Amount of substance : Chemistry 2
Relative Atomic Mass Definition
What is Relative Atomic Mass? 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 the unified atomic mass unit. This unified atomic mass is defined as one-twelfth of the mass of a carbon-12 isotope.
Definition and Formula
The relative atomic mass (Ar) 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 Ar has no units as it is a ratio, and the units cancel each other out.
Relative atomic mass of X = average mass of one atom of X / one twelfth of the mass of one carbon−12 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 the average relative atomic mass. This is known as the weighted average of the masses of the isotopes.
Relative Molecular Mass (Mr)
The relative molecular mass (Mr) is the ratio of the weighted average mass of a molecule of a molecular compound to the unified atomic mass unit. The Mr has no units.
Mr = weighted average mass of molecules in a given sample of a molecular compound / unified atomic mass unit.
The Mr can be found by adding up the relative atomic masses of all atoms present in one molecule. When calculating the Mr, the simplest formula for the compound is used, also known as the formula unit. For example, silicon dioxide has a giant covalent structure; however, the simplest formula (the formula unit) is SiO2.
Example Mr Calculations
Substance | Atoms Present | Mr Calculation |
|---|---|---|
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 (Mr)
The relative formula mass (Mr) 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 examples above, the Mr for potassium carbonate, calcium hydroxide, and ammonium sulfate are relative formula masses.
Examiner Tips and Tricks
Students often confuse relative atomic mass (Ar) with mass number. Ar is a weighted average across all isotopes, whereas mass number applies to a single isotope.
In percentage abundance calculations, a common error is summing the isotope contributions without dividing by 100; you should check that your answer is close in magnitude to the individual atomic masses.
Remember that Ar and Mr are dimensionless ratios (no units).