Key Concepts
 Mole is the generally accepted SI unit for measuring the amount of substance^{1}.
 Mole is abbreviated to mol
 Mole has the symbol n
 1 mole contains the same number of particles as there are in 12 g of carbon12 atoms by definition.
12 g of carbon12 atoms = 6.022 x 10^{23} carbon atoms
6.022 x 10^{23} is called the Avogadro number or Avogadro constant
N_{A} is the symbol used to represent the Avogadro Number^{2} .
 1 mole of any sort of particle has the number of particles

= Avogadro's number of particles
= N_{A} particles
= 6.022 x 10^{23} particles

 1 mole of any pure substance has a mass

= relative molecular mass of substance in grams
= M_{r}(substance) in grams
= molar mass^{3} (symbol M, units^{4} g mol^{1})

 1 mole of any ideal gas has a volume V_{m}

V_{m} = 22.71 L 
at 0^{o}C (273.15K) 
and 
100 kPa ^{5} (0.987atm) 
Standard Temperature and Pressure (STP) 

V_{m} = 24.79 L 
at 25^{o}C (298.15K) 
and 
100 kPa ^{6} (0.987atm) 
Standard Laboratory Conditions (SLC) Standard Ambient Temperature and Pressure (SATP) 
V_{m} is the symbol used to represent the molar volume of the gas at a specified temperature and pressure.
Mole Concepts
Avogadro's Number, N_{A}
On the right is a diagram of 1 dozen eggs, each egg represented as 0.
"Dozen" is the term used to refer to a particular number, 12 in fact.
1 dozen eggs = 12 eggs


If you had 12 boxes of a dozen eggs you would have a gross of eggs.
"Gross" is the term used to refer to 12 dozen of something.
The term "Avogadro number" is just the name given to a particular number.
The Avogadro number is an extremely large number: 602 200 000 000 000 000 000 000
which is why we usually write it using scientific (exponential) notation: 6.022 x 10^{23}
A Mole, n
On the right is a diagram of 1 dozen eggs, each egg represented as 0 and each egg is sitting in its own space in a carton.
1 carton of eggs contains 1 dozen eggs
1 carton of eggs = 1 dozen eggs
The word "carton" refers to the collection of 1 dozen eggs.
1 carton of eggs = 1 dozen eggs = 12 eggs


When you have a collection of 6.022 x 10^{23} things, the collection is referred to as a mole.
1 mole of anything contains Avogadro's number of things:
1 mole of eggs = N_{A} eggs = 6.022 x 10^{23} eggs
1 mole of dust particles = N_{A} dust particles = 6.022 x 10^{23} dust particles
1 mole of sand grains = N_{A} sand grains = 6.022 x 10^{23} sand grains
1 mole of water droplets = N_{A} water droplets = 6.022 x 10^{23} water droplets
1 mole of water molecules = N_{A} water molecules = 6.022 x 10^{23} water molecules
1 mole of hydrogen atoms = N_{A} hydrogen atoms = 6.022 x 10^{23} hydrogen atoms
Molar Mass, M
On the right is a diagram of 1 dozen extra large eggs, each extra large egg represented as 0 and each egg is sitting in its own space in a carton.
Each extra large egg has a mass of 55 grams.
mass of eggs in 1 carton of extra large eggs
= 1 dozen eggs x mass of each extra large egg
= 12 x 55 g = 660 g


On the right is a diagram of 1 dozen small eggs, each small egg represented as 0 and each egg is sitting in its own space in a carton.
Each small egg has a mass of 25 grams.
mass of eggs in 1 carton of small eggs
= 1 dozen eggs x mass of each small egg
= 12 x 25 g = 300 g


