4. Numbers of Atoms
Imagine a cube containing one mole of carbon atoms lined up
in rows and columns. There would be approximately 84½
million carbon atoms lined up along each side.
1.Work out what 84½ million cubed is. If your calculator
conks out, just try doing 84½ cubed and then add a suitable
number of zeros!
Avogadro’s number, the number of atoms in one mole, is
often given as 6.022 x 1023 mol-1. You can calculate the actual
number of atoms simply by multiplying Avogadro’s number by 84½ million atoms
the number of moles:
To type in Avogadro’s number to your
scientific calculator, type in 6.022,
Example 1 then press ‘EXP’ and type in 23. 3. Calculate the number of
Calculate the number of atoms in the following:
atoms in 0.02 mol of iron. a) 0.016g of copper
23
number of atoms = 0.02 x 6.022 x 10 b) 9g of carbon
= 1.204 x 1022 c) 0.001g of sulfur
d) 0.12g of silver
If the mass of substance is given, we have e) 80 tonnes of iron (1 tonne = 1000kg)
to use the moles triangle to convert it into
moles: 4. In 1999 a group of American scientists
at the Georgia Institute of Technology
Example 2 claimed to have made the smallest ever
Calculate the number of atoms in 0.0014g measurement of mass by using a carbon
of iron. nanotube to weigh a speck of graphite.
moles of iron = mass / RAM
= 0.0014 / 56
= 2.5 x 10-5 mol
number of atoms = 2.5 x 10-5 x 6.022 x 1023
= 1.506 x 1019
2. Calculate the number of atoms in the They estimated that the graphite weighed
following: 22 femtograms. If 1 femtogram = 1 x 10-15
a) 0.05 moles of lead grams, calculate the number of carbon
b) 8 moles of helium atoms in their speck.
c) 1.5 moles of copper
d) 0.0036 moles of magnesium 5. How many hydrogen atoms are there in
e) 0.2 moles of any substance 180g of water, H2O?
6. How many oxygen atoms are there in
50g of hydrated copper(II) sulfate,
CuSO4.5H2O?

Answers to ‘4. Numbers of Atoms’ Worksheet
1. 603 351 125 000 000 000 000 000 or 6.0335 x 1023
2. (a) 3.011 x 1022, (b) 4.818 x 1024, (c) 9.033 x 1023, (d) 2.16 x 1021, (e) 1.204 x 1023
3. (a) 1.505 x 1020, (b) 4.517 x 1023, (c) 1.882 x 1019, (d) 6.691 x 1020, (e) 8.603 x 1029
4. number of carbon atoms = 1.833 x 10-15 x 6.022 x 1023 = 1.1 x 109 atoms
5. number of hydrogen atoms = 1.204 x 1023 atoms
6. number of oxygen atoms = 1.084 x 1023 atoms