1.1 The Mole Concept and Avogadro’s Constant
*Introducing the Mole - The “Baking” Analogy
*A recipe calls for flour, chocolate chips, eggs, milk, vinegar, baking
soda and sugar.
Q. Which ingredients do you measure by counting?

Q. What do you measure by volume/mass?

Q. Why does the recipe not tell you exactly how many chocolate chips or grains of sugar you will
need?

Q. What units do you think the chocolate chips and sugar are given in?

*These units are used as a matter of convenience.
*In some ways, chemistry is similar to baking.
Consider the reaction between vinegar (acetic acid solution) and baking soda (sodium
bicarbonate):
CH3COOH(aq) + NaHCO3(s)  NaCH3COO(aq) + CO2(g) + H2O(l)
According to the balanced chemical equation, one molecule of acetic acid reacts with one
molecule of sodium bicarbonate to form a salt, carbon dioxide and water.
Q. How would you know the amount of baking soda and vinegar to use?
*Their molecules are much too small and numerous to count like eggs.
Example 2
Chef :
2 eggs + 3 mushrooms + 1 pepper  1 omelette
(balanced)
*Advantage: Ingredients are all macroscopic; that is, they can be seen with the unaided eye.
Chemist:
2H2(g) + O2(g)  2H2O(l)
(balanced)
*Entities are submicroscopic – cannot be seen clearly with the most powerful microscopes.
*However, chemists have developed methods that allow them to predict, with great accuracy, the
number of entities (atoms, ions, or molecules) that take part in chemical reactions.
*Chemists count atoms by organizing very large numbers of them into convenient, measurable
groups.
Q. What are some examples of convenient, measurable groups that are commonly used?
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Examples: Grouping for Convenience
1 ream = 500 sheets (photocopy paper)
1 goal (football) = 6 points
1 kilometre = 1000 metres
1 Kilobyte = 1024 bytes
1 carat (jewels) = 200 mg
1 pack or deck = 52 cards
1 decade = 10 years
1 century = 100 years
1 millennium = 1,000 years
Coulomb = 6 x 1024 electrons

**1 mole = 6.02 x 1023 particles
*THE
1 Astronomical Unit = 150,000,000 Km
1 dollar = 100 cents
1 litre = 1000 ml
1 megabyte = 1048576 bytes
1 horsepower = 746 watts (joule/sec)
1 light-year = 9,461,000,000,000 km
A gold record = 1,000,000 copies sold
1 octave = 12 notes

Faraday = 9.65 x 104 Coulombs
AVOGADRO CONSTANT AND THE MOLE
*Amedeo Avogadro (1776 – 1856)
The Definition of the Mole:

One mole (1 mol) of a substance contains _____________particles (usually: atoms,
molecules, formula units, ions or electrons) of the substance. This value is called the
____________ constant. Its symbol is NA or ___.

