The Mole

What is a mole???

As we have seen in previous chapters the masses of atoms are very small e.g.

mass of proton = 1.67 x 10-27kgmass of neutron = 1.67 x 10-27 kg mass of electron = negligible

Subsequently it is not possible to count individual atoms or molecules directly !!!

Amedeo Avogadro was an Italian chemist who devised a method for counting atoms and molecules

1 atom of Mg = 24 (Ar)1 atom of C = 12 (Ar)

So can say 100 Magnesium atoms is twice as heavy as 100 Carbon atoms

Therefore if we have a piece of Mg that is twice the weight of a piece of carbon can say the two amounts contain equal numbers of atoms

Similarly if we had 2g of Mg and 1g of C they would contain the same number of atoms

1 atom of carbon = 12 Ar

1 atom of Hydrogen = 1 Ar

1g of hydrogen atoms and 12 g of carbon atoms both contain the same number of atoms

So, if we were to weigh out elements in the same proportions as their relative atomic masses, we will always be dealing with the same number of atoms of these elements.

12g 24g 63.5g 108gCarbon Magnesium Copper Silver

If we take the relative atomic mass in grams of a number of elements:

All of these amounts can be said to contain the same number of atoms - shown by Avogadro to be

L = 6 x 1023 mol-1 Avogadro’s Constant (Number)

Avogadro’s Constant ( 6 x 1023 ) is the number of atoms of carbon in 12g of the carbon 12 isotope

One mole of a substance is the amount of that substance which contains 6 x 1023 particles (atoms, ions, molecules) of that substance

Points to Note• Symbol for mole – mol

• 12g carbon = 6 x 1023 atoms of carbon = 1 mole of carbon atoms Similarly,

– 48g of Mg = 2 moles of magnesium atoms

• Must specify what particle amount refers to :1 mol of Hydrogen atoms/1 mol of H ( = 1g H atoms)1 mol of Hydrogen molecules/ 1 mol of H2 (= 2g H2

(molecules)

1. Calculations Involving the Mole

1. Converting Moles to Grams

2. Converting Grams to Moles

3. Calculations involving Avogadro’s Number

4. More complicated problems

Molar Mass – is the mass (in grams) of one mole of a substance.

Molar mass of carbon is 12g/molMolar mass of magnesium is 24g/mol

Converting Moles to Grams

Mass of 1 mole of an element = Relative Atomic Mass in grams

e.g.1 mole of Na = 23 g1 mole of Mg = 24g1 mole of copper = ???1 mole of iron = ???1 mole of zinc = ???

The relative molecular mass (Mr) of a compound is the sum of the relative atomic masses of all the atoms in a molecule of the compound.

The relative molecular mass (Mr)of a compound may be defined as the mass of one molecule of that compound compared with one twelfth of the mass of the carbon-12 isotope

Mass of 1 mole of = Relative Molecular Mass a compound in grams

Converting Moles to Grams

Mass (in grams) = Relative x Number ofMolecular Mass Moles

Example 1:What is the mass of a mole of helium atoms?Solution:

Example 2:What is the mass of three moles of aluminium atoms?Solution:

Example 3:What is the mass of a mole of nitrogen molecules? Solution:

Example 4:What is the relative molecular mass of water? What is mass of a mole of water?Solution:

Example 5:What is the mass of one mole of sulphate ions, SO4

2- ?Solution

Example 6:What is the mass of one mole of aluminium sulphate Al2(SO4)3 ?Solution:

Example 7:What is the mass of 0.2 moles of CaCO3 ?Solution:

Converting Grams To MolesNo. of Moles of = Mass of Element

an element Relative Atomic Mass

No. of Moles of = Mass of Compound Compound Relative Molecular

Mass

No. of Moles of = Mass of Substance Substance Mass of 1 mole

of Substance

Example 1:How many moles are there in 1g of Helium atoms?Solution:

Example 2:How many moles of atoms are there in 10g of Helium?Solution:

Example 3:How many moles of water are in 90g of waterSolution:

Example 4:How many moles of sulphuric acid, H2SO4, are there in 12.25g of sulphuric acid?Solution:

Calculations Involving Avogadro’s Number

Remember:

Avogadro's Number represents the number of carbon atoms in 12g of the carbon-12 isotope:

6 x 1023

It is important to remember that the atomic mass of any other element, expressed in grams, will also contain the same number of atoms.

A mole is the amount of a substance which contains 6 x 1023 particles – atoms, ions or molecules, of that substance.

Calculations involving Avogadro’s number may be divided into four types:

1) Converting Moles to number of Atoms or Molecules

2) Converting Grams to number of Atoms or Molecules

3) Converting Numbers of Atoms or Molecules to Moles

4) Converting Numbers of Atoms or Molecules to Grams

1 Mole of a substance contains 6 x 1023 particles of

that substance

Key to solving these problems:

1. Converting Moles to number of Atoms or Molecules

a) Atoms:How many atoms of sodium are present in 0.25 moles of sodium? (composed of Na atoms)Answer:

b) Molecules: How many molecules are present in 5 moles of water (Composed of water molecules) Answer:

c) How many i) molecules ii) atoms are present in 1.5 moles of water (composed of water molecules) Answer:

2. Converting Grams to number of Atoms or Molecules

Steps Involved:

1) Find number of moles – moles = mass/molar mass

2) Find number of molecules(atoms) –molecules (atoms) = moles x 6 x 1023

3) Find number of atoms (Compound) – atoms = no. of atoms x no. of

molecules

a) How many atoms are there in 28.75g of sodium (composed of Na atoms)

Answer:

b) How many molecules are contained in 4.9g of sulphuric acid? (composed of molecules of sulphuric acid)

c) How many atoms are contained in 34g of ammonia? (Composed of molecules of ammonia)

3. Converting numbers of Atoms or Molecules to Moles

Example: How many moles of atoms are present in 5 x 1024 atoms of carbon? Answer:

*Note: Use brackets in calculations

4. Converting numbers of Atoms or Molecules to Grams

Example 1: How many grams of zinc are present in 3 x 1020 atoms of zinc? Answer:

Example 2:What is the mass (in grams) of 3 x 1022 molecules of ethanol C2H5OH

More Complicated Problems

Example 1:How many moles of Al3+ are in 3 moles of Al2(SO)4?Answer:

Example 2:How many moles of oxygen atoms are there in 6.3g of nitric acid, HNO3

Answer:

Example 3:What mass of magnesium contains the same number of atoms as 7g of iron?Answer: