Relative Atomic Mass

Section 1 of 6What relative atomic mass means

Why a relative scale

• Why a relative scale Single atoms are so light that their masses in grams are awkward numbers.
  • Chemists compare masses against a standard instead.

The standard

• The standard Atoms are compared with 1/12 of the mass of a carbon-12 atom.
  • Relative atomic mass has the symbol A_r.

No units

• No units Because it is a ratio, A_r has no units.
  • Hydrogen has A_r = 1, so 12 hydrogen atoms have the same mass as one carbon-12 atom.

An average

• An average A_r is a weighted average of the mass numbers of all the isotopes of the element, which is why it is often not a whole number.

Section 2 of 6The calculation

1

List each isotope with its mass number and its percentage abundance.

2

Multiply each mass number by its percentage abundance.

3

Add all of these products together.

4

Divide the total by 100 (or by the total abundance if it is not given as percentages).

5

Give the answer to the number of decimal places asked for, with no units.

Section 3 of 6Formula

Quantity	Equation	Notes
Relative atomic mass, Ar	Ar = Σ(abundance × mass number) ÷ 100	Abundances as percentages; add a term for every isotope
Two isotopes	Ar = [(% A × mass A) + (% B × mass B)] ÷ 100	The percentages must add up to 100
Three isotopes	Add a third term (% C × mass C) to the top line	Still divide by 100

Section 4 of 6Worked example: rubidium

Data

• Data A sample of rubidium contains 72% of the isotope with mass number 85 and 28% of the isotope with mass number 87.

Calculation

• Calculation A_r = [(72 × 85) + (28 × 87)] ÷ 100 = (6120 + 2436) ÷ 100 = 8556 ÷ 100.

Answer

• Answer A_r = 85.6 to one decimal place. It lies closer to 85 because that isotope is more abundant.

Sense check

• Sense check The answer must always fall between the lightest and heaviest isotope masses.
  • If it does not, an arithmetic slip has happened.

Section 5 of 6Key terms

Term	Meaning
Relative atomic mass (Ar)	The average mass of the atoms of an element, taking account of isotope abundances, compared with 1/12 of the mass of a carbon-12 atom.
Isotope	An atom of an element with a different number of neutrons from other atoms of that element.
Percentage abundance	The proportion of atoms in a sample that are a particular isotope, given as a percentage.
Carbon-12	The isotope of carbon used as the standard for relative atomic masses.
Weighted average	An average in which more common values count for more than rarer ones.

Section 6 of 6Exam technique

1

Forgetting to divide by 100 at the end, which gives an answer far too large.

2

Taking a simple average of the mass numbers (for example (85 + 87) ÷ 2) without allowing for abundance.

3

Adding a unit such as g to A_r. Relative atomic mass has no units.

4

Expecting A_r to be a whole number. It is not, because of the mixture of isotopes.

5

Using the atomic number instead of the mass number in the calculation.