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The Mole and Avogadro’s Number
Chapter 9
The Mole
• Derived from the
Greek word Mole
meaning large heap.
The Mole
• The Chemical Mole is
a heap of atoms or
molecules.
Dalton
• In 1808 Dalton proposed that the atoms
of each element had a characteristic
atomic weight, and that it was atoms that
were the combining units in chemical
reactions to make compounds.
• Dalton had no method of measuring atomic weights
unambiguously, so made the incorrect assumption that in
the most common compound between two elements, there
was one atom of each element e.g. water was made from
one atom of hydrogen and one of oxygen, oxygen gas
contained only one atom of oxygen
Gay-Lussac
• Gay-Lussac studied the chemical reactions
of gases, and found that the ratios of
volumes of the reacting gases were small
integer numbers, e.g. two volumes of
hydrogen react with one volume of oxygen to
produce two volumes of water.
• Dalton couldn’t reconcile this with his new
atomic theory, and therefore rubbished the
work of Gay-Lussac.
Avogadro
The Mole Concept
Avogadro’s Number = 6.022 x 1023
Particles in a Mole
Amedeo
Avogadro
(1776 – 1856)
?
quadrillions
thousands
trillions
billions
millions
1 mole = 602213673600000000000000
or 6.022 x 1023
There is Avogadro's number of particles in a mole of any substance.
Avogadro
• In 1811, Avogadro clearly drew the distinction between a molecule
and a atom.
• He pointed out that Dalton had confused the concepts of atoms and
molecules. The Dalton “atom" of oxygen gas was in reality a molecule
containing two atoms of oxygen.
• Avogadro also suggested that “equal volumes of all gases at the
same temperature and pressure contain the same number of
molecules.” This is now known as Avogadro's Principle.
• Avogadro was Italian so everybody ignored his work until Stanislao
Cannizarro showed how it could be used to determine molar and
indirectly atomic masses at the Karlsruhe Conference in 1860.
Counting Atoms
• Chemistry is a quantitative science - we
need a "counting unit."
• The MOLE
• 1 mole is the amount of substance that
contains as many particles (atoms or
molecules) as there are in 12.0 g of C-12.
The Mole Argument
• From atomic masses one atom of magnesium is twice as heavy as
one atom of carbon (Mg = 24 and C = 12). Therefore
– If one atom of Mg is twice as heavy as one atom of C then 1000 atoms of
Mg are twice as heavy as 1000 atoms of C etc.
– a piece of Mg twice as heavy as a piece of C must contain the same
number of atoms e.g. 2 tonne of Mg contains the same number of atoms
as 1 tonne of carbon
• Therefore the relative atomic mass of any element in grams contains
the same number of atoms:
12 g
C
24 g
Mg
56 g
Fe
108 g
Ag
197 9
Au
• This number of atoms is known as the Mole
207 g
Pb
238 g
U
Extend this to molecules
• molecules are made up of atoms in different
ratios
• the relative molecular mass of a molecule in
grams contains one mole that specific molecule
16 g
CH4
17 g
NH3
18 g
H2O
32 g
O2
34 g
H2S
44 g
CO2
46 g
C2H6O
Definitions
One Mole is the amount of substance containing the same
number of units are there are atoms in exactly 12 g of 12C.
The substance must be specified and may be atoms,
molecules, ions, crystals, grains of sand, flies, sheep, trucks,
dolly’s, anything
Avogadro’s Number is the number of units in a mole
It is given the symbol L and is 6.022 1415 x 1023
How to find Avogadro Number
• Mid C19 kinetic theory of gas measurements
• Late C19 Sedimentation measurements of colloidal
particles.
• Early C20 Millikan's oil drop experiment
• Current – from the density of a crystal, the relative atomic
mass, and the unit cell length, determined from x-ray
methods. The crystal must be free of defects, Si is
commonly used.
So What?
• What is difficult to grasp is the size of Avogadro’s number,
6.022 1415 x 1023 , that is
602 214 150 000 000 000 000 000
• Basically if you can see a particle with your naked eye you won’t be
able to gather together a mole of it on this earth
• A mole of coke cans would cover the earth to a depth of over 200
miles
• Counting at a rate of 10 million per second, it would take about 2
billion years to count all the atoms in one mole
• What it means is that molecules are really very very small and there
are just unbelievable numbers of them
How Big is a Mole?
One mole of marbles would cover the entire Earth
(oceans included) for a depth of three miles.
One mole of $100 bills stacked one on top of another
would reach from the Sun to Pluto and back 7.5 million
times.
It would take light 9500 years to travel from the
bottom to the top of a stack of 1 mole of $1 bills.
1 Mole of Particles
Avogadro’s Number
 A MOLE of any substance contains as many elementary units
(atoms and molecules) as the number of atoms in 12 g of the
isotope of carbon-12.
 This number is called AVOGADRO’s number NA = 6.02 x 1023
particles/mol
 The mass of one mole of a substance is called MOLAR MASS
symbolized by MM
 Units of MM are g/mol
 Examples
H2
hydrogen
2.02
g/mol
He
helium
4.0
g/mol
N2
nitrogen
28.0
g/mol
O2
oxygen
32.0
g/mol
CO2
carbon dioxide
44.0
g/mol
Mole Calculations
• The molar mass of an element or compound is the
same as the atomic or molecular mass (as appropriate)
but is a more general term. The molar mass of a
particular substance contains 6.022 x 1023 atoms or
molecules. The symbol for the molar mass is M and the
units are g/mol.
• Example; H2S
– Mr = (1x2) + 32 = 34
– M = 34 g/mol
– 34g of H2S is one mole of H2S and therefore contains
6.022 x 1023 molecules of H2S
Mole Calculations (I)
• The number of moles of a substance is defined as the
amount of substance, n. To calculate n, just divide the
mass of the substance, m, by the molar mass, M.
n =
mass
= m
Molar mass
M
g
-1 = mol
g mol
units
Mole Calculations (II)
• To calculate the number of atoms or molecules
number of atoms or molecules = n x L
number
mass
of atoms =
x Avogradro's
Molar mass
constant
or molecules
=
mL = nL
M
g
-1
x
mol
g mol-1
units
Examples
• Calculate the number of atoms in 5x10-4 g
of Calcium
• Calculate the mass of 8.5 moles of HCl
Calculate the number of atoms
in 5 x 10-4 g of Calcium
1 mole of Calcium contains 6 x 1023 atoms
• 5 x 10 -4 mole of Calcium contains
Calculate the mass of 8.5 moles of
HCl
1 Mole of HCl is 36.5g
8.5 moles of HCl are 8.5 x 36.5
= 310.25g