Relative Masses (CIE AS Chemistry)

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 =  

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

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

• 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

Substance	Atoms present	Mr
Hydrogen (H2)	2 x H	(2 x 1.0) = 2.0
Water (H2O)	(2 x H) + (1 x O)	(2 x 1.0) + (1 x 16.0) = 18.0
Potassium carbonate (K2CO3)	(2 x K) + (1 x C) + (3 x O)	(2 x 39.1) + (1 x 12.0) + (3 x 16.0) = 138.2
Calcium hydroxide (Ca(OH)2)	(1 x Ca) + (2 x O) + (2 x H)	(1 x 40.1) + (2 x 16.0) + (2 x 1.0) = 74.1
Ammonium sulfate ((NH4)2SO4)	(2 x N) + (8 x H) + (1 x S) + (4 x O)	(2 x 14.0) + (8 x 1.0) + (1 x 32.1) + (4 x 16.0) = 132.1

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