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
the number of moles:
Example 1
Calculate the number of
atoms in 0.02 mol of iron.
number of atoms
To type in Avogadro’s number to your
scientific calculator, type in 6.022,
then press ‘EXP’ and type in 23.
= 0.02 x 6.022 x 10
= 1.204 x 1022
23
If the mass of substance is given, we have
to use the moles triangle to convert it into
moles:
Example 2
Calculate the number of atoms in 0.0014g
of iron.
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
following:
a) 0.05 moles of lead
b) 8 moles of helium
c) 1.5 moles of copper
d) 0.0036 moles of magnesium
e) 0.2 moles of any substance
a)
b)
c)
d)
e)
84½ million atoms
3. Calculate the number of
atoms in the following:
0.016g of copper
9g of carbon
0.001g of sulfur
0.12g of silver
80 tonnes of iron (1 tonne = 1000kg)
4. In 1999 a group of American scientists
at the Georgia Institute of Technology
claimed to have made the smallest ever
measurement of mass by using a carbon
nanotube to weigh a speck of graphite.
They estimated that the graphite weighed
22 femtograms. If 1 femtogram = 1 x 10-15
grams, calculate the number of carbon
atoms in their speck.
5. How many hydrogen atoms are there in
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