Amount of

Substance

Amount Electric Current Luminosity Mass Temperature Time Length Mole Mole Ampere Ampere Metre Metre Candela Candela Kilogram Kilogram Kelvin Kelvin Seconds Seconds
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: 
Derived Units
Conversions Conversions Derived Units Derived Units SI Units Home SI Units Home Unit Conversions 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 around 6.02214078 x 10 23  particles of that substance. Let's just look at that number again. Written out fully it is: 
602,214,078,000,000,000,000,000 
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 number 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 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 cut of tea. Other SI units are available from the menus at the top of the page.
This is known as Avogadro's number, and we will round it here to 6.022 x 10 23 . 
Unit Conversions
Advertisement

Amount of Substance

Amount Electric Current Luminosity Mass Temperature Time Length Copyright  www.si-units-explained.info About & cookie policy
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: 
Unit Conversions 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 around 6.02214078 x 10 23  particles of that substance. Let's just look at that number again. Written out fully it is: 
602,214,078,000,000,000,000,000 
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 number 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 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 cut of tea. Other SI units are available from the menus at the top of the page.
This is known as Avogadro's number, and we will round it here to 6.022 x 10 23 .