The mass of an atom is compared to the mass of other atoms to give us a relative mass. Today the atom used to measure the relative masses of other atoms is carbon-12 (an isotope of carbon with 6 protons, 6 neutrons and 6 electrons).
The unit of atomic mass is called the unified atomic mass unit and is given the symbol u. If we convert this to kilograms 1u is approximately equal to 1.66 x 10-27 kg.
Therefore, in unified atomic mass units the mass of carbon-12 is equal to 12u. This assumes that the mass of a proton and a neutron are both equal to 1u and that the mass of an electron is so small that it can be ignored.
Relative Isotopic Mass
Relative Isotopic Mass – the mass of an isotope relative to one twelfth of the mass of an atom of carbon-12.
All atoms of a single isotope have exactly the same mass when measured relative to carbon-12. This means that the relative isotopic mass of an isotope is equal the nucleon number (the number of protons and neutrons).
For example if we take nitrogen-14 (with a nucleon number of 14) the relative isotopic mass is 14u.
Relative Atomic Mass
Relative Atomic Mass (Ar) – the average mass of an atom of an element relative to one twelfth of the mass of an atom of carbon-12.
For most elements we have a mixture of different isotopes, with varying amounts of each isotope. Each isotope has a different mass and so we need to average them out to get the overall mass of the element.
The relative mass of each isotope and its abundance within an element determine how much a particular isotope contributes to the overall mass. The overall mass is equal to the relative atomic mass of the element.
The relative atomic mass can be calculated using this equation:
Where Ir is the relative isotopic mass of an isotope and f is the fractional abundance of that isotope.
For example naturally occurring Rubidium has two isotopes with the following relative abundances:
- Rb85 72.15%
- Rb87 27.85%
We know that the relative isotopic mass of Rb85 is 85u and the relative isotopic mass of Rb87 is 87u.
To get the fractional abundance of each isotope from the percentage we simply have to divide by 100. So for Rb85 the fractional abundance is 0.7215 and for Rb87 the fractional abundance is 0.2785. We can now plug these numbers into the formula to get:
Ar = (85 x 0.7215) + (87 x 0.2785)
Ar = 85.6 u (1d.p.)
Relative Molecular Mass
Relative Molecular Mass (Mr) – the average mass of a molecule compared to one twelfth of the mass of an atom of carbon-12.
The relative molecular mass of a molecule can be found by adding up the relative atomic masses of each atom in the molecule.
For example we can calculate the relative molecular mass of sulphuric acid by looking at the relative atomic masses of each element within the molecule.
Sulphuric acid has the following formula: H2SO4.
Hydrogen has an Ar of 1.0u, Sulphur has an Ar of 32.1u and Oxygen has an Ar of 16.0u.
We need to remember that we have two hydrogen atoms and 4 oxygen atoms so the relative molecular mass of sulphuric acid is given by:
Mr = (2 x 1.0) + 32.1 + (4 x 16.0)
Mr = 98.1 u
You can find the Ar for each element on the periodic table. Sometimes the accuracy of the Ar varies depending on the periodic table you are looking at. If you are preparing for an exam always use the the values on the periodic table provided by your exam board or teacher.
Worked Examples
Example 1
Given that naturally occurring copper has 2 isotopes:
- Cu63 69.15%
- Cu65 30.85%
Calculate the relative atomic mass of copper.
Example 2
Calculate the relative molecular mass of Ca3(PO4)2.
Example 3
Naturally occurring boron is composed of two isotopes; boron-10 and boron-11. Given that the relative atomic mass of boron is 10.80u calculate the percentage composition of boron in terms of these two isotopes.
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