The mole is defined as the amount of substance that contains as many elementary entities
(atoms, molecules, or formula units) as exactly 12.00 grams of _________-12, ( 126 C).
Mole Calculations
“Warm-Up” Activity  Provide the Formula.
1. You have 57 pencils. How many dozen pencils to you have? Provide a formula indicating how
you calculated your answer.
2. You have an electrical device having a power rating o 1500 Watts. How many horsepower is
this equal to? Provide a Formula.
3. You have 4 dozen doughnuts. How many doughnuts do you have in total? Provide a formula.
4. You have 5 decks of cards. How many cards do you have in total? Provide a formula.
Mole Related:
5. Consider a sample containing 1.2 x 1024 atoms of iron. How many moles of atoms do you
have? Provide a formula.
6. You have 7.4 x 1012 formula units of sodium chloride. How many moles of sodium chloride to
you have?
7. Consider a sample containing 3.45 mol of water molecules. How many water molecules are
present in total? Provide a formula.
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Part A  More Practice: Converting Moles to Number of Particles
1. A small pin contains 0.0178 mol of iron. How many atoms of iron are in the pin?
(Ans. 1.07 x 1022)
2. A sample contains 4.70 x 10-4 mol of gold. How many atoms of gold are in the sample?
(Ans. 2.83 x 1020)
3. How many formula units are contained in 0.21 mol of magnesium nitrate? (Ans. 1.3 x 1023)
4. A litre of water contains 55.6 mol of water. How many molecules of water are in this sample?
(Ans. 3.35 x 1025)
5. Ethyl acetate, C4H8O2, is frequently used in nail polish remover. A typical bottle of nail polish
remover contains about 2.5 mol of ethyl acetate.
a) How many molecules are in the bottle of nail polish remover? (Ans. 1.5 x1024)
b) How many atoms are in the bottle? *Hint – How many total atoms are there in one
molecule? (Ans. 2.1 x 1025)
c) How many carbon atoms are in the sample? *Hint – How many carbon atoms are in one
molecule? (Ans. 6.0 x 1024)
6. Consider a 0.829 mol sample of sodium sulfate, Na2SO4.
a) How many formula units are in the sample? (Ans. 4.99 x 1023)
b) How many sodium ions, Na+, are in the sample? (Ans. 9.98 x 1023)
7. Consider a 1 mol sample of H2SO4.
a) How many molecules of H2SO4 are in the sample?
b) How many moles of atoms are in the sample?
c) How many atoms are in the sample?
d) How many moles of oxygen atoms are there in the sample?
Part B  More Practice: Converting Number of Particles to Moles
1. A sample of bauxite ore contains 7.71 x 1024 molecules of aluminum oxide, Al203. How many
moles of aluminum oxide are in the sample? (Ans. 12.8 mol)
2. A sample of cyanic acid, HCN, contains 3.33 x 1022 atoms. How many moles of cyanic acid are
in the sample? *Hint – Find the number of molecules of HCN first. (Ans. 1.84 x 10-2 mol)
3. A sample of pure acetic acid, HC2H3O2, contains 1.40 x 1023 carbon atoms. How many moles
of acetic acid are in the sample? (Ans. 1.16 x 10-1 mol)
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*MOLAR MASS
*Each of the following samples contain 1.00 mol, or 6.02 x 1023 entities. Why do you
think the mass of each sample is different?
Substance
Carbon (graphite)
Sulfur (powder or rock form)
Sodium hydroxide
Ethanol
Iron filings
Sodium chloride
Sodium bicarbonate
Chloroform
Cesium chloride
Lead
Hydrated copper sulphate
Sucrose (cane sugar)
Chemical formula
C
S
NaOH
C2H5OH
Fe
NaCl
NaHCO3
CHCl3
CsCl
Pb
CuSO4.5H2O
C12H22O11
Mass weighed out (g)
12.01
32.06
40.01
46.08
55.85
58.44
84.00
119.37
168.37
207.21
249.69
342.30
Try the Following Activity:
*one coin = one “atom”
Determine the mass of:
a) One penny “atom” m = _____
b) One nickel “atom” m = _____
c) One quarter “atom” m = _____
d) One loonie “atom” m = ____
“Element”
Mass of one
“atom” (i.e. one coin)
in grams
Mass of 1.00 mol
(i.e. 6.02 x1023 “atoms”)
in grams
“Molar mass”
(grams per mole)
Penny
Nickel
Quarter
Loonie
Q. Why are the “molar masses” different?

*Define molar mass in your own words:

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*The masses of real atoms are much, much smaller. But the relationship is the same!!
Element
Helium
Iron
Lead
Uranium
Mass of one
atom
in grams
Mass of 1.00
mol of atoms
(i.e. 6.02 x1023 atoms)
in grams
Molar mass
(grams per
mole)
Average
Atomic mass
(atomic mass
units)
-24
6.64 x 10
9.28 x 10-23
3.44 x 10-22
3.95 x 10-22
Q. a) What is the relationship between molar mass and the average atomic mass of an
element?

b) What is the simplest way to determine the molar mass of an element?