A carton always holds 1 dozen eggs.
1 dozen eggs is always equal to 12 eggs.
But, the mass of a carton of 1 dozen eggs depends on the "identity" of the eggs, that is, small eggs have less mass than extra large eggs.
Molar Mass of Atoms
Moles of atoms are just like the carton of eggs analogy above:
1 mole of atoms always contains Avogadro's number of atoms
1 mole of atoms always contains N_{A} atoms
1 mole of atoms always contains 6.022 x 10^{23} atoms
But, the mass of 1 mole of atoms will depend on the "identity" of the atoms.
The "identity" of an atom is determined by which element the atoms belong to.
Atoms of different elements have different relative atomic masses (atomic weights).
You can find the relative atomic mass (or atomic weight), M_{r}, for an atom of any element in the Periodic Table of the Elements.
The mass of 1 mole of atoms of an element is the relative atomic mass (atomic weight) of the element expressed in grams.
The mass of 1 mole of atoms of an element is known as the molar mass of the element and has the units grams per mole, g mol^{1}
Below is a table of some of the elements you will encounter during your chemistry course:
Name of Element 
Symbol of Element 
Relative Atomic Mass (Atomic Weight) 
Number of Atoms in 1 Mole (N_{A}) 
Mass of 1 Mole of Atoms (g) 
Molar Mass of Atoms (g mol^{1}) 
hydrogen 
H 
1.008 
6.022 x 10^{23} H atoms 
1.008 g 
1.008 g mol^{1} 
carbon 
C 
12.01 
6.022 x 10^{23} C atoms 
12.01 g 
12.01 g mol^{1} 
nitrogen 
N 
14.01 
6.022 x 10^{23} N atoms 
14.01 g 
14.01 g mol^{1} 
oxygen 
O 
16.00 
6.022 x 10^{23} O atoms 
16.00 g 
16.00 g mol^{1} 
Molar Mass of Molecules^{7}
A molecule is made up of 2 or more atoms chemically joined (bonded) together.
1 mole of molecules always contains Avogadro's number of molecules
1 mole of molecules always contains N_{A} molecules
1 mole of molecules always contains 6.022 x 10^{23} molecules
But the mass of 1 mole of molecules will depend on the "identity" of the molecules.
The "identity" of a molecule is determined by the number of atoms of each element making up the molecule.
For every molecule we can write a molecular formula.
For every molecular formula we can write, we can determine the relative molecular mass of the molecule.
And, just like we did for the examples of atoms of elements above, 1 mole of molecules will have a mass equal to its relative molecular mass expressed in grams.
Relative molecular mass expressed in grams is known as the molar mass of the molecule.
Below is a table of some of the molecules you will encounter during your chemistry course:
Name of Molecule 
Molecular Formula 
Relative Molecular Mass 
Number of Molecules in 1 Mole (N_{A}) 
Mass of 1 Mole of Molecules (g) 
Molar Mass of Molecule (g mol^{1}) 
oxygen 
O_{2} 
32.00 
6.022 x 10^{23} O_{2} molecules 
32.00 g 
32.00 g mol^{1} 
nitrogen 
N_{2} 
28.02 
6.022 x 10^{23} N_{2} molecules 
28.02 g 
28.02 g mol^{1} 
water 
H_{2}O 
18.016 
6.022 x 10^{23} H_{2}O molecules 
18.016 g 
18.016 g mol^{1} 
ammonia 
NH_{3} 
17.034 
6.022 x 10^{23} NH_{3} molecules 
17.034 g 
17.034 g mol^{1} 
Molar Volume of Gas, V_{m}
You've probably watched as a balloon is filled with helium from a gas cylinder.
As more helium enters the balloon, the volume of the balloon increases.
This is because the atoms of helium making up the helium gas occupy as large a volume as possible.
And that volume is determined by the number of helium atoms there are in the balloon as well as by the air temperature and pressure.
If you were to simultaneously fill one balloon with 1 mole of helium atoms, and another balloon with 1 mole of argon atoms, you would find that both balloons would fill up to occupy the same volume.
The volume of 1 mole of gas depends on the surrounding temperature and pressure, and not really on the "identity" of the atoms or molecules making up the gas!^{8}
The volume of 1 mole of gas is called its molar volume and is given the symbol V_{m}.
Molar gas volume is a useful term ONLY if you known the prevailing conditions of temperature and pressure.
Molar Gas Volume, V_{m}, at Standard Temperature and Pressure
Standard Temperature is defined as 0^{o}C (or 273.15 K)
Standard Pressure is defined as 100 kPa (or 0.987 atm)
Therefore the conditions of standard temperature and pressure are 0^{o}C (273.15 K) and 100 kPa (0.987 atm).
Standard temperature and pressure are usually abbreviated as STP.
The volume of 1 mole of any ideal gas at a temperature of 0^{o}C and a pressure of 100 kPa is 22.71 L.
The volume of 1 mole of any ideal gas at standard temperature and pressure is 22.71 L.
The volume of 1 mole of any ideal gas at STP is 22.71 L.
For an ideal gas at 0^{o}C and 100 kPa, the molar gas volume, V_{m}, is 22.71 L.
For an ideal gas at standard temperature and pressure the molar gas volume V_{m}, is 22.71 L.
For an ideal gas at STP the molar gas volume V_{m}, is 22.71 L.
Below is a table of some gases you will encounter during your chemistry course:
Name of Gas 
Molecular Formula 
Relative Molecular Mass 
Molar Mass of Gas (g mol^{1}) 
Number of Gas Molecules in 1 Mole (N_{A}) 
Molar Volume of Gas at STP (L) 
helium 
He 
4.003 
4.003 g mol^{1} 
6.022 x 10^{23} He atoms 
22.71 L 
nitrogen 
N_{2} 
28.02 
28.02 g mol^{1} 
6.022 x 10^{23} N_{2} molecules 
22.71 L 
carbon monoxide 
CO 
28.01 
28.01 g mol^{1} 
6.022 x 10^{23} CO molecules 
22.71 L 
carbon dioxide 
CO_{2} 
44.01 
44.01 g mol^{1} 
6.022 x 10^{23} CO_{2} molecules 
22.71 L 
Molar Gas Volume, V_{m}, at 25^{o}C and 100 kPa
While 0^{o}C is a very useful standard for temperature, it isn't really a temperature you'd like to keep the laboratory at while you work.
So, Chemists will define as standard a useful temperature and pressure based on the kind of work that they do.
