AMOUNT of substance

Learning objectives
understand the origin of, and how to calculate relative atomic, molecular and formula mass
understand the Avogadro number and mole of (particles)
be able to carry out calculations involving quantities of substances expressed in moles

Counting atoms and molecules
When conducting a chemical reaction, it is often important to mix reactants in the correct proportions. This prevents contamination of the products by wasted reactants.
However, atoms are very small and impossible to count out. In order to estimate the number of atoms in a sample of an element, it is necessary to find their mass.
The mass of an atom is quantified in terms of relative atomic mass.

How is the mass of atoms measured?

What is relative atomic mass?

Relative atomic mass
The relative atomic mass (Ar) of an element is the mass of one of its atoms relative to 1/12 the mass of one atom of carbon-12.
Most elements have more than one isotope. The Ar of the element is the average mass of the isotopes, taking into account the abundance of each isotope. This is why the Ar of an element is frequently not a whole number.

Where are r.a.m. values found?
The values of relative atomic mass (r.a.m.) are usually given in a data book or found in the periodic table. So you don’t have to work them out or remember them all!
When looking up relative atomic mass in the periodic table, remember that it always the larger of the two numbers given.
What is the other number?

Identifying relative atomic mass

Why isn’t r.a.m. always a whole number?
Relative atomic mass (r.a.m.) is not always a whole number.
For example, the r.a.m. of chlorine is 35.5.
Chlorine has two isotopes:
chlorine-35 (75%) and chlorine-37 (25%).
The standard r.a.m. value of each element is actually the average relative atomic mass, which takes all the isotopes of each element into account.
average r.a.m. of chlorine
= (35 x 75%) + (37 x 25%)
= (35 x 0.75) + (37 x 0.25)
= 26.25 + 9.25
= 35.5

Calculating average r.a.m. from isotopes
What is the average r.a.m. of naturally-occurring bromine?
Naturally-occurring bromine is composed of two isotopes:
bromine-79 (50.5%) and bromine-81 (49.5%).
average r.a.m.
= (79 x 50.5%) + (81 x 49.5%)
= (79 x 0.505) + (81 x 0.495)
= 39.895 + 40.095
= 79.99
To calculate the average r.a.m. of a mixture of isotopes, multiply the percentage of each isotope by its relative atomic mass and then add these together.

What about the mass of compounds?

Relative molecular mass
Example: what is the Mr of H2SO4?
(2 × H) + (1 × S) + (4 × O)
1. Count number of atoms
(2 × 1.0) + (1 × 32.1) + (4 × 16.0)
2. Substitute the Ar values
2.0 + 32.1 + 64.0 = 98.1
3. Add the values together
The relative molecular mass (Mr) of a covalent substance is the mass of one molecule relative to 1/12 the mass of one atom of carbon-12.
Mr can be calculated by adding together the masses of each of the atoms in a molecule.

Relative formula mass
The equivalent of relative molecular mass for an ionic substance is the relative formula mass.
This is the mass of a formula unit relative to 1/12 the mass of one atom of carbon-12. It is calculated in the same way as relative molecular mass, and is represented by the same symbol, Mr.
Example: what is the Mr of CaCl2?
(1 × Ca) + (2 × Cl)
1. Count number of atoms
(1 × 40.1) + (2 × 35.5)
2. Substitute the Ar values
40.1 + 71.0 = 111.1
3. Add the values together

Calculating relative formula mass

Relative atomic mass – true or false?

What is a mole?
For example, the relative atomic mass of carbon is 12, so one mole of carbon atoms weighs 12 grams.
What is the mass of one mole of hydrogen atoms?
The term mole is also used to
talk about mass. One mole of a substance is its relative atomic mass, or relative formula mass, in grams.

What is Avogadro's number?
The number of particles can be calculated by multiplying the number of moles by Avogadro’s number. The number of moles can be calculated by dividing the number of particles by Avogadro’s number.
The number of particles in one mole of a substance is 6.02 x 1023. This is known as Avogadro's number, L.
(Number of particles) = (number of moles) x L

What is molar mass?
The mass of one mole of a substance is known as its molar mass, and has units of gmol-1.

What is the mass of one mole?

Calculating number of moles and mass
Mass (m), molar mass (mr or ar) and number of moles (n) are thus related by the following equation:
This relationship can be solved for any one of the three variables in the expression.
Mass must be measured in grams and molar mass in gmol-1.

Calculate the number of moles in 58g of CO2 , then calculate the number of molecules present in the sample, and the number of each type of atom present.

How can we predict the amount of substance that will be created in a reaction?

In the reaction
2 Mg + O2 MgO
How much MgO will be produced if we start with 12 of Mg?
How much O2 will be required?

Glossary (1/2)
relative atomic mass – The mass of one of its atoms relative to 1/12 the mass of one atom of carbon-12. Designated by the symbol Ar.
relative molecular mass – the mass of one molecule relative to 1/12 the mass of one atom of carbon-12. Designated by the symbol Mr.
relative formula mass – The mass of a formula unit relative to 1/12 the mass of one atom of carbon-12. Designated by the symbol Mr.
isotopes – Atoms of the same element with a different relative atomic mass.