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The Mole
What is a mole???
As we have seen in previous chapters the masses of
atoms are very small e.g.
mass of proton = 1.67 x 10-27kg
mass of neutron = 1.67 x 10-27 kg
mass of electron = negligible
Subsequently it is not possible to count individual
atoms or molecules directly !!!
Amedeo Avogadro was an Italian chemist who devised
a method for counting atoms and molecules
1 atom of Mg = 24 (Ar)
1 atom of C = 12 (Ar)
So can say 100 Magnesium atoms is twice as heavy
as 100 Carbon atoms
Therefore if we have a piece of Mg that is twice the
weight of a piece of carbon can say the two amounts
contain equal numbers of atoms
Similarly if we had 2g of Mg and 1g of C they would
contain the same number of atoms
1 atom of carbon = 12 Ar
1 atom of Hydrogen = 1 Ar
1g of hydrogen atoms and 12 g of carbon atoms
both contain the same number of atoms
So, if we were to weigh out elements in the same
proportions as their relative atomic masses, we will
always be dealing with the same number of atoms
of these elements.
If we take the relative atomic mass in grams of a number
of elements:
12g
Carbon
24g
Magnesium
63.5g
Copper
108g
Silver
All of these amounts can be said to contain the same
number of atoms - shown by Avogadro to be
L = 6 x 1023 mol-1
Avogadro’s Constant
(Number)
Avogadro’s Constant ( 6 x 1023 ) is the number of
atoms of carbon in 12g of the carbon 12 isotope
One mole of a substance is the amount of that
substance which contains 6 x 1023 particles (atoms,
ions, molecules) of that substance
Points to Note
• Symbol for mole – mol
• 12g carbon = 6 x 1023 atoms of carbon = 1 mole of
carbon atoms
Similarly,
– 48g of Mg = 2 moles of magnesium
atoms
• Must specify what particle amount refers to :
1 mol of Hydrogen atoms/1 mol of H ( = 1g H atoms)
1 mol of Hydrogen molecules/ 1 mol of H2 (= 2g H2
(molecules)
1. Calculations Involving the Mole
1.
Converting Moles to Grams
2.
Converting Grams to Moles
3.
Calculations involving Avogadro’s Number
4.
More complicated problems
Molar Mass – is the mass (in grams) of one
mole of a substance.
Molar mass of carbon is 12g/mol
Molar mass of magnesium is 24g/mol
Converting Moles to Grams
Mass of 1 mole of an element = Relative Atomic Mass
in grams
e.g.
1 mole of Na = 23 g
1 mole of Mg = 24g
1 mole of copper = ???
1 mole of iron = ???
1 mole of zinc = ???
The relative molecular mass (Mr) of a compound is the
sum of the relative atomic masses of all the atoms in a
molecule of the compound.
The relative molecular mass (Mr)of a compound may
be defined as the mass of one molecule of that
compound compared with one twelfth of the mass of
the carbon-12 isotope
Mass of 1 mole of
a compound
=
Relative Molecular Mass
in grams
Converting Moles to Grams
Mass (in grams) = Relative x Number of
Molecular Mass
Moles
Example 1:
What is the mass of a mole of helium atoms?
Solution:
Example 2:
What is the mass of three moles of aluminium
atoms?
Solution:
Example 3:
What is the mass of a mole of nitrogen molecules?
Solution:
Example 4:
What is the relative molecular mass of water? What is
mass of a mole of water?
Solution:
Example 5:
What is the mass of one mole of sulphate ions, SO42- ?
Solution
Example 6:
What is the mass of one mole of aluminium sulphate
Al2(SO4)3 ?
Solution:
Example 7:
What is the mass of 0.2 moles of CaCO3 ?
Solution:
Converting Grams To Moles
No. of Moles of
an element
=
Mass of Element
Relative Atomic
Mass
No. of Moles of
Compound
=
Mass of Compound
Relative Molecular
Mass
No. of Moles of
Substance
=
Mass of Substance
Mass of 1 mole of
Substance
Example 1:
How many moles are there in 1g of Helium atoms?
Solution:
Example 2:
How many moles of atoms are there in 10g of Helium?
Solution:
Example 3:
How many moles of water are in 90g of water
Solution:
Example 4:
How many moles of sulphuric acid, H2SO4, are there in
12.25g of sulphuric acid?
Solution:
Calculations Involving Avogadro’s
Number
Remember:
Avogadro's Number represents the number of
carbon atoms in 12g of the carbon-12 isotope:
6 x 1023
It is important to remember that the atomic mass
of any other element, expressed in grams, will also
contain the same number of atoms.
A mole is the amount of a substance which
contains 6 x 1023 particles – atoms, ions or
molecules, of that substance.
Calculations involving Avogadro’s number may be
divided into four types:
1) Converting Moles to number of Atoms or
Molecules
2) Converting Grams to number of Atoms or
Molecules
3) Converting Numbers of Atoms or Molecules to
Moles
4) Converting Numbers of Atoms or Molecules to
Grams
Key to solving these problems:
1 Mole of a substance
23
contains 6 x 10 particles of
that substance
1. Converting Moles to number of Atoms or Molecules
a) Atoms:
How many atoms of sodium are present in 0.25
moles of sodium? (composed of Na atoms)
Answer:
b) Molecules:
How many molecules are present in 5 moles of water
(Composed of water molecules)
Answer:
c) How many i) molecules ii) atoms are present in 1.5
moles of water (composed of water molecules)
Answer:
2. Converting Grams to number of Atoms or Molecules
Steps Involved:
1) Find number of moles –
moles = mass/molar mass
2) Find number of molecules(atoms) –
molecules (atoms) = moles x 6 x 1023
3) Find number of atoms (Compound) –
atoms = no. of atoms x no. of molecules
a) How many atoms are there in 28.75g of sodium
(composed of Na atoms)
Answer:
b) How many molecules are contained in 4.9g of
sulphuric acid? (composed of molecules of sulphuric
acid)
c) How many atoms are contained in 34g of ammonia?
(Composed of molecules of ammonia)
3. Converting numbers of Atoms or Molecules to Moles
Example:
How many moles of atoms are present in 5 x 1024
atoms of carbon?
Answer:
*Note: Use brackets in calculations
4. Converting numbers of Atoms or Molecules to Grams
Example 1:
How many grams of zinc are present in 3 x 1020
atoms of zinc?
Answer:
Example 2:
What is the mass (in grams) of 3 x 1022 molecules of
ethanol C2H5OH
More Complicated Problems
Example 1:
How many moles of Al3+ are in 3 moles of Al2(SO)4?
Answer:
Example 2:
How many moles of oxygen atoms are there in 6.3g of
nitric acid, HNO3
Answer:
Example 3:
What mass of magnesium contains the same number
of atoms as 7g of iron?
Answer: