Moles of Elements
How many atoms are there in 12.000g of carbon? This is not an easy question because carbon
atoms are unbelievably tiny and too small to count. Even if we couldn’t count them, we could
say: “The number of atoms in 1.000g of hydrogen should be the same as the number of atoms
in 12.000g of carbon”. We know from the Periodic Table that the relative atomic mass of
hydrogen is one and carbon is 12. Carbon atoms are 12 times heavier than hydrogen atoms.
This explains why 1g of hydrogen and 12g of carbon contain the same number of atoms.
The Amount of Substance
Whatever this number is (it’s actually called Avogadro’s number and is approximately 602 214
179 000 000 000 000 000 or in scientific notation, 6.02214179 x 1023) the important thing is
that this idea of number of atoms gives us a way of measuring the amount of carbon, which
chemists find very useful. You might think that the units for measuring the amount of
substance would be ‘atoms’. For example, I might decide to burn 100 atoms of carbon and see
how much carbon dioxide I get. The balanced chemical equation for the complete combustion
carbon implies that we would end up with 100 molecules of carbon dioxide if we burnt 100
atoms of carbon:
C + O2 → CO2
100 atoms of C + 100 O2 molecules → 100 molecules of CO2
This seems nice and simple. The only problem with it is that 100 carbon atoms is a tiny
amount of carbon – a tiny speck too small to be seen. We normally do experiments with a few
grams or a few kilograms of carbon.
When chemists talk about the amount of a substance they find
it more convenient to use the units moles instead of ‘atoms’. A
‘mole of something’ just means 6.02214179 x 1023 of that thing.
Don’t be confused by us using a word to describe a number. The
word ‘dozen’ means 12. A chemist talking about ‘five moles of
carbon atoms’ is exactly like a chicken farmer talking about ‘five
dozen eggs’. The only difference is that the chemist has quite a
lot more carbon atoms than the chicken farmer has eggs
because one mole is such a gigantically enormous number!
Similarly I could burn one mole of carbon and I’d end up with one mole of carbon dioxide:
C + O2 → CO2
1 mole of C atoms + 1 mole of O2 molecules → 1 mole of CO2
In fact when you read balanced chemical equations out loud (like C + O2 → CO2), you should
actually say, ‘One mole of carbon plus one mole of oxygen goes to one mole of carbon dioxide.’
An Equation for Calculating the Amount of Substance
How do you find out how many moles of carbon atoms there are in, say, a lump of graphite?
You can’t tell just by looking – you’d have to weigh it using a balance. Mass is a different way
of measuring how much ‘stuff’ you have got. Let’s suppose you had 120g of a lump of some
pure substance. The lump might contain a large number of relatively light atoms (e.g. 10
moles of carbon atoms) or you might have a smaller number of heavier atoms (e.g. three
moles of calcium atoms).
We’re going to use our imagination to do a couple of thought experiments. Imagine a big
block of 20 moles of iron, which weighs 1.12kg. What effect would doubling the amount of
moles have on the mass? If we doubled the number of moles from 20 to 40, the mass of the
block of iron would also double, to 2.24kg. We can therefore say that mass is proportional to
amount (in moles).
You are a magician and you can magically turn carbon atoms (with a RAM of 12) into
magnesium atoms (with a RAM of 24). If you started off with 10 moles of carbon, which
weighed 120g, waved your magic wand and turned all the
carbon atoms into magnesium atoms, the lump would end
up twice as heavy because 10 moles of magnesium weighs
240g. Doubling the RAM doubles the mass. In other
words, Mass is also proportional to RAM.
mass
We can combine mass is proportional to moles and mass
is proportional to RAM to obtain the expression
mass = moles x RAM.
Example One
What is the mass of 0.5 mol of magnesium?
mass of Mg = moles x RAM
= 0.5 x 24
= 12 g
Example Two
What is the amount of calcium in 48g?
moles of Ca = mass / RAM
= 48 / 40
1.2 mol
1) Calculate the mass of:
a) 0.55 mol of oxygen
b) 0.4 mol of zinc
c) 0.14 mol of helium
d) 0.003 mol of calcium
e) 7.5 mol of copper
f) 0.25 mol of silver
g) 0.05 mol of nickel
h) 0.7 mol of carbon
i) 0.7 mol of arsenic
j) 4 mol of chromium
moles RAM
2) Calculate the amount (in moles) of:
a) 200 g of sulfur
b) 19.5 g of potassium
c) 115 g of sodium
d) 17.6 g of hydrogen
e) 5 g of bromine
f) 4.75 g of fluorine
g) 0.49 g of nitrogen
h) 2.7 g of aluminium
i) 3.195 g of chlorine
j) 18.216 g of lead
Answers
1. Calculate the mass of…
(a) 8.8 g, (b)26 g , (c) 0.56 g, (d) 0.12 g, (e) 480 g, (f) 27 g,
(g) 2.95g, (h) 8.4 g, (i) 52.5 g, (j) 208 g
2. Calculate the amount (in moles) of…
(a) 6.25 mol, (b) 0.5 mol, (c)5 mol, (d) 17.6, (e) 0.0625 mol,
(f) 0.25 mol, (g) 0.035 mol, (h)0.1 mol, (i) 0.09 mol,
(j) 0.088 mol