SCH 3U
UNIT 3: CHEMICAL QUANTITIES
In Unit 1, you learned how to use isotopic abundances and isotopic masses to find
the average atomic mass of an element. The average atomic mass (found on the
periodic table) describes the average mass of an atom in a large sample of matter.
Why is relating average atomic mass to the mass of large samples important? In a
laboratory, as in everyday life, we deal with macroscopic samples (i.e. one we can
directly measure with a balance). These samples contain incredibly large numbers
of atoms or molecules. Imagine if a procedure asked for six septillion molecules
(6 x 1024 or 6,000,000,000,000,000,000,000,000,000) of water to be added! The
numbers involved would be ridiculously inconvenient. Chemists needed a way to
deal with the large number of particles present, and the answer was the Mole.
The Mole (n)
The mole is a convenient unit to measure the very large number of particles
present in a substance.
a pair of shoes;
a dozen eggs;
a mole of particles
The mole was based on the number of atoms in 12 grams of carbon-12:
12 g
 6.022 10 23 atoms
 24
1.994 10 g / atom
This number, 6.022 x 1023 particles, was defined as a mole and is known as
Avogadro’s Constant. The number of moles of a substance can be determined
using this formula:
n
Where:
N
NA
n = number of moles.
N = number of particles
NA = Avogadro’s Constant = 6.022 x 1023
Relating Moles to Mass
When you purchase a pharmaceutical from a drugstore, you are confident that each
tablet contains the correct amount of the active ingredient. If the drug is present in
too small a quantity, the product will be ineffective. If it is present in too high an
amount, it may cause unintended side effects. When testing a product, chemist
need to be sure the correct number of molecules (or moles of molecules) of the active
ingredient are present. On its own, the mass of an active ingredient is not very
useful; it does not tell him or her to number of molecules present. Yet the effect of a
drug depends on the number of molecules, not their mass. Chemists need a way to
relate the mass of a substance to the number of particles that are present.
Molar Mass (M)
The molar mass is the mass of 1 mole (or 6.022 x 1023 particles) of any substance.
Therefore:
Where:
M 
m
n
m = mass of a substance (g)
n = number of moles of a substance (mol)
M = molar mass (g/mol)
Calculating Molar Masses
The mass of 6.022 x 1023 particles of any chemical can easily be calculated from the
sum of the atomic masses from the periodic table.
e.g.1
What is the molar mass (M) of magnesium chloride, MgCl2?
MMg = 24.31 g/mol
MCl = 35.45 g/mol
Therefore: MMgCl2 = MMgCl2 = 24.31 +(2x35.46) = 95.23 g/mol
e.g. 2
What is the molar mass of Fe(OH)3?
MFe(OH)3
= MFe + 3xMO + 3xMH = 55.85 + (3x16.00) + (3x1.01)
= 106.88 g/mol
e.g. 3
How many moles of MgCl2 are there in 250 g of this salt?
number of moles  n 
e.g. 4
m
250 g

 2.63 mol
M 95.23 g / mol
How many actual “molecules” are present?
* MgCl2 is actually ionic so they are called “formula units”!
number of particles  N  n  N A
N  (2.63  6.022 1023 ) 1.58 1024 formula units
SCH3U1
THE MOLE
1. One litre of air contains 2 x 1022 molecules of nitrogen gas. How many moles of
nitrogen are there in one litre of air?
2. A cup of water (250 mL) contains approximately 13.9 mol of H2O. How many
molecules of water are present in a cup of water?
3. a) Calculate the molar mass of carbon dioxide (CO2)?
b) Calculate the number of moles in 110 g of carbon dioxide.
c) How many molecules are there in 110 g of carbon dioxide?
d) How many atoms are there in 110 g of carbon dioxide?
4. A grain of sand has a mass of 0.012 g. If the sand is composed of silicon dioxide,
how many molecules of SiO2 are there in the grain of sand?
MOLES AND MOLAR MASS WORKSHEET
1. Using the periodic table, calculate the molar mass of the following substances:
XeF4
________________
H2SO3
________________
BaSO4
________________
Hg
________________
I2
________________
S8
________________
SiO2
________________
CH4
________________
NH4NO3
________________
Fe3[Fe(CN)6]2 ______________
2. Calculate the mass of the following:
4 mol H2SO4 ___________________________________
2.5 mol MgCO3
___________________________________
0.5 mol FeCl2
___________________________________
0.01 mol CaCO3
___________________________________
0.25 mol KF ___________________________________
6.0 mol NaOH
___________________________________
1.8 mol Al2(SO4)3
___________________________________
3. Calculate the number of moles in the following:
68 g H2S
______________
23.2 g Zn(ClO3)2
____________
1.7 g NH3
______________
1.7 g AgNO3
______________
5.6 g KOH ______________
174 g MnO2
______________
0.58 g Li3PO4 ____________
11.0 g CO2
_______________
4. A sample of the mineral hematite ( iron (III) oxide ) has a mass of 12.4 g.
a) How many moles of the mineral are present?
b) How many molecules of the mineral are present?
c) How many atoms of iron and oxygen are present?
4. One sample of gold contains 9.0 x 1021 atoms of gold sells for $50. Another sample
of gold with a mass of 3.6 g of gold also sells for $50. \Which sample contains more
gold? Hint: convert both values to moles to compare them!
HOW MUCH IS A MOLE?
1. Observe the substances at this station and complete the table.
Substance 1
Substance 2
Substance 3
Name
Chemical
Formula
Mass (g)
Molar Mass
(g/mol)
Number of
Moles (mol)
Number of
Particles
Useful Formulas:
N
n
NA
m
M 
n
n = number of moles (mol)
N = number of particles
NA = Avogadro’s number = 6.022 x 1023
M = molar mass (g/mol)
m = mass (g)
n = number of moles (mol)
Remember that the mass of 1 mole af any element is equal to the atomic mass in
grams (e.g. Mhelium = 4.0 g/mol).