Calculating relative atomic masses from isotopic composition
Why are atomic masses given in the periodic table not integers?
The naturally-occurring form of an element is usually a mixture of its various isotopes. Because each of the isotopes has a different relative atomic mass, the relative atomic masses of elements are not integers, and their mass depends on the proportion of the various isotopes.
How do we know what isotopes are present and how much of each is present?
The relative proportions of the isotopes can be determined experimentally using an instrument known as a mass spectrometer. Mass spectrometers use both electric and magnetic fields to sort the atoms by atomic mass. The relative proportion of atoms with the various mass numbers are then recorded on a graph in which the height of the peak for each isotope depends on its relative abundance.
How can we use the isotopic composition to calculate the relative atomic mass? The resulting number is relative atomic mass of atoms of that element. This is the number that is included in the box with the symbol for the element in the periodic table.
The naturally-occurring form of an element is usually a mixture of its various isotopes. Because each of the isotopes has a different relative atomic mass, the relative atomic masses of elements are not integers, and their mass depends on the proportion of the various isotopes.
How do we know what isotopes are present and how much of each is present?
As the mass spectrum of neon shows, it is common for one isotope to be predominant in the mixture. The distribution of isotopes shown for neon means that the relative atomic mass of neon will be close to, but not equal to, 20 amu (atomic mass units).
The relative atomic mass of an atom of an element can be calculated if the percentage isotopic composition is known. Unlike the relative abundance data from the mass spectrum, the sum of the percentage compositions of the various isotopes add to give 100%.For neon the ratio of the relative abundances is roughly 10:1. This means that naturally occurring neon is roughly 90% 20Ne and 10% 21Ne.
How can we use the isotopic composition to calculate the relative atomic mass?
Method 1: Convert each percentage to a decimal and multiply by the mass number of that isotope. Then add.
Method 2 (easier in practice): Multiply each percentage by the mass number. Add and then divide by 100%.
Example:
Calculate the relative atomic mass (Mr) of chlorine from the 35Cl (75.78%) and 37Cl (24.22%).
Mr(Cl) = 0.7578 × 35 + 0.2422 × 37 = 35.48
Calculate the relative atomic mass (Mr) of chlorine from the 35Cl (75.78%) and 37Cl (24.22%).
Mr(Cl) = 0.7578 × 35 + 0.2422 × 37 = 35.48
Method 2 (easier in practice): Multiply each percentage by the mass number. Add and then divide by 100%.
| Mr(Cl) = | (75.78 × 35 + 24.22 × 37)% | = 35.48 |
| 100 % |
While most commonly, the relative atomic masses are given under the symbol. In some cases they appear above the symbol. You can always tell which is the atomic number and which is the relative atomic mass because ALL atomic numbers are integers.