Section 1 d) Summary

Relative atomic mass (Ar) is the mass of an atom, relative to Carbon, which has an Ar of 12. This is because of the tiny size of atoms, measuring in fractions of a gram would be extremely impractical.

Relative formula mass (Mr) is the total relative mass of a molecule. It is the Ar of each atom in a molecule added together. (e.g. CO2 would be 1 x 12, because there is one carbon, plus 2 x 16, because there are two oxygens, adding to a Mr of 44)

Mr can be used to calculate the mass of a substance that can be obtained from a chemical reaction, or how much of a substance is necessary to neutralise another substance.
This formula triangle is useful in calculating masses:

When the Mr of a substance is equal to the number of grams there are of it, that is one mole. A mole is 6.022 x 10^23 particles. This is called Avagadro's number, or Avagadro's constant.
A mole of gas at room temperature and pressure always takes up 24 dm^3, or 24000 cm^3. 

Section 1 d) Key Words

Ar/Relative Atomic Mass: The mass of a single atom relative to Carbon 12

Avagadro's Number: The number of particles of a substance in 1 mole of it: 6.022 x 10^23

Molar Volume: The volume of space 1 mole of any gas takes up at room temperature and pressure: 24dm^3 or 24000cm^3

Mole: The number of particles it takes for Mr to equal mass in grams. Avagadro's number of particles are in 1 mole.

Mr/Relative Formula Mass: The mass of a molecule relative to carbon 12.

Section 1 d) Specification

1.16 calculate relative formula masses (Mr) from relative atomic masses (Ar)

From the chemical formula of a compound, the Mr can be found by adding the individual relative atomic masses of each atom.
e.g. CO2
C = 12, O = 16
12 + (2 x 16) = 44

1.17 understand the use of the term mole to represent the amount of substance

A mole is the amount of a substance with the same number of molecules as Carbon 12 at a mass of 0.012kg (12g). Otherwise defined as having 6.022 x 10^23 molecules of it.

1.18 understand the term mole as the Avogadro number of particles
(atoms, molecules, formulae, ions or electrons) in a substance

Avagadro's number is how many particles of a substance there must be for its mass in grams to be equal to its relative atomic mass. Avagadro's number is 6.02214154 x 10^23, but at GCSE level we shorten it to 6.022 x 10^23 unless otherwise specified.

1.19 carry out mole calculations using relative atomic mass (Ar) and relative
formula mass (Mr)

The above formula triangle can be used to calculate different parts of a chemical formula.
Examples:

2Ca + O2 --> 2CaO
2mol 1mol    2mol
1 mole of any substance contains the same number of particles.
If we have 5g of Calcium, what mass of Calcium Oxide will we get?
Mass of Ca = 5g       Mr of Ca = 40       5 / 40 = 1 / 8 moles
The ratio of Ca:CaO is 1:1, so there is the same number of moles.
1/8 mol of CaO must be multiplied by its Mr to find the mass
Mr of CaO = 56      56 x 1/8 = 7
There are 7 grams of CaO from 5g Ca.

CuSO4 + Zn --> ZnSO4 + Cu
1mol     1mol     1mol      1mol
If we have 1.5g Zinc,  what mass of Copper will we get?
1.5g / 65 = 3/130 mol
ratio 1:1 so same number of moles
Mr of copper = 63.5
3/130 x 63.5 = 1.47 g

2Fe + 3Cl2 --> 2FeCl3
How much Chlorine is needed to react with 20g of Iron?
20 / 56 = 5/14 mol
ratio is 2:3 so we first divide by 2 to get 5/28
then multiply by 3 to get 15/28
we then find the Mr of Cl2     35.5 x 2 = 71
15/28 x 71 = 38 1/28 g

1.20 understand the term molar volume of a gas and use its values
(24 dm^3 and 24,000 cm^3) at room temperature and pressure (rtp) in
calculations.

1 mole of any gas takes up the volume of 24dm^3 at room temperature and Earth's atmospheric pressure. We can use this in gas calculations to calculate gas volumes, or use it the other way around and find how many moles there are based on its volume.