In some circumstances, 25^{o}C (298.15 K) and 100 kPa (0.987 atm) is used to define the standard, and is then referred to as Standard Laboratory Conditions (abbreviated as SLC) or as Standard Ambient Temperature and Pressure (abbreviated as SATP).
1 mole of any ideal gas at 25^{o}C and 100 kPa has a volume of 24.79 L.
The molar volume, V_{m}, of any ideal gas at 25^{o}C and 100 kPa is 24.79 L.
Below is a table of some gases you will encounter during your chemistry course:
Name of Gas 
Molecular Formula 
Relative Molecular Mass 
Molar Mass of Gas (g mol^{1}) 
Number of Gas Molecules in 1 Mole (N_{A}) 
Molar Volume of Gas at SLC (L) 
helium 
He 
4.003 
4.003 g mol^{1} 
6.022 x 10^{23} He atoms 
24.79 L 
nitrogen 
N_{2} 
28.02 
28.02 g mol^{1} 
6.022 x 10^{23} N_{2} molecules 
24.79 L 
carbon monoxide 
CO 
28.01 
28.01 g mol^{1} 
6.022 x 10^{23} CO molecules 
24.79 L 
carbon dioxide 
CO_{2} 
44.01 
44.01 g mol^{1} 
6.022 x 10^{23} CO_{2} molecules 
24.79 L 
Summary
1 mole of molecules:
 contains N_{A} molecules
1 mole of molecules = 6.022 x 10^{23} molecules
 has mass equal to its relative molecular mass in grams
mass of 1 mole of molecules = M_{r} g
 has molar mass equal to relative molecular mass in grams per mole
molar mass in g mol^{1} = M_{r} in grams = M g mol^{1}
1 mole of gas molecules also has a volume of
 22.71 L at 0^{o}C (273.15 K) and 100 kPa (0.987 atm) (STP)
 24.79 L at 25^{o}C (298.15 K) and 100 kPa (0.987 atm) (SLC)
Examples
Avogadro Number (N_{A})
How many chlorine molecules, Cl_{2}, are present in 1 mole of chlorine gas, Cl_{2}(g)?
 What is the question asking you to do?
Calculate the number of chlorine molecules in 1 mole of chlorine gas.
 What information (data) has been given in the question?
molecular formula for chlorine molecules: Cl_{2}
amount of chlorine gas = 1 mole
 What relationship exits between moles and the number of molecules present?
1 mole molecules = N_{A} molecules = 6.022 x 10^{23} molecules
 Substitute the word "molecules" above with the particular molecule given in the question, "Cl_{2} molecules":
1 mole Cl_{2} molecules = N_{A} Cl_{2} molecules = 6.022 x 10^{23} Cl_{2} molecules
 1 mole of chlorine gas contains 6.022 x 10^{23} chlorine molecules.
Molar Mass (M)
What is the mass of 1 mole of methane, CH_{4}, molecules?
 What is the question asking you to do?
Calculate the mass of 1 mole of methane molecules.
 What information (data) has been given in the question?
molecular formula for methane molecules: CH_{4}
amount of methane = 1 mole
 What relationship exits between moles and the mass of molecules?
mass of 1 mole molecules = relative molecular mass expressed in grams
 Calculate the relative molecular mass of methane, M_{r}(CH_{4}),
Use the Periodic Table to find the relative atomic mass (atomic weight) of carbon, M_{r}(C), and hydrogen, M_{r}(H):
M_{r}(C) = 12.01
M_{r}(H) = 1.008
CH_{4} contains 1 carbon atom and 4 hydrogen atoms, so
M_{r}(CH_{4}) = 1 x M_{r}(C) + 4 x M_{r}(H) = 1 x 12.01 + 4 x 1.008 = 16.042
 Calculate the mass of 1 mole of CH_{4}:
mass of 1 mole CH_{4} = M_{r}(CH_{4}) expressed in grams
mass of 1 mole CH_{4} = 16.042 g
 The mass of 1 mole of methane, CH_{4}, is 16.042 g
Molar Volume of Gases
What is the volume occupied by 32.00 g of oxygen gas, O_{2}(g), at a temperature of 0^{o}C and a pressure of 100 kPa?
 What is the question asking you to do?
Calculate the volume of oxygen gas.
 What information (data) has been given in the question?
molecular formula for oxygen gas: O_{2}(g)
mass of oxygen gas = m(O_{2(g)}) = 32.00 g
conditions for the experiment: temperature = 0^{o}C, pressure = 100 kPa
recognise that 0^{o}C and 100 kPa = Standard Temperature and Pressure (STP)
 What relationship exists between the mass of a gas and its volume at STP?
At STP 1 mole of gas has a volume of 22.71 L
1 mole of gas has a mass equal to its relative molecular mass expressed in grams.
 Calculate the relative molecular mass of oxygen gass, M_{r}(O_{2(g)}):
Use the Periodic Table to find the relative atomic mass (atomic weight) for oxygen atoms, M_{r}(O):
M_{r}(O) = 16.00
Each oxygen molecule, O_{2}, contains 2 oxygen atoms (O), so
M_{r}(O_{2}) = 2 x M_{r}(O) = 2 x 16.00 = 32.00
 Calculate the mass of 1 mole of oxygen molecules, m(O_{2(g)})
mass of 1 mole of O_{2} molecules = m(O_{2}) = M_{r}(O_{2}) in grams = 32.00 g
Note that the mass of O_{2}(g) given in the question is 32.00 g, so the question is asking for the volume of 1 mole of O_{2}(g).
 Calculate the volume of 1 mole of O_{2}(g):
At STP, 1 mole of gas has a volume of 22.71 L
At STP, 1 mole of O_{2}(g) has a volume of 22.71 L
 32.00 g of oxygen gas has a volume of 22.71 L at 0^{o}C and 100 kPa.
Problem Solving Using Definitions of a Mole
The Problem: Bo the Biologist has been collecting the gas emitted overnight by pea plants in a sealed plastic bag.
Bo suspects the gas is either oxygen, carbon monoxide or carbon dioxide, but would like to know for sure.
Bo took the gas sample in the sealed plastic bag to Chris the Chemist for analysis.
Chris the Chemist cooled the gas down to 0^{o}C at 100 kPa and weighed it.
The mass of gas was found to be 44.01 g.
Next Chris plunged the sealed plastic bag full of gas into a filled container of ice cold water at 0^{o}C and measured the volume of water displaced by the plastic bag full of gas.
The volume of the gas was then found to be 22.71 L.
What was the chemical formula for the gas in the plastic bag?
Solving the Problem
Using the StoPGoPS model for problem solving:
STOP!
 State the question. 
What is the question asking you to do?
Determine the molecular formula of the gas.
What chemical principle will you need to apply?
Apply stoichoimetry (definitions of a mole)
What information (data) have you been given?
 substance is a gas
 gas could be oxygen, carbon monoxide or carbon dioxide
 m(gas) = mass of gas = 44.01 g
 V(gas) = volume of gas = 22.71 L
 conditions of experiment: 0^{o}C and 100 kPa (standard temperature and pressure, STP)

