Download The Mole (Avogadro Constant)

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The Mole (Avogadro Constant)
A Mole (mol)
One mole of a substance is the amount of substance which contains as many particles (atoms or
molecules) as there are atoms in 12g (0.12kg) of the carbon – 12 isotope. This value has been found
experimentally to be 6.022 × 1023.
Avogadro Constant (NA)
This constant is numerically equal to the number of atoms in one mole (the number of atoms in 12g of
carbon – 12 isotope). NA = 6.022 × 1023 mol-1
Molar Mass
The molar mass of a substance is the defined as the mass per mole of the substance (SI Unit: kgmol-1 or
gmol-1). This value is numerically equal to its atomic mass.
Atomic Mass Unit (µ)
of the mass of the carbon – 12 atom.
One unit of the atomic mass equals
Note: 6.022 × 1023 carbon atoms have a mass of 12g
Therefore, 1 carbon atom has a mass of [
Hence 1 atomic mass unit =
(1 µ =
[
.
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.
×
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×
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The mass of a single atom of an element is equal to its atomic mass expressed in atomic mass units.
Example 3.1
Using Avogadro Constant (NA)
a. Using NA = 6.022 × 1023 mol-1, calculate the number of atoms in 14g of iron (atomic mass = 56)
56 g of iron contains 6.022 × 1023 atoms
1g of iron contains
.
14 g of iron contains
.
×
= .
×
×
×
atoms
=
.
×
atoms
b. Using NA = 6.022 × 1023 mol-1, calculate the number of atoms in 81mg of aluminum, (atomic
mass = 27)
27 g of aluminum contains 6.022 × 1023 atoms
1g of iron contains
.
86 mg of iron contains
×
.
= .
×
×
×
atoms
×
−
=
.
×
atoms
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c. Find the number of free electrons in 1m3 of copper given that the density of copper is 8.9 × 103
kgm-3. The molar mass of copper is 63.5 g.
Each copper atom as one free electron and NA = 6.022 × 1023 mol-1.
mass = density × volume
= 8.9 × 103 × 1
= 8.9 × 103 kg
0.0635 kg (63.5 g) of copper contains 6.022 × 1023 atoms
1 kg of copper contains
3
.
.
×
= .
×
3
atoms
8.9 × 10 kg of copper contains (8.9 × 10 ) × (9.48 × 1024) = 8.44 × 1028 atoms
d. Estimate the following:
i. the mass of one water molecule
ii. the number of molecules in 1 m3 of water
iii. the diameter of a water molecule assuming it is spherical in shape
Given that molar mass of water is 18g, density of water is 1000 kgm-3 and NA = 6.022 × 1023 mol-1
i.
6.022 × 1023 moles of water has a mass of 0.018 kg
1 mole of water has a mass of
ii.
.
.
= .
×
1m3 of water has a mass (1000 × 1) = 1000 kg
the number of molecules in 1m3 of water =
iii.
3.35 × 1028 molecules occupy 1m3 of water
1 molecule occupies
=
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= √ .
Problems 3.1
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=
ℎ
×
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=
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=
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=
×
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= .
×
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= .
= .
×
×
−
−
×
− 6
−
m3
= .
×
×
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−
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kg
= .
×
−
m
−
m
Breithaupt, J. (2000) Understanding Physics for Advanced Level (4th edition)
Page 101
Numbers: 6.2, 6.3, 6.4
D.Whitehall