Isotope Abundance and Relative Atomic Mass

Elements often have multiple different isotopes.

For example, the element oxygen (atomic number 8) has three naturally occurring isotopes: oxygen-16, oxygen-17 and oxygen-18.

A sample of an element usually contains a mixture of its different isotopes. For example, in a sample of oxygen gas, some of the atoms will be oxygen-16, some will be oxygen-17, and some will be oxygen-18.

The proportion of a sample that is a particular isotope is called the abundance of that isotope.

For example, if you took a sample of all of the oxygen atoms on Earth, you would find that the abundances of the three isotopes are approximately the following:

As you can see, the vast majority of oxygen atoms on Earth are oxygen-16 atoms, with only a tiny proportion of oxygen-17 and oxygen-18 atoms.

It is quite often the case that one isotope has a very high abundance, while the other isotopes are relatively rare.

Relative atomic mass is the average realtive mass of the atoms in a sample

In chemistry we often use a quantity called relative atomic mass (abbreviated to A_r). It is the average relative mass of all the atoms in a sample of an element.

For example, the element chlorine has two naturally occurring isotopes: chlorine-35 and chlorine-37, both shown below.

The two isotopes of chlorine.

On Earth, the abundances of the two chlorine isotopes are as follows:

This means that in a typical sample of chlorine on Earth, roughly three quarters of the atoms are chlorine-35 atoms and roughly one quarter are chlorine-37 atoms:

In a typical sample of chlorine atoms, roughly three quarters of them are chlorine-35 and the other quarter are chlorine-37.

In order to calculate the relative atomic mass of a sample of chlorine, we first need to know the relative mass of each atom.

As explained in the previous section, the relative mass of an atom is roughly the same as its mass number. Although there is usually a slight difference between the two, this difference is so small that for the purposes of this course we will ignore it and say that the relative mass of each atom is equal to its mass number.

In other words, we can assume that each chlorine-35 atom has a relative mass of 35 and each chlorine-37 atom has a relative mass of 37.

We now have enough information to calculate the relative atomic mass of the sample. To do so we need to use the following equation:

The equation for calculating relative atomic mass.

The equation is written out for a sample that contains three different isotopes, but we can easily use it for any number of isotopes by just changing the number of terms on the top line.

What the equation tells us is that we need to multiply the mass number of each isotope by its abundance, add all of those numbers together, and then divide by 100.

In our example, multiplying the mass number of each chlorine isotope by its abundance gives the following numbers.

Chlorine-35:

35 x 75.77 = 2651.95

Chlorine-37:

37 x 24.23 = 896.51

Next, we add these numbers together:

2651.95 + 896.51 = 3548.46

Finally, we divide by 100:

3548.46 ÷ 100 = 35.4846

This tells us that the relative atomic mass of our sample of chlorine is 35.4846, or, roughly speaking, 35.5.

The periodic table lists the relative atomic mass of each element

In the periodic table, the relative atomic mass of each element is shown. The relative atomic mass that is shown in the periodic table is based on the abundances of the isotopes on Earth. It is calculated by measuring the isotope abundances in a range of different samples to come up with an estimate of the abundances for the whole planet.

In most periodic tables, the relative atomic mass values are rounded. This makes it seem like many of them are whole numbers. However, in reality none of the relative atomic masses are actually whole numbers (although many are very close to whole numbers).

The periodic table lists the relative atomic mass of each element.

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