Amount of
Substance
How many atoms are there in a diamond? Naturally it depends on the size, or more
specifically the mass, of the diamond. Let's consider a particularly interesting example, the
Wittelsbach-Graff Diamond:
One diamond, but how many atoms?
This famous diamond has a mass of 6.21g (31.06 carats), and like all diamonds is made up
almost entirely of carbon atoms. So, how many carbon atoms does it contain? This is where
the concept of a mole of substance comes into play.
The amount of a pure substance is expressed by the SI base unit of the mole. One mole of
any pure substance contains exactly 6.02214076 x 10
23
particles of that substance. Let's
just look at that number again. Written out fully it is:
602,214,076,000,000,000,000,000
So, by definition, 1 mole of carbon will contain 6.022 x 10
23
carbon atoms. Likewise, one
mole of gold will contain the same number of gold atoms, and a mole of oxygen will likewise
contain the same number of oxygen atoms. But, of course, gold atoms weigh a lot more than
oxygen atoms so we now need to consider the molar mass (which is related to, and very
close to, the atomic weight of a substance). In short, the molar mass is the mass of one
mole of any particular substance.
In the SI units system a mole is defined by the amount of carbon atoms there are in 12g of
carbon-12 (the nucleus of a carbon-12 atom contains 6 protons and 6 neutrons, hence
carbon-12). This is one of the reasons why a diamond, being composed almost entirely of
carbon atoms, was chosen as the main subject of this page.
Returning to our particular diamond, we know that it has a mass of 6.21g. We also know that
the molar mass of carbon-12 is 12g (that is, 1 mole of carbon-12 has a mass of 12g), and
finally we know how many atoms there are in a mole, so we now have all of the information
we need to calculate the number of atoms in the Wittelsbach-Graff Diamond.
The first thing to do is to calculate how many moles of diamond we have:
Amount of substance: 6.21g/12g = 0.5175 mol
We can now simply multiply this by Avogadro's constant to find the number of atoms in the
diamond:
0.5175 x 6.022 x 10
23
= 3.116 x 10
23
atoms
Writing that out fully we get:
311,600,000,000,000,000,000,000 atoms
One thing is very clear from such calculations - atoms are very, very small! To give an idea
of just how small, a typical adult’s small fingernail contains something in the region of 10
16
atoms, in other words, 1,000,000,000,000,000 atoms.
To recap, by definition a mole of any pure substance has a mass in grams equal to that of
the substance's molecular mass. For example, oxygen has a molar mass or atomic weight of
16g, so 1 mole of oxygen is 16g. In contrast, gold has a molar mass of 197g, so 1 mole of
gold is 197g. But, and this is the essential part, one mole of either pure oxygen or pure gold
still contains the same number of atoms, i.e. 6.022 x 10
23
.
Finally, it's important to note that while atoms have been used in the examples here other
particles can also be measured in moles, such as electrons, ions, molecules and so on.
The next SI Unit is the ampere (A). Find out how many electrons is takes to make a cup of
tea. Other SI units are available from the menus at the top of the page.
This is known as Avogadro's constant, and here we will round it to 6.022 x 10
23
.
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Amount of Substance
How many atoms are there in a diamond? Naturally it depends
on the size, or more specifically the mass, of the diamond. Let's
consider a particularly interesting example, the Wittelsbach-Graff
Diamond:
One diamond, but how many atoms?
This famous diamond has a mass of 6.21g (31.06 carats), and
like all diamonds is made up almost entirely of carbon atoms. So,
how many carbon atoms does it contain? This is where the
concept of a mole of substance comes into play.
The amount of a pure substance is expressed by the SI base
unit of the mole. One mole of any pure substance contains
exactly 6.02214076 x 10
23
particles of that substance. Let's just
look at that number again. Written out fully it is:
602,214,076,000,000,000,000,000
So, by definition, 1 mole of carbon will contain 6.022 x 10
23
carbon atoms. Likewise, one mole of gold will contain the same
number of gold atoms, and a mole of oxygen will likewise
contain the same number of oxygen atoms. But, of course, gold
atoms weigh a lot more than oxygen atoms so we now need to
consider the molar mass (which is related to, and very close to,
the atomic weight of a substance). In short, the molar mass is
the mass of one mole of any particular substance.
In the SI units system a mole is defined by the amount of carbon
atoms there are in 12g of carbon-12 (the nucleus of a carbon-12
atom contains 6 protons and 6 neutrons, hence carbon-12). This
is one of the reasons why a diamond, being composed almost
entirely of carbon atoms, was chosen as the main subject of this
page.
Returning to our particular diamond, we know that it has a mass
of 6.21g. We also know that the molar mass of carbon-12 is 12g
(that is, 1 mole of carbon-12 has a mass of 12g), and finally we
know how many atoms there are in a mole, so we now have all
of the information we need to calculate the number of atoms in
the Wittelsbach-Graff Diamond.
The first thing to do is to calculate how many moles of diamond
we have:
Amount of substance: 6.21g/12g = 0.5175 mol
We can now simply multiply this by Avogadro's constant to find
the number of atoms in the diamond:
0.5175 x 6.022 x 10
23
= 3.116 x 10
23
atoms
Writing that out fully we get:
311,600,000,000,000,000,000,000 atoms
One thing is very clear from such calculations - atoms are very,
very small! To give an idea of just how small, a typical adult’s
small fingernail contains something in the region of 10
16
atoms,
in other words, 1,000,000,000,000,000 atoms.
To recap, by definition a mole of any pure substance has a mass
in grams equal to that of the substance's molecular mass. For
example, oxygen has a molar mass or atomic weight of 16g, so 1
mole of oxygen is 16g. In contrast, gold has a molar mass of
197g, so 1 mole of gold is 197g. But, and this is the essential
part, one mole of either pure oxygen or pure gold still contains
the same number of atoms, i.e. 6.022 x 10
23
.
Finally, it's important to note that while atoms have been used in
the examples here other particles can also be measured in
moles, such as electrons, ions, molecules and so on.
The next SI Unit is the ampere (A). Find out how many electrons
is takes to make a cup of tea. Other SI units are available from
the menus at the top of the page.
This is known as Avogadro's constant, and here we will round it
to 6.022 x 10
23
.
