Relative Masses (Cambridge (CIE) A Level Chemistry): Revision Note

Relative Masses

Atomic Mass Unit

• The mass of a single atom is so small that it is impossible to weigh it directly

• Atomic masses are therefore defined in terms of a standard atom which is called the unified atomic mass unit

• This unified atomic mass is defined as one-twelfth of the mass of a carbon-12 isotope

• The symbol for the unified atomic mass is u (often Da, Dalton, is used as well)

• 1 u = 1.66 x 10^-27 kg

Relative atomic mass, A_r

• The relative atomic mass (A_r) of an element is the ratio of the average mass of the atoms of an element to the unified atomic mass unit

• The relative atomic mass is determined by using the average mass of the isotopes of a particular element

• The A_r has no units as it is a ratio and the units cancel each other out

Relative atomic mass of X = $\frac{\mathrm{average}\mathrm{mass}\mathrm{of}\mathrm{one}\mathrm{atom}\mathrm{of}\mathbf{X}}{\mathrm{one}\mathrm{twelfth}\mathrm{of}\mathrm{the}\mathrm{mass}\mathrm{of}\mathrm{one}\mathrm{carbon}-12\mathrm{atom}}$ 

Relative isotopic mass

• The relative isotopic mass is the mass of a particular atom of an isotope compared to the value of the unified atomic mass unit

• Atoms of the same element with a different number of neutrons are called isotopes

• Isotopes are represented by writing the mass number as ²⁰Ne, or neon-20 or Ne-20

  • To calculate the average atomic mass of an element the percentage abundance is taken into account

  • Multiply the atomic mass by the percentage abundance for each isotope and add them all together

  • Divide by 100 to get average relative atomic mass

  • This is known as the weighted average of the masses of the isotopes

$\mathrm{Relative}\mathrm{atomic}\mathrm{mass}=\frac{\mathrm{\Sigma }\left(\mathrm{isotope}\mathrm{percentage}\mathrm{abundance}\times \mathrm{isotope}\mathrm{mass}\mathrm{number}\right)}{100}$

Relative molecular mass, M_r

• The relative molecular mass (M_r) is the ratio of weighted average mass of a molecule of a molecular compound to the unified atomic mass unit

• The M_r has no units

$M_{\mathrm{r}}=\frac{\mathrm{weighted}\mathrm{average}\mathrm{mass}\mathrm{of}\mathrm{molecules}\mathrm{in}\mathrm{a}\mathrm{given}\mathrm{sample}\mathrm{of}\mathrm{a}\mathrm{molecular}\mathrm{compound}}{\mathrm{unified}\mathrm{atomic}\mathrm{mass}\mathrm{unit}}$

• The M_r can be found by adding up the relative atomic masses of all atoms present in one molecule

• When calculating the M_r the simplest formula for the compound is used, also known as the formula unit

  • Eg. silicon dioxide has a giant covalent structure, however the simplest formula (the formula unit) is SiO₂

Example M_r calculations

Relative formula mass, M_r 

• The relative formula mass (M_r) is used for compounds containing ions

• It has the same units and is calculated in the same way as the relative molecular mass

• In the table above, the M_r for potassium carbonate, calcium hydroxide and ammonium sulfates are relative formula masses