Mole Concept

Atoms, molecules, and formula units are extremely small and cannot be counted directly. It is impossible
to count individual atoms instead chemist uses the concept of the mole which allows them to count
atoms by weighing them.

Relative atomic, molecular and formula masses

Relative Atomic Mass (RAM)

Because the mass of atoms is extremely small, relative atomic mass is used to compare their masses.

A carbon-12 atom has been assigned a mass of 12.00 atomic mass units or amu. This means that 1/12th
the mass of a carbon-12 has a mass of 1.00 amu.

Relative Atomic Mass (RAM) is the average mass of one atom of an element compared to one-twelfth
the mass of an atom of carbon-12.

- RAM is unit less because it is a ratio of mass of one atom to the mass of another atom.

Relative Molecular Mass (RMM)

Relative Molecular Mass is the sum of the relative atomic masses of the individual elements which
makes up a covalent molecule/ compound.

- RMM is also unit less.

Relative Formula Mass (RFM)

Relative Formula Mass is the sum of the relative atomic masses of the individual elements within an
ionic compound.

- RFM is also unit less.

Calculating relative atomic, molecular and formula masses

Examples:

Relative atomic Masses (RAM): Al=27, S=32, Fe=56

1. Calculate the Relative Molecular Mass (RMM) of the following from the above RAM.

a) Hydrogen, H2O

H2O consists of two H atoms and one O atom.

 RMM (H2O) = 2(1) + 16 = 18

b) Sulphur trioxide, SO3

SO3 consist of one S atom and three O atoms.

 RMM (SO3) = 32 + 3(16) = 80

c) Glucose, C6H12O6

RMM (C6H12O6) = 6(12) + 12(1) + 6(16) = 180

2. Calculate the Relative Formula Mass (RMM) of the following given the RAM.

RAM: K= 39, S= 32, Mg= 24, N=14, O=16

a) Potassium sulphide, K2S

RFM (K2S) = 2(39) + 32 = 110

b) Magnesium nitrate, Mg (NO3)2

RFM (Mg (NO3)2) = 24 + 2(14) + 2(3)(16) = 148

Evaluation

RAMs:

Na=23, O= 16, H=1, Fe= 56, C=12, S=32, Ag= 108, Al = 27, F= 19, Mg= 24, Cl= 35.5, Pb =207, Ba= 137.4, P=
31, N=14, Mn= 55

Given the above RAM, calculate the RFM/ RMM of the following compounds.

1. NaOH
2. Fe2(SO4)3
3. CO2
4. C6H12
5. AgCl
6. PbO2
7. Ba3 (PO4)2
8. HNO3
9. MnO2
10. MgSO4. 7H2O
11. Na3AlF6
12. CuSO4.5H2O
Percentage Composition by mass

Percentage composition is the percentage, by mass, of each element in a compound. This can be
calculated once the formula of the compound is known.

Examples:

1. Calculate the percentage (%) of Oxygen in H2O.

Relative Molecular Mass (RMM) of H2O= 2(1) + 16 = 18

RMM of O= 16

percentage of oxygen in H2O= x 100% = 88.8 %

2. Calculate the percentage (%) of Carbon in aluminium carbonate, Al2(CO3)3

RMM (Al2(CO3)3) = 2(27) + 3(12) + 3(3)(16) = 234

RMM of C = 3(12) = 36

 percentage of Carbon in Al2(CO3)3 = x 100% = 15.38 %

Evaluation

1. Calculate the percentage by mass of fluorine in cryolite, Na3AlF6

2. What is the percentage by mass of water in hydrated copper (II) sulphate?
3. Deduce the percentage of copper in malachite, CuCO3.Cu(OH)2
4. Which of the following nitrogen containing fertilisers contain the greatest percentage (%) of mass of
nitrogen?
a) Ammonium sulphate (NH4)2SO4
b) Ammonium nitrate NH4NO3

The Mole

The Mole (mol) is the amount of substance that contains 6.02 x 1023 atoms/ particles/ molecules/
formula units/ ions.

One mole of any substance contains 6.02 x 1023 particles. This number 6.02 x 1023 is known as Avogadro’s
constant.

12 g of Carbon-12 was found to contain 6.02 x 1023 atoms. This equals one mole of carbon.

32g of Oxygen (O2) contains 6.02 x 1023 atoms.

80g of Sulphur trioxide (SO3) contains 6.02 x 1023 molecules.

148g of Magnesium nitrate (Mg (NO3)2) contains 6.02 x 1023 formula units.
The Mole and mass

The Molar mass is the mass, in grams, of one mole of a chemical substance. The molar mass of an
element or compound is given the unit grams per mole or gmol-1. For example, the molar mass of
carbon is 12 gmol-1.

NB. Molar mass has the same numeric value as RAM, RMM and RFM but it has units.