PAUSE!
 Plan. 
Step 1: Determine the amount, in moles, of gas present
Assume gas is behaving like an ideal gas
At STP, 1 mole of ideal gas has a volume of 22.71 L
At STP, volume of unknown gas, V_{(gas)} = 22.71 L
moles of unknown gas = ? mol
Step 2: Write the molecular formula for each of the three possible gasses:
molecular formula of oxygen gas:
molecular formula of carbon monoxide gas:
molecular formula of carbon dioxide gas:
Step 3: Determine the molar mass, M, for each of the three possible gases
Use the Periodic Table to find the relative atomic mass (atomic weight) of oxygen and carbon:
M_{r}(O) = atomic weight of oxygen
M_{r}(C) = atomic weight of carbon
Use the molecular formula above to determine the relative molecular mass of each of the three possible gasses:
relative molecular mass of oxygen gas:
relative molecular mass of carbon monoxide gas:
relative molecular mass of carbon dioxide gas:
Convert each relative molecular mass, M_{r}, to a molar mass, M:
molar mass = relative molecular mass expressed as grams per mole
molar mass of oxygen gas:
molar mass of carbon monoxide gas:
molar mass of carbon dioxide gas:
Step 4: Determine which of the three gases is present
Assume the gas in the plastic bag is a pure substance, that is, only one type of molecule is present
Compare the molar mass of each gas to that of the amount of gas in the plastic bag.

GO!
 Go with the Plan. 
Step 1: Determine the amount, in moles, of gas present
Assume gas is behaving like an ideal gas
At STP, 1 mole of ideal gas has a volume of 22.71 L
At STP, volume of unknown gas, V_{(gas)} = 22.71 L
moles of unknown gas = 1 mol because its volume at STP is 22.71 L
Step 2: Write the molecular formula for each of the three possible gasses:
molecular formula of oxygen gas: O_{2}
molecular formula of carbon monoxide gas: CO
molecular formula of carbon dioxide gas: CO_{2}
Step 3: Determine the molar mass, M, for each of the three possible gases
Use the Periodic Table to find the relative atomic mass (atomic weight) of oxygen and carbon:
M_{r}(O) = atomic weight of oxygen = 16.00
M_{r}(C) = atomic weight of carbon = 12.01
Use the molecular formula above to determine the relative molecular mass of each of the three possible gasses:
relative molecular mass of oxygen gas = M_{r}(O_{2}) = 2 x 16.00 = 32.00
relative molecular mass of carbon monoxide gas = M_{r}(CO) = 12.01 + 16.00 = 28.01
relative molecular mass of carbon dioxide gas = M_{r}(CO_{2}) = 12.01 + 2 x 16.00 = 12.01 + 32.00 = 44.01
Convert each relative molecular mass, M_{r}, to a molar mass, M:
molar mass = relative molecular mass expressed as grams per mole
molar mass of oxygen gas = M(O_{2}) = 32.00 g mol^{1}
molar mass of carbon monoxide gas = M(CO) = 28.01 g mol^{1}
molar mass of carbon dioxide gas = M(CO_{2}) = 44.01 g mol^{1}
Step 4: Determine which of the three gases is present
Assume the gas in the plastic bag is a pure substance, that is, only one type of molecule is present
Compare the molar mass of each gas to that of the amount of gas in the plastic bag.
molar mass of unknown gas = mass of 1 mole of unknown gas = 44.01 g mol^{1}
M(CO_{2}) = 44.01 g mol^{1}
Unknown gas most likely to be CO_{2}

PAUSE!
 Ponder Plausability. 
Have you answered the question that was asked?
Yes, we have determined the molecular formula for the gas most likely to be in the plastic bag.
Is your solution to the question reasonable?
Let's work backwards to see if the formula for the gas we have chosen will give us the correct mass and volume at STP.
M_{r}(CO_{2}) = 12.01 + 2 x 16.00 = 12.01 + 32.00 = 44.01 g
1 mole CO_{2}(g) has volume = 22.71 L at STP (0^{o}C, 100 kpa)
Experiment has conducted at STP, and unknown gas had volume of 22.71 L = 1 mole, and this 1 mole had a mass of 44.01 g,
CO_{2} does look like a reasonable answer to the question.

STOP!
 State the solution. 
The molecular formula for the gas in the plastic bag is CO_{2}(g). 