Mole Calculations (Part 2)
“Warm-Up” Activity  Finding the Molar Mass of Compounds:
1. Consider a sample of 12 carbon monoxide, CO(g), molecules.
*How many carbon atoms are in the sample? _______
*How many oxygen atoms are in the sample?_______
*The ratio of carbon atoms to oxygen atoms is ____:____
*Therefore, in a sample containing 1 dozen CO(g) molecules, there is ___ dozen carbon
atoms and ____ dozen oxygen atoms.
2. Consider a sample of 6.02 x 1023 molecules of CO(g).
*How many carbon atoms are in the sample? _____
*How many oxygen atoms are in the sample? _____
*Therefore in a 1.0 mol sample of CO(g), there is ____ mole of carbon atoms and ____
mole of oxygen atoms.
 1.0 mol of carbon atoms has a mass of _________
 1.0 mol of oxygen atoms has a mass of _________
 1.0 mol of CO(g) molecules is therefore the sum of the above 2 masses.
MCO(g) = nC(MC) + nO(MO)
= 1(________ g/mol) + 1(_______g/mol)
= _________ g/mol
*Symbol for molar mass is “M”.
*Determine the molar mass, M, of the following compounds:
a) MgCl2
b) Al2S3 c) C6H12O6 d) Ca3(PO4)2
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More Mole Calculations
“Warm-Up Activity  Provide the Formula
1. The molar mass of oxygen gas, O2(g) is 32.00 g mol-1. How many moles of oxygen are there in
a 64.00 g sample of oxygen gas? Provide a formula.
2. What is the mass of 3.0 mol sample of O2(g)? Provide a formula.
Part A  More Practice: Converting from Moles to Mass
1. Calculate the mass of each of the following molar quantities.
a) 3.90 mol of carbon (Ans. 46.8 g) b) 1.45 x 10-5 mol of (NH4)2Cr2O7 (Ans. 3.66 x 10-3 g)
2. A litre of water contains 55.6 mol of water. What is the mass of a litre of water?
(Ans. 1.00 x 103 g)
3. To carry out a particular reaction, a chemical engineer needs 255mol of styrene, C8H8. How
many kilograms of styrene does the engineer need? (Ans. 26.6 kg)
Part B  More Practice: Converting from Mass to Moles
1. Calculate the number of moles in each of the following samples.
a) 1.32 x 104 g of Pd b) 0.736 kg of Cr
c) 56.3 mg of Ge
d) 1.55 x 105 kg of carbon tetrafluoride, CF4
e) 8.11 x 10-3 mg of C8H9I
[Ans. a) 1.24 x 102 mol b) 14.2 mol c) 7.75 x 10-4 mol d) 1.76 x 106 mol e) 3.49 x 10-8 mol]
2. Sodium chloride can be used to melt snow. How many moles of sodium chloride are in a 10 kg
bag? (Ans. 1.7 x 102 mol)
3. Octane, C8H18, is a principal ingredient in gasoline. Calculate the number of moles in a 20.0 kg
sample. (Ans. 1.75 x 102 mol)
Part C  More Practice: Converting Between Moles, Mass, and Number of Particles
1. Determine the mass of each of the following samples.
a) 6.02 x 1024 formula units of ZnCl2
b) 9.11 x 1023 molecules of C15H21N3O15
3
2
[Ans. a) 1.36 x 10 g b) 7.32 x 10 g]
2. What is the mass of lithium in 254 formula units of lithium chloride? (Ans. 2.93 x 10-21 g)
3. Express the mass of a single atom of titanium in grams. (Ans. 7.95 x 10-23 g)
4. Vitamin B2, C17H20N4O6, is also called riboflavin. What is the mass, in grams, of a single
molecule of riboflavin? (Ans. 6.25 x 10-22 g)
5. Determine the number of molecules or formula units in each of the following samples.
a) 52.4 g of methanol, CH3OH
b) 0.337 g of lead(II) phosphate
c) 64.3 mg of tetraphosphorus decoxide
d) 4.35 x 10-2 g of potassium chlorate / How many ions (chlorate and potassium) are in the
sample?
