0.9 Quantitative aspects of chemical change

This result is so important that scientists decided to use a special unit of measurement to define this quantity: the mole or 'mol'. A mole is defined as being an amount of a substance which contains the same number of particles as there are atoms in 12 g of carbon. In the examples that were used earlier, $24,31\mathrm{g}$ magnesium is one mole of magnesium, while $40,08\mathrm{g}$ of calcium is one mole of calcium. A mole of any substance always contains the same number of particles.

Mole

The mole (abbreviation 'n') is the SI (Standard International) unit for 'amount of substance'. It is defined as an amount of substance that contains the same number of particles (atoms, molecules or other particle units) as there are atoms in $12\mathrm{g}$ carbon.

In one mole of any substance, there are $6,022\times {10}^{23}$ particles.

Avogadro's number

The number of particles in a mole, equal to $6,022\times {10}^{23}$ . It is also sometimes referred to as the number of atoms in $12\mathrm{g}$ of carbon-12.

If we were to write out Avogadro's number then it would look like: $602200000000000000000000$ . This is a very large number. If we had this number of cold drink cans, then we could cover the surface of the earth to a depth of over $300\mathrm{km}$ ! If you could count atoms at a rate of 10 million per second, then it would take you 2 billion years to count the atoms in one mole!

We can build up to the idea of Avogadro's number. For example, if you have 12 eggs then you have a dozen eggs. After this number we get a gross of eggs, which is 144 eggs. Finally if we wanted one mole of eggs this would be $6,022\times {10}^{23}$ . That is a lot of eggs!

Moles and mass

1. Complete the following table:

   Element	Relative atomic mass (u)	Sample mass (g)	Number of moles in the sample
   Hydrogen	1.01	1.01
   Magnesium	24.31	24.31
   Carbon	12.01	24.02
   Chlorine	35.45	70.9
   Nitrogen		42.08

2. How many atoms are there in...
   1. 1 mole of a substance
   2. 2 moles of calcium
   3. 5 moles of phosphorus
   4. $24,31\mathrm{g}$ of magnesium
   5. $24,02\mathrm{g}$ of carbon

Molar mass

Molar mass

Molar mass (M) is the mass of 1 mole of a chemical substance. The unit for molar mass is grams per mole or $\mathrm{g}·\mathrm{mol}{}^{-1}$ .

Refer to [link] . You will remember that when the mass, in grams, of an element is equal to its relative atomic mass, the sample contains one mole of that element. This mass is called the molar mass of that element.

You may sometimes see the molar mass written as $M_m$ . We will use $M$ in this book, but you should be aware of the alternate notation.

It is worth remembering the following: On the periodic table, the relative atomic mass that is shown can be interpreted in two ways.

1. The mass of a single, average atom of that element relative to the mass of an atom of carbon.
2. The mass of one mole of the element . This second use is the molar mass of the element.