Number of moles (mol) =

Mass(g) = Number of moles (mol) x Molar Mass (gmol-1)

Molar Mass =
Examples:
1. How many moles are there in 27g of water?
Molar mass of H2O= 2(1) + 16 = 18 g/mol
We know that: Number of moles (mol) =
 Number of moles in 27g of H2O (mol) = = 1.5 mol

2. What is the mass of 0.25 mol of iron (III) sulphate?

Molar mass of Fe2(SO4)3 = 2(56) + 3(32) + 3(4)(16) = 400 g/mol

We know that: Mass(g) = Number of moles (mol) x Molar Mass (gmol-1)

 Mass (g) = 0.25 mol x 400 g/mol = 100 g

Evaluation

1. Calculate the number of moles of NaCl present in 100 g sample of the salt. [Na=23, Cl= 35.5]
2. How many moles of O2 (g) are present in 27.3 g of the gas at room temperature? [O=16]
3. Deduce the number of moles of MgSO4. 7H2O found in 1 kg sample of the ore. [Mg=24, S=32]
4. Determine the mass of substance equivalent to the following moles.
a. 2.73 mol CuSO4 [ RAM: Cu= 64]
b. 17.6 mol Fe [ RAM: Fe= 56]
c. 25 mol H2O2
d. 1.001 mol Na2CO3
e. 0.01 mol of H2SO4
5. 2 mol of a substance X weighs 17 g. What is the mass of 1 mol of X?
6. It was determined that 2 Tonne of an ore contained 5 mol of compound. Deduce the molar mass
of the ore.

Mole Ratio
A mole ratio is ​the ratio between the amounts in moles of any two compounds. The chemical formula tells
us the mole ratio.
Examples:
1. Determine the number of moles of carbon that is present in a 1 mol sample of CO2.
CO2: C atom: O atoms.
1 :1 :2
1 mol CO2: 1 mol of C: 2 mol of O
The mole ratio between CO2 and C is 1:1. For every 1 mol sample of CO2 there is 1 mol of C.

2. Determine the number of moles of oxygen atoms present in 5 moles of oxygen gas.
O2: O atoms
1 :2
5 moles : 10 moles
Therefore, for every 5 moles of oxygen gas, there is 10 moles of oxygen atoms.

Evaluation

1. Calculate the following:

a) The number of moles of carbon found in 0.01 mol of Ethene (C2H4)
b) The number of moles of oxygen in 6.5 mol of MgSO4.7H2O.
c) The number of moles of nitrogen in 0.5 mol of NH4NO3.
d) The number of moles of hydrogen in 17 mol of H2SO4.
e) The number of moles of water in 0.375 mol of CuSO4.5H2O.

2. Calculate the number of moles of carbon present in 37g of CO2.

3. Calculate the number of moles of oxygen in 6.205g of Barium Phosphate, Ba3(PO4)2
[RAM: Ba= 137.4, P=31, O=16]
4. Calculate the number of moles of water in 100g of CaCl2.2H2O.
[RAM: Ca= 40, Cl= 35.5]
5. Calculate the number of moles of iodine atoms in 127g of solid iodine (I2)
[RAM: I =127]
6. Calculate the number of moles of sulphur atoms in 1 kg of sulphur flower (S8)
7. Calculate the number of moles of aluminium in 1 megagram of Bauxite, Al2O3.2H2O
The moles and number of particles
The fact that the number of particles in one mole is always 6.0 x 1023 can be used to convert a given
number of particles in a substance to number of moles, or to convert a given number of moles to the
number of particles.
Number of moles (mol) =
Number of particles = Number of moles (mol) x 6.0 x 1023 mol -1
(atoms/ions/molecules/formula units)

Examples:

1. Calculate the number of atoms of iron present in 2 moles of Fe.

We know that: Number of atoms = Number of moles (mol) x 6.0 x 1023 atoms mol -1
 Number of atoms of Fe= 2 mol x 6.02 x 1023 mol -1
= 1.204 x 10 24 atoms of Fe

2. How many moles are in 1.8 x 1023 molecules of nitrogen?

We know that: Number of moles (mol) = 1 mol N2 contains 6.02 x 1023 N2 molecules

 Number of moles of N2 molecules (mol) =

= 0.3 mol of N2 molecules

The mole, mass, and number of particles
Examples:
1. How many ammonia molecules are there in 4.25 g of ammonia?

We know that: Number of moles (mol) =

Molar mass of NH3 = 14 + 3(1) = 17 g/ mol

 Number of moles (mol) =

= 0.25 mol

Using 0.25 mol of NH3 and 6.03 x 10 23 NH3 molecules, we can use:
Number of molecules = Number of moles (mol) x 6.0 x 1023 mol -1
 Number of molecules of NH3 = 0.25 mol x 6.0 x 1023 molecules mol -1
= 1.5 x 1023 NH3 molecules

Evaluation:

1. Determine the number of atoms of zinc present in 0.5 mol sample of metal.
2. Calculate the number of atoms of hydrogen present in 0.001 mol of H2O.
3. How many oxygen atoms are found in 20 g of O2 at rtp?
4. Deduce the number of moles of water in a 500 g sample of liquid.
5. Find the number of Cl- ions in 2g of NaCl.
6. How many formula units of KI are present in 100g of the salt? [RAM: K= 39, I=127]
7. Calculate the number of CO2 molecules present in a 500g sample of air that is 25% of by the mass
of CO2.
8. Determine the number of atoms of 17.3 mg of methane gas (CH4)
9. Calculate the mass of tin that contains 5 tin atoms.
10. What is the mass of Ni that contains 100 atoms of Ni?
11. Deduce the molar mass of a compound in which 50 g of it contains 2 x 10 -3 molecules.
12. Calculate the mass of carbon in 3.1 x 10-9 molecules of CO2
13. What mass of lead is found in 1.02 x 10 21 PbI2 molecules?
14. What mass of C2H4 contains 1 X 1021 molecules of the gas?