[Ans. a) 9.84 x 1023 b) 2.50 x 1020 c) 1.36 x 1020 d) 2.14 x 1020 / 4.27 x 1020 ]
6. How many atoms of hydrogen are in 5.3 x 104 molecules of sodium glutamate, NaC5H8NO4?
(Ans. 4.2 x 105)
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Molar Mass: More Practice (I)
Complete the following table. The first few have been done for you.
Substance
Mass of One Entity
(Include Type of Entity)
Ne (atomic)
atomic mass; 20.18 u
NH3 (molecular)
molecular mass; 17.04 u
NaCl (ionic)
formula mass; 58.44 u
O3
MgCl2
C6H12O6
Pb
LiBr
Be
CCl4
Al2S3
Mass of 6.02 x 1023 Entities
(i.e., molar mass)
molar mass; 20.18 g
molar mass; 17.04 g
molar mass; 58.44 g
Molar Mass: More Practice (II)
The Mole Box  Within each box, list all the equivalent descriptions of one mole of the specified
substance. The first few have been done for you. **1 mole of any gas occupies a volume of 22.4 L at STP
(i.e., at 25°C / 100kPa).
CO(g)
W(s)
Equivalents:
- 1 mole
- 6.02 x 1023 molecules
- 28.0 g
- 22.4 L at STP
Equivalents:
- 1 mole
- 6.02 x 1023 atoms
- 183.84 g
Rb2O(s)
Sn(s)
Equivalents:
- 1 mole
- 6.02 x 1023 formula units
- 186.94 g
Equivalents:
SF6(g)
NaOH(s)
Equivalents:
Equivalents:
HNO3(l)
N2O4(g)
Equivalents:
Equivalents:
O3(g)
BaCl2(s)
Equivalents:
Equivalents:
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More Review:
1. How many atoms of C are in a mixture containing 0.237 mol of CO2 and 2.38 mol of CaC2?
2. How many atoms of H are in a mixture of 3.49 x 10 23 molecules of H2O and 78.1 g of CH3OH?
3. How many nitrate ions are in a solution that contains 3.76 x 10 -1 mol of calcium nitrate, Ca(NO3)2?
SCH3U1  Making Connections Assignment (The Mole)
1. The RNI (Recommended Nutrient Intake) of iron for women is listed as 14.8 mg per day. Ferrous
gluconate, Fe(C6H11O7)2 is often used as an iron supplement for those who do not get enough iron in
their diet because it is relatively easy for the body to absorb. Some iron-fortified breakfast cereals
contain elemental iron metal as their source of iron.
a) Calculate the number of moles of elemental iron, Fe, required by a woman, according to the RNI.
b) What mass, in milligrams, of ferrous gluconate, would satisfy the RNI for iron?
2. The daily RNI of calcium for adolescent females is 700 to 1100 mg. A supplement tablet contains 950
mg of calcium citrate. Each gram of calcium citrate contains 5.26 x 10-3 mol of calcium. How many
tablets would a 16-year-old female have to take to meet her daily RNI?
3. Vitamin B3, also known as niacin, helps maintain the normal function of the skin, nerves, and digestive
system. The disease pellagra results form a severe niacin deficiency. People with pellagra experience
mouth sores, skin irritation, and mental deterioration. Niacin has the following formula: C 6H5NO2. Often
vitamin tablets contain vitamin B3 in the form of niacinamide, C6H6N2O, which is easier for the body to
absorb.
a) A vitamin supplement tablet contains 100 mg of niacinamide. What mass of niacin contains an
equivalent number of moles as 100 mg of niacinamide?
*4. Ethanol, C2H5OH, is frequently used as the fuel in wick-type alcohol lamps. One molecule of C2H5OH
requires three molecules of O2 for complete combustion. What mass of O2 is required to react
completely with 92.0 g of C2H5OH?
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