• Print a hardcopy (or save your work
on a disk) when you complete the
“counting by the mole” spreadsheet.
Remember to use scientific notations with correct
number of significant figures!
7
1 Mole = 6.022 x 1023
Named Avogadro’s number in honor of Amedeo Avogadro (1776-1856)
Slides 6 and 7 showed how counting eggs in dozens is similar to
counting atoms by the mole. We use similar math equations for both
mole  number conversions and dozen  number conversions.
Since everyday items contain astronomical
numbers of atoms and molecules, it is easier to
count them by a huge lump sum:
1 mole = 6.022 x 1023.
Pictured on the right are 1 mole each of H2O
molecules and Fe atoms (in the pile of staples).
But why do we use Avogadro’s number, 6.022
x 1023, for one mole? Did he invent the
number? No, neither he nor anyone else did.
The number is defined by how the mass units,
amu and gram, relate to each other:
1 amu = 1.66058 x 10-24 grams
8
atomic mass (amu)  molar mass (gram)
Complete this table in Sheet 3 of your downloaded Excel file. Print a
hardcopy or save it on a disk.
= given values. Start with these.
B
2
1 amu =
3 quantity of atoms
4
5
element
potassium ,K
6 sodium, Na
7 hydrogen, H
8 oxygen, O
9 nitrogen, N
10 iron, Fe
11 aluminum, Al
12 carbon, C
13 zinc, Zn
14 sulfur, S
C
1.66058E-24
D
6.02200E+23
1 atom mass
1 mole atoms
(amu)
3.91E+01
2.299E+01
1.01E+00
1.600E+01
E
grams
1 mole =
(amu)
= answers calculated by cell equations.
2.35E+25
molar mass
(grams)
3.90E+01
If one K atom weighs
39.01 amu, how much
would 1 mole of K
atoms weigh:
in amu (column D)?
In grams (column E)?
1.401E+01
HINT: $C$2 and $D$3 are absolute references. Input
appropriate equations in cells D5 and E5 that produce
the numbers in those cells shown here. Then Click and
drag anchors to add similar equations in the other cells.
Complete Column C with values of atomic mass from your periodic table.
9
Weighing in Grams and the Mole
Examine the spreadsheet you prepared in Slide 9.
How do the numerical values in Column C and those in Column
E compare for each element?
Are they exactly the same?
They should be, as Avogadro’s number is defined by the way amu
and gram relate to each other.
Experimental data:
1 amu = 1.66058 x 10-24 grams leads to this equality:
6.022 x 1023 amu = 1 gram
because: 1  (1.66058 x 10-24) = 6.022 x 1023
One H2O
molecule
= 18.00 amu
Avogadro’s
number
20
15
6.022 x1023
10
H2O molecules
5
One mole H2O
Molecules
= 18.00 gram
10
Grams  Mole Conversions
Complete this table in Sheet 4 of your downloaded Excel file.
Print a hardcopy or save it on a disk.
1 mole of any element = molar mass in grams from the periodic table.
2
3
B
C
D
Une the periodic table to find molar mass.
practice exercise
How many grams are there in
15.0 moles of Al atoms?
How many grams are there in
5 2.60 moles of Fe atoms?
How many grams are there in
6 2.6 moles FeO?
How many grams are there in
7 1.23 moles Br2?
How many moles are there in
8 57.0 grams of Al atoms?
How many moles are there in
10
9.60 grams H2O molecules?
4
How many moles are there in
11 15.7 grams Carbon atoms?
How many moles are there in
12 264g Br2?
molar mass
(g)
2.698E+01
quantity
(Mol)
1.50E+01
E
quantity
(g)
4.05E+02
= given
values. Start
with these.
= answers
calculated by
cell equations.
2.698E+01
2.11E+00
5.70E+01
Express all numbers in
scientific notation and
the correct number of
significant figures.
11
No. of atoms  Mole  Grams Conversions
Answer these questions concerning sucrose (C12H22O11) using this spreadsheet.
1. How many moles are there in 74.3 gr sucrose? How many molecules are there?
2. How many grams are there in 1.297 moles of sucrose? How many molecules are threre?
28
3. How many moles are in 4.30x10 molecules of sucrose? How many grams are there?
Input cell equation here
to find answer.
Start here if given #
atoms or molecules.
number
Start here if given moles.
mole
Start here if given
grams.
gram
74.3
1.297
4.30E+28
lump sum:
1 mole =
Use Avogadros' number for atoms mole conversions
molar mass
=
Use molar mass for grams-mole
conversions
This composite
diagram in Sheet 5 of
the Excel file
summarizes all
conversions among
number of atoms
and molecules,
moles, and grams.
Supply cell equations
to answer the
questions given on the
sheet. Print a
hardcopy of the
completed sheet or
save it on a disk.
The color coding of yellow, green, blue, and brown cells is shown on the spreadsheet.
12
About the problem of determining the number of
atoms or molecules in everyday items …
Given the chemical composition of an everyday item, we can easily
determine the number of atoms or molecules present in it by
applying the conversions we have practiced in the previous slides:
grams  moles  numbers of atoms or molecules.
• If the item is more or less “pure” in that it has only one type of
element or compound, we can readily determine the number of
atoms or molecules in it by (a) weighing the item to obtain its
mass in grams, (b) converting grams to moles, using the
periodic table for molar mass, and then (c) converting moles to
number of atoms or molecules, using Avogadro’s number.
Examples in this category include: distilled water (H2O), regular
staples (Fe) and table sugar (sucrose, C12H22O11).
• If the item is a mixture, we may need to do some chemical
analyses to determine the mass of each element or compound.
After finding the respective mass of each element or
compound, we can readily convert that to moles and atoms or
molecules..
13
A Sample Problem: How many atoms are there in a paper clip?
One of the most important
problem-solving strategies is to
frame the problem so that it
can be answered under
conditions consistent with
available information.
Because the question did not
specify any details, it is
obviously not looking for an
exhaustive answer about
every paper clip in the world.
Can you frame the problem
by defining some
conditions that are
reasonable for you to obtain a
satisfactory answer and be
consistent with a ‘generic’
paper clip in common use?
Paper clips vary in style, size
and chemical composition.
• The familiar Gem style pictured above varies
in size from over 2 inches to less than 1 inch
long. The wire itself differs in thickness.
• Though paper clips may be made of colorful
plastics or brass, most are made of steel
(>99.7% iron). To prevent rusting, they often
have a thin surface coating of zinc. If you
immerse a zinc-coated clip in dilute acid, the
reactive zinc metal will readily oxidize and
dissolve away to reveal the iron. Iron, being
less active, does not react as zinc does. 14
A Sample Problem: How many atoms are there in a paper clip?
(Continued from slide 14) Your task is to:
• Specify the conditions under which you can determine the
number of atoms present in a paper clip.
• Conduct experiments and collect data on this paper clip
using available supplies and equipment in the Chem lab.
• Submit a brief one-page summary report of your lab results
and calculations in answer to the question.
Sample data and calculations for a hypothetical paper clip:
Original mass of the paper clip = 0.403 g.
Mass after removing zinc with 1 M HCl = 0.365 g
Adapt the composite diagram in slide 12 (Sheet 5 of the Excel file) to
convert grams  moles  atoms :
Fe = 0.365 gram  moles Fe  atoms Fe
Zn = 0.403– 0.365 = 0.038 gram  moles Zn  atoms Zn
For some interesting paper clip history, check out this web site:
http://www.ideafinder,com/history/inventions/paperclip.htm
15
End-of-Module Assignments
Submit answers to the following:
1. How many water (H2O) molecules are there
in the cup of coffee pictured on the right?
2. Two teaspoons each of table sugar and a
non-dairy creamer are in the coffee. How
many sucrose molecules are there?
3. How many carbon atoms are present in your
body? Discuss whether these C atoms are
sufficient to make a 5-carat diamond? (Hint:
18% body weight is C; 1 carat = 205 mg.)
• Frame each problem by specifying
reasonable conditions.
• Specify the sources of all data, which can be
from your own experiment, a publication
and/or a product label, etc.
• Show calculations and report answers in
correct significant figures and scientific
notation.
• Also submit the spreadsheets completed in
Slides 6, 7, 9, 11 & 12 and the summary
report in Slide 